Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Projective Geometry
$PGA | Geometric Algebra {3,0,1} |
RegionPGA | |
PGARegions |
Load the context with Projective Geometry functionality:
In[197]:=
Get["Wolfram`GeometricAlgebra`ProjectiveGeometry`"]
In[115]:=
$PGA["Basis"]
Out[115]=
In[211]:=
$PGA[1,2,3]
Out[211]=
e
123
Construct a geometric scene:
In[227]:=
SeedRandom[2];points=Point/@RandomReal[{-3,3},{3,3}];line=InfiniteLine[RandomReal[{-3,3},{2,3}]];plane=InfinitePlane[RandomReal[{-3,3},{3,3}]];Graphics3D[{Opacity[0.5],PointSize[0.03],Thickness[0.01],(*3bluepoints*)Blue,points,(*Redline*)Red,line,(*Greenplane*)Green,plane,(*Bluelinethroughfirsttwobluepoints*)Blue,PGARegions[Wedge@@RegionPGA@Take[points,2]]["Line"],(*Pointofredlineandgreenplaneintersection*)Opacity[1],Yellow,PGARegions[RegionPGA[plane]⋁RegionPGA[line]]["Point"],(*Blueplanethrough3bluepoints*)Opacity[0.4],Blue,PGARegions[Wedge@@RegionPGA[points]]["Plane"],(*Cyanlineofblueandgreenplaneintersection*)Cyan,PGARegions[Wedge@@RegionPGA[points]⋁RegionPGA[plane]]["Line"],PGARegions[Wedge@@RegionPGA@Take[points,2]⋁RegionPGA[plane]]["Point"],(*Purplepointofblueplaneandredlineintersection*)Purple,PGARegions[Wedge@@RegionPGA[points]⋁RegionPGA[line]]["Point"],(*Orangelinegoingthroughyellowpointperpendiculartoblueplane*)Orange,PGARegions[PGAWeightExpansion[RegionPGA[plane]⋁RegionPGA[line],Wedge@@RegionPGA[points]]]["Line"],(*Redplanegoingthroughyellowpointperpendiculartoredline*)Red,PGARegions[PGAWeightExpansion[RegionPGA[plane]⋁RegionPGA[line],RegionPGA[line]]]["Plane"]},BoxedFalse]
Out[231]=
""