ConicHullRegion

ConicHullRegion[{p1,,pm+1}]
represents the m-dimensional affine hull region passing through points .

ConicHullRegion[p,{v1,,vm}]
represents the m-dimensional affine hull region passing through the point p and parallel to .

ConicHullRegion[{p1,,pm+1},{w1,,wn}]
represents the m-dimensional affine hull plus the conic hull generated by the vectors .

ConicHullRegion[p,{v1,,vm},{w1,,wn}]
represents the m-dimensional affine hull plus the conic hull generated by the vectors .

DetailsDetails

  • ConicHullRegion is also known as affine space, half-space, and affine hull in special cases.
  • ConicHullRegion can be used as a geometric region and graphics primitive.
  • The cases ConicHullRegion[{p1,,pm+1}] and ConicHullRegion[p,{v1,,vm}] represent an affine hull, which is commonly known as an infinite line, infinite plane, or infinite space.
  • The conic directions represent a pure conic hull that is added to each point in the affine hull, also known as a Minkowski sum of an affine hull and a conic hull.
  • Parametric representions are given by:
  • ConicHullRegion[{p1,,pm+1}]
    ConicHullRegion[p,{v1,,vm}]
    ConicHullRegion[{p1,,pm+1},{w1,,wn}]
    ConicHullRegion[p,{v1,,vm},{w1,,wn}]
  • Low-dimensional versions of ConicHullRegion have special representations:
  • ConicHullRegion[{p1,p2}]InfiniteLine[{p1,p2}]
    ConicHullRegion[{p1,p2,p3}]InfinitePlane[{p1,p2,p3}]
    ConicHullRegion[{p1},{w1}]HalfLine[p1,w1]
    ConicHullRegion[{p1,p2},{w1}]HalfPlane[{p1,p2},w1]
  • ConicHullRegion[p,{v1,,vm}] represents an m-dimensional region if are linearly independent.
  • ConicHullRegion can be used in Graphics and Graphics3D.
  • In graphics, the points p, and vectors , can be Dynamic expressions.
  • Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.
Introduced in 2014
(10.0)