Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Projective Geometry
Special algebras for Projective Geometry.
$PGA | Geometric Algebra 3,0,1 |
$2DPGA | Geometric Algebra 2,0,1 |
PGAPoint | |
PGALine | |
PGAPlane | |
RegionPGA | |
PGARegions |
Load the context with Projective Geometry functionality:
<<Wolfram`GeometricAlgebra`
In[56]:=
<<Wolfram`GeometricAlgebra`ProjectiveGeometry`
Flat Projective Geometry
In[935]:=
$2DPGA["OrderedBasis"]
Out[935]=
Out[2019]=
Rigid Projective Geometry
In[922]:=
$PGA["OrderedBasis"]
Out[922]=
Join
Join
In[1411]:=
ResourceFunction["NiceGrid"][Outer[Wedge,#,#]&@$PGA["OrderedBasis"]//Once,$PGA["OrderedBasis"],$PGA["OrderedBasis"],ItemSize2]/."""⋀"
Out[1411]=
Line through two points
Line through two points
Out[999]=
Plane through a point and a line
Plane through a point and a line
Out[1008]=
Meet
In[1412]:=
ResourceFunction["NiceGrid"][Outer[Vee,#,#]&@$PGA["OrderedBasis"]//Once,$PGA["OrderedBasis"],$PGA["OrderedBasis"],ItemSize2]/."""⋁"
Out[1412]=
Intersection of two planes
Intersection of two planes
Plane and line intersection
Plane and line intersection
Expansion
Line through a point and orthogonal to a plane
Line through a point and orthogonal to a plane
Plane containing a point and orthogonal to a line
Plane containing a point and orthogonal to a line
Plane containing a line and orthogonal to a plane
Plane containing a line and orthogonal to a plane
Projections
Orthogonal projections
Orthogonal projections
Orthogonal anti-projections
Orthogonal anti-projections
Central projections
Central projections
Central anti-projections
Central anti-projections
Transformations
Transformations
Reflection
Reflection
Vectors:
Shapes:
Translation
Translation
Rotation
Rotation
Motor
Motor
Motor is a composition of translation and rotation:
Flector
Flector
Complex scene
Construct a geometric scene: