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<!-- Weave of 'Spatial Geometry' generated by Inweb -->
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< ul class = "crumbs" > < li > < a href = "../index.html" > Home< / a > < / li > < li > < a href = "../compiler.html" > Inter Modules< / a > < / li > < li > < a href = "index.html" > codegen< / a > < / li > < li > < a href = "index.html#6" > Chapter 6: Index< / a > < / li > < li > < b > Spatial Geometry< / b > < / li > < / ul > < / div >
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< p class = "purpose" > To deal with vectors and cuboids in a three-dimensional integer lattice.< / p >
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< ul class = "toc" > < li > < a href = "6-sg.html#SP4" > § 4. Vectors< / a > < / li > < li > < a href = "6-sg.html#SP7" > § 7. Lengths< / a > < / li > < li > < a href = "6-sg.html#SP8" > § 8. Angles< / a > < / li > < li > < a href = "6-sg.html#SP9" > § 9. Cuboids< / a > < / li > < / ul > < hr class = "tocbar" >
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< p class = "commentary firstcommentary" > < a id = "SP1" class = "paragraph-anchor" > < / a > < b > § 1. < / b > We will store 3-vectors in the obvious way:
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< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
< span class = "reserved-syntax" > typedef< / span > < span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > struct< / span > < span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > {< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > } < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > ;< / span >
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< / pre >
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< ul class = "endnotetexts" > < li > The structure vector is accessed in 6/sm, 6/hm, 6/rem and here.< / li > < / ul >
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< p class = "commentary firstcommentary" > < a id = "SP2" class = "paragraph-anchor" > < / a > < b > § 2. < / b > Some useful constant vectors, including those pointing in each direction.
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Note that these are not of unit length — rather, they are the ideal grid
offsets on the map we will eventually draw.
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > Zero_vector< / span > < span class = "plain-syntax" > = {0, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > N_vector< / span > < span class = "plain-syntax" > = {0, < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > NE_vector< / span > < span class = "plain-syntax" > = {1, < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > NW_vector< / span > < span class = "plain-syntax" > = {-1, < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > S_vector< / span > < span class = "plain-syntax" > = {0, -1, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > SE_vector< / span > < span class = "plain-syntax" > = {1, -1, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > SW_vector< / span > < span class = "plain-syntax" > = {-1, -1, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > E_vector< / span > < span class = "plain-syntax" > = {1, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > W_vector< / span > < span class = "plain-syntax" > = {-1, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > U_vector< / span > < span class = "plain-syntax" > = {0, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > , < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > };< / span >
< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > D_vector< / span > < span class = "plain-syntax" > = {0, < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > , -1};< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP3" class = "paragraph-anchor" > < / a > < b > § 3. < / b > A cuboid is a volume of space with opposing corners at integer grid
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positions which form a tightest-possible bounding box around a finite
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number of points (of size < span class = "extract" > < span class = "extract-syntax" > population< / span > < / span > ); when this is 0, of course, the
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corners are meaningless and are by convention at the origin.
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
< span class = "reserved-syntax" > typedef< / span > < span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > struct< / span > < span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > {< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > struct< / span > < span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > struct< / span > < span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > corner1< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > } < / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > ;< / span >
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< / pre >
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< ul class = "endnotetexts" > < li > The structure cuboid is accessed in 6/sm, 6/hm, 6/rem and here.< / li > < / ul >
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< p class = "commentary firstcommentary" > < a id = "SP4" class = "paragraph-anchor" > < / a > < b > § 4. Vectors. < / b > < / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec< / span > < button class = "popup" onclick = "togglePopup('usagePopup1')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup1" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP15_1" > § 15.1< / a > , < a href = "6-sm.html#SP7_30" > § 7.30< / a > , < a href = "6-sm.html#SP7_31_1_1" > § 7.31.1.1< / a > , < a href = "6-sm.html#SP7_31_1_2" > § 7.31.1.2< / a > , < a href = "6-sm.html#SP7_31_1_3" > § 7.31.1.3< / a > < br / > HTML Map - < a href = "6-hm.html#SP9" > § 9< / a > , < a href = "6-hm.html#SP9_3_1_1" > § 9.3.1.1< / a > , < a href = "6-hm.html#SP9_3_2_1" > § 9.3.2.1< / a > , < a href = "6-hm.html#SP9_3_3_1" > § 9.3.3.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP5" class = "paragraph-anchor" > < / a > < b > § 5. < / b > A vector is "lateral" if lies in the \(x\)-\(y\) plane.
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< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_eq< / span > < button class = "popup" onclick = "togglePopup('usagePopup2')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup2" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_eq< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP7_11" > § 7.11< / a > , < a href = "6-sm.html#SP20" > § 20< / a > , < a href = "6-sm.html#SP21" > § 21< / a > , < a href = "6-sm.html#SP32" > § 32< / a > < br / > HTML Map - < a href = "6-hm.html#SP1_3_4" > § 1.3.4< / a > , < a href = "6-hm.html#SP1_3_4_1" > § 1.3.4.1< / a > , < a href = "6-hm.html#SP1_3_4_2" > § 1.3.4.2< / a > , < a href = "6-hm.html#SP2_1" > § 2.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > ((< / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > == < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) & & (< / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > == < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) & & (< / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > == < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > )) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > TRUE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_lateral< / span > < button class = "popup" onclick = "togglePopup('usagePopup3')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup3" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_lateral< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP7_10" > § 7.10< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > ((< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) & & (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > )) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > TRUE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP6" class = "paragraph-anchor" > < / a > < b > § 6. < / b > The vector space operations:
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< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_plus< / span > < button class = "popup" onclick = "togglePopup('usagePopup4')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup4" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_plus< / span > < / span > :< br / > < a href = "6-sg.html#SP11" > § 11< / a > , < a href = "6-sg.html#SP14" > § 14< / a > < br / > Spatial Map - < a href = "6-sm.html#SP7_20" > § 7.20< / a > , < a href = "6-sm.html#SP7_25" > § 7.25< / a > , < a href = "6-sm.html#SP7_26" > § 7.26< / a > , < a href = "6-sm.html#SP20" > § 20< / a > , < a href = "6-sm.html#SP22_1_4_1" > § 22.1.4.1< / a > , < a href = "6-sm.html#SP32" > § 32< / a > , < a href = "6-sm.html#SP36_1" > § 36.1< / a > , < a href = "6-sm.html#SP7_30" > § 7.30< / a > , < a href = "6-sm.html#SP7_31_1_2" > § 7.31.1.2< / a > , < a href = "6-sm.html#SP7_31_1_3" > § 7.31.1.3< / a > < br / > HTML Map - < a href = "6-hm.html#SP1_3_4_2" > § 1.3.4.2< / a > , < a href = "6-hm.html#SP2" > § 2< / a > , < a href = "6-hm.html#SP2_1" > § 2.1< / a > , < a href = "6-hm.html#SP3" > § 3< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_minus< / span > < button class = "popup" onclick = "togglePopup('usagePopup5')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup5" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_minus< / span > < / span > :< br / > < a href = "6-sg.html#SP13" > § 13< / a > , < a href = "6-sg.html#SP14" > § 14< / a > < br / > Spatial Map - < a href = "6-sm.html#SP20" > § 20< / a > , < a href = "6-sm.html#SP21" > § 21< / a > , < a href = "6-sm.html#SP22_1_4_1" > § 22.1.4.1< / a > , < a href = "6-sm.html#SP34_1" > § 34.1< / a > , < a href = "6-sm.html#SP7_31_1_2" > § 7.31.1.2< / a > , < a href = "6-sm.html#SP7_31_1_3" > § 7.31.1.3< / a > , < a href = "6-sm.html#SP7_32" > § 7.32< / a > < br / > HTML Map - < a href = "6-hm.html#SP1_3_4_1" > § 1.3.4.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > U< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_negate< / span > < button class = "popup" onclick = "togglePopup('usagePopup6')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup6" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_negate< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP7_31_1_3_1" > § 7.31.1.3.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = -< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = -< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = -< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_scale< / span > < button class = "popup" onclick = "togglePopup('usagePopup7')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup7" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_scale< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP22_1_4_1" > § 22.1.4.1< / a > , < a href = "6-sm.html#SP32" > § 32< / a > , < a href = "6-sm.html#SP36_1" > § 36.1< / a > < br / > HTML Map - < a href = "6-hm.html#SP1_3_4_1" > § 1.3.4.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > lambda< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > lambda< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > lambda< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > lambda< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > R< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP7" class = "paragraph-anchor" > < / a > < b > § 7. Lengths. < / b > < / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_length_squared< / span > < button class = "popup" onclick = "togglePopup('usagePopup8')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup8" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_length_squared< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP20" > § 20< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_length< / span > < button class = "popup" onclick = "togglePopup('usagePopup9')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup9" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_length< / span > < / span > :< br / > < a href = "6-sg.html#SP8" > § 8< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > ) (< / span > < span class = "identifier-syntax" > sqrt< / span > < span class = "plain-syntax" > (< / span > < a href = "6-sg.html#SP7" class = "function-link" > < span class = "function-syntax" > Geometry::vec_length_squared< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > )));< / span >
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< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP8" class = "paragraph-anchor" > < / a > < b > § 8. Angles. < / b > We compute unit vectors in the D and E directions and then the squared
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length of their difference. This is a fairly sharply increasing function of
the absolute value of the angular difference between D and E, and is such
that if the angles are equal then the result is zero; and it's cheap to
compute. So although it might seem nicer to calculate actual angles, this
is better.
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::vec_angular_separation< / span > < button class = "popup" onclick = "togglePopup('usagePopup10')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup10" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::vec_angular_separation< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP20" > § 20< / a > , < a href = "6-sm.html#SP21" > § 21< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > E< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > E_distance< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP7" class = "function-link" > < span class = "function-syntax" > Geometry::vec_length< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > E< / span > < span class = "plain-syntax" > );< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > uex< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > E< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > /< / span > < span class = "identifier-syntax" > E_distance< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > uey< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > E< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > /< / span > < span class = "identifier-syntax" > E_distance< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > uez< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > E< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > /< / span > < span class = "identifier-syntax" > E_distance< / span > < span class = "plain-syntax" > ;< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > D_distance< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP7" class = "function-link" > < span class = "function-syntax" > Geometry::vec_length< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > );< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > float< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > udx< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > /< / span > < span class = "identifier-syntax" > D_distance< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > udy< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > /< / span > < span class = "identifier-syntax" > D_distance< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > udz< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > /< / span > < span class = "identifier-syntax" > D_distance< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > uex< / span > < span class = "plain-syntax" > -< / span > < span class = "identifier-syntax" > udx< / span > < span class = "plain-syntax" > )*(< / span > < span class = "identifier-syntax" > uex< / span > < span class = "plain-syntax" > -< / span > < span class = "identifier-syntax" > udx< / span > < span class = "plain-syntax" > ) + (< / span > < span class = "identifier-syntax" > uey< / span > < span class = "plain-syntax" > -< / span > < span class = "identifier-syntax" > udy< / span > < span class = "plain-syntax" > )*(< / span > < span class = "identifier-syntax" > uey< / span > < span class = "plain-syntax" > -< / span > < span class = "identifier-syntax" > udy< / span > < span class = "plain-syntax" > ) + (< / span > < span class = "identifier-syntax" > uez< / span > < span class = "plain-syntax" > -< / span > < span class = "identifier-syntax" > udz< / span > < span class = "plain-syntax" > )*(< / span > < span class = "identifier-syntax" > uez< / span > < span class = "plain-syntax" > -< / span > < span class = "identifier-syntax" > udz< / span > < span class = "plain-syntax" > );< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP9" class = "paragraph-anchor" > < / a > < b > § 9. Cuboids. < / b > To form a populated cuboid, first request an empty one, and then adjust it
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for each vector to join the population.
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::empty_cuboid< / span > < button class = "popup" onclick = "togglePopup('usagePopup11')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup11" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::empty_cuboid< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP7" > § 7< / a > , < a href = "6-sm.html#SP11" > § 11< / a > , < a href = "6-sm.html#SP7_17" > § 7.17< / a > , < a href = "6-sm.html#SP18" > § 18< / a > , < a href = "6-sm.html#SP7_31" > § 7.31< / a > , < a href = "6-sm.html#SP7_33" > § 7.33< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > void< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > population< / span > < span class = "plain-syntax" > = < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > Zero_vector< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > Zero_vector< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > void< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::adjust_cuboid< / span > < button class = "popup" onclick = "togglePopup('usagePopup12')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup12" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::adjust_cuboid< / span > < / span > :< br / > < a href = "6-sg.html#SP10" > § 10< / a > < br / > Spatial Map - < a href = "6-sm.html#SP18" > § 18< / a > , < a href = "6-sm.html#SP7_33" > § 7.33< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > ++ == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) {< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ; < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > } < / span > < span class = "reserved-syntax" > else< / span > < span class = "plain-syntax" > {< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP10" class = "paragraph-anchor" > < / a > < b > § 10. < / b > The following expands \(C\) minimally so that it contains \(X\).
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< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > void< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::merge_cuboid< / span > < button class = "popup" onclick = "togglePopup('usagePopup13')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup13" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::merge_cuboid< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP7_31_1" > § 7.31.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > X< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > X< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > > < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) {< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > population< / span > < span class = "plain-syntax" > == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) {< / span >
< span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > X< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > } < / span > < span class = "reserved-syntax" > else< / span > < span class = "plain-syntax" > {< / span >
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< span class = "plain-syntax" > < / span > < a href = "6-sg.html#SP9" class = "function-link" > < span class = "function-syntax" > Geometry::adjust_cuboid< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > X< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > );< / span >
< span class = "plain-syntax" > < / span > < a href = "6-sg.html#SP9" class = "function-link" > < span class = "function-syntax" > Geometry::adjust_cuboid< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > X< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > );< / span >
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< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > population< / span > < span class = "plain-syntax" > += < / span > < span class = "identifier-syntax" > X< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > population< / span > < span class = "plain-syntax" > - < / span > < span class = "constant-syntax" > 2< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
< span class = "plain-syntax" > }< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP11" class = "paragraph-anchor" > < / a > < b > § 11. < / b > Here we shift an entire cuboid over (assuming all of the points inside
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it have made the same shift).
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > void< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::cuboid_translate< / span > < button class = "popup" onclick = "togglePopup('usagePopup14')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup14" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::cuboid_translate< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP7_20" > § 7.20< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > > < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP6" class = "function-link" > < span class = "function-syntax" > Geometry::vec_plus< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > );< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > corner1< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP6" class = "function-link" > < span class = "function-syntax" > Geometry::vec_plus< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > D< / span > < span class = "plain-syntax" > );< / span >
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< span class = "plain-syntax" > }< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP12" class = "paragraph-anchor" > < / a > < b > § 12. < / b > < / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::within_cuboid< / span > < button class = "popup" onclick = "togglePopup('usagePopup15')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup15" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::within_cuboid< / span > < / span > :< br / > < a href = "6-sg.html#SP13" > § 13< / a > < br / > Spatial Map - < a href = "6-sm.html#SP15" > § 15< / a > < br / > HTML Map - < a href = "6-hm.html#SP2" > § 2< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > x< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > TRUE< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP13" class = "paragraph-anchor" > < / a > < b > § 13. < / b > Suppose we have a one-dimensional array whose entries correspond to the
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integer grid positions within a cuboid (including its faces and corners).
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The following returns \(-1\) if a point is outside the cuboid, or returns
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the index if it is.
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::cuboid_index< / span > < button class = "popup" onclick = "togglePopup('usagePopup16')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup16" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::cuboid_index< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP13" > § 13< / a > , < a href = "6-sm.html#SP15" > § 15< / a > , < a href = "6-sm.html#SP15_1" > § 15.1< / a > < br / > HTML Map - < a href = "6-hm.html#SP1" > § 1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < a href = "6-sg.html#SP12" class = "function-link" > < span class = "function-syntax" > Geometry::within_cuboid< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > ) == < / span > < span class = "identifier-syntax" > FALSE< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > -1;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > O< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP6" class = "function-link" > < span class = "function-syntax" > Geometry::vec_minus< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > P< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > );< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > width< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > + < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > height< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > + < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > O< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > O< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > width< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > O< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > width< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > height< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::cuboid_volume< / span > < button class = "popup" onclick = "togglePopup('usagePopup17')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup17" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::cuboid_volume< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP15_1" > § 15.1< / a > < br / > HTML Map - < a href = "6-hm.html#SP1_1" > § 1.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > width< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > + < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > height< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > + < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > int< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > depth< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > + < / span > < span class = "constant-syntax" > 1< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > return< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > width< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > height< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > depth< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< p class = "commentary firstcommentary" > < a id = "SP14" class = "paragraph-anchor" > < / a > < b > § 14. < / b > Thickening a cuboid is a little more than adjusting; we give it some
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extra room. (The result is thus no longer minimally bounding, but we
sacrifice that.)
< / p >
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< pre class = "displayed-code all-displayed-code code-font" >
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< span class = "reserved-syntax" > void< / span > < span class = "plain-syntax" > < / span > < span class = "function-syntax" > Geometry::thicken_cuboid< / span > < button class = "popup" onclick = "togglePopup('usagePopup18')" > < span class = "comment-syntax" > ?< / span > < span class = "popuptext" id = "usagePopup18" > Usage of < span class = "code-font" > < span class = "function-syntax" > Geometry::thicken_cuboid< / span > < / span > :< br / > Spatial Map - < a href = "6-sm.html#SP15_1" > § 15.1< / a > < / span > < / button > < span class = "plain-syntax" > (< / span > < span class = "reserved-syntax" > cuboid< / span > < span class = "plain-syntax" > *< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > , < / span > < span class = "reserved-syntax" > vector< / span > < span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > population< / span > < span class = "plain-syntax" > ++ == < / span > < span class = "constant-syntax" > 0< / span > < span class = "plain-syntax" > ) {< / span >
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< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > corner0< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP6" class = "function-link" > < span class = "function-syntax" > Geometry::vec_minus< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > );< / span >
< span class = "plain-syntax" > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "identifier-syntax" > corner1< / span > < span class = "plain-syntax" > = < / span > < a href = "6-sg.html#SP6" class = "function-link" > < span class = "function-syntax" > Geometry::vec_plus< / span > < / a > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > , < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > );< / span >
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< span class = "plain-syntax" > } < / span > < span class = "reserved-syntax" > else< / span > < span class = "plain-syntax" > {< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > .< / span > < span class = "element-syntax" > x< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > y< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > < < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner0< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > - < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > < / span > < span class = "reserved-syntax" > if< / span > < span class = "plain-syntax" > (< / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > > < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ) < / span > < span class = "identifier-syntax" > C< / span > < span class = "plain-syntax" > -> < / span > < span class = "element-syntax" > corner1< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > = < / span > < span class = "identifier-syntax" > V< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > + < / span > < span class = "identifier-syntax" > S< / span > < span class = "plain-syntax" > .< / span > < span class = "identifier-syntax" > z< / span > < span class = "plain-syntax" > ;< / span >
< span class = "plain-syntax" > }< / span >
< span class = "plain-syntax" > }< / span >
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< / pre >
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< nav role = "progress" > < div class = "progresscontainer" >
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< ul class = "progressbar" > < li class = "progressprev" > < a href = "6-ae2.html" > ❮ < / a > < / li > < li class = "progresschapter" > < a href = "1-cm.html" > 1< / a > < / li > < li class = "progresschapter" > < a href = "2-mt.html" > 2< / a > < / li > < li class = "progresschapter" > < a href = "3-sh.html" > 3< / a > < / li > < li class = "progresschapter" > < a href = "4-cg.html" > 4< / a > < / li > < li class = "progresschapter" > < a href = "5-ft.html" > 5< / a > < / li > < li class = "progresscurrentchapter" > 6< / li > < li class = "progresssection" > < a href = "6-ii.html" > ii< / a > < / li > < li class = "progresssection" > < a href = "6-ifs.html" > ifs< / a > < / li > < li class = "progresssection" > < a href = "6-ir.html" > ir< / a > < / li > < li class = "progresssection" > < a href = "6-lxc.html" > lxc< / a > < / li > < li class = "progresssection" > < a href = "6-ce.html" > ce< / a > < / li > < li class = "progresssection" > < a href = "6-ce2.html" > ce2< / a > < / li > < li class = "progresssection" > < a href = "6-be.html" > be< / a > < / li > < li class = "progresssection" > < a href = "6-re.html" > re< / a > < / li > < li class = "progresssection" > < a href = "6-ee.html" > ee< / a > < / li > < li class = "progresssection" > < a href = "6-fe.html" > fe< / a > < / li > < li class = "progresssection" > < a href = "6-te.html" > te< / a > < / li > < li class = "progresssection" > < a href = "6-ve.html" > ve< / a > < / li > < li class = "progresssection" > < a href = "6-rfse.html" > rfse< / a > < / li > < li class = "progresssection" > < a href = "6-ee2.html" > ee2< / a > < / li > < li class = "progresssection" > < a href = "6-se.html" > se< / a > < / li > < li class = "progresssection" > < a href = "6-ie.html" > ie< / a > < / li > < li class = "progresssection" > < a href = "6-ve2.html" > ve2< / a > < / li > < li class = "progresssection" > < a href = "6-ge.html" > ge< / a > < / li > < li class = "progresssection" > < a href = "6-le.html" > le< / a > < / li > < li class = "progresssection" > < a href = "6-ae.html" > ae< / a > < / li > < li class = "progresssection" > < a href = "6-pe.html" > pe< / a > < / li > < li class = "progresssection" > < a href = "6-ce3.html" > ce3< / a > < / li > < li class = "progresssection" > < a href = "6-pe2.html" > pe2< / a > < / li > < li class = "progresssection" > < a href = "6-te2.html" > te2< / a > < / li > < li class = "progresssection" > < a href = "6-ce4.html" > ce4< / a > < / li > < li class = "progresssection" > < a href = "6-ge2.html" > ge2< / a > < / li > < li class = "progresssection" > < a href = "6-ae2.html" > ae2< / a > < / li > < li class = "progresscurrent" > sg< / li > < li class = "progresssection" > < a href = "6-em.html" > em< / a > < / li > < li class = "progresssection" > < a href = "6-me.html" > me< / a > < / li > < li class = "progresssection" > < a href = "6-ins.html" > ins< / a > < / li > < li class = "progresssection" > < a href = "6-spt.html" > spt< / a > < / li > < li class = "progresssection" > < a href = "6-tp.html" > tp< / a > < / li > < li class = "progresssection" > < a href = "6-bck.html" > bck< / a > < / li > < li class = "progresssection" > < a href = "6-rgn.html" > rgn< / a > < / li > < li class = "progresssection" > < a href = "6-tm.html" > tm< / a > < / li > < li class = "progresssection" > < a href = "6-sm.html" > sm< / a > < / li > < li class = "progresssection" > < a href = "6-hm.html" > hm< / a > < / li > < li class = "progresssection" > < a href = "6-rem.html" > rem< / a > < / li > < li class = "progressnext" > < a href = "6-em.html" > ❯ < / a > < / li > < / ul > < / div >
2020-05-03 03:01:21 +03:00
< / nav > <!-- End of weave -->
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< / main >
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< / body >
< / html >
