# ConicHullRegion

ConicHullRegion[{p1,,pm+1}]

represents the m-dimensional affine hull region passing through points pi.

ConicHullRegion[p,{v1,,vm}]

represents the m-dimensional affine hull region passing through the point p and parallel to vi.

ConicHullRegion[{p1,,pm+1},{w1,,wn}]

represents the m-dimensional affine hull plus the conic hull generated by the vectors wj.

ConicHullRegion[p,{v1,,vm},{w1,,wn}]

represents the m-dimensional affine hull plus the conic hull generated by the vectors wj.

# Details  • 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 wj 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 representations 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 the vi are linearly independent.
• ConicHullRegion can be used in Graphics and Graphics3D.
• In graphics, the points p, pi and vectors vi, wj can be Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.

# Examples

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## Basic Examples(3)

A ConicHullRegion in 2D:

 In:= Out= And in 3D:

 In:= Out= Different styles applied to a conic hull region:

 In:= In:= Out= Determine if points belong to a given conic hull region:

 In:= In:= Out= ## Neat Examples(1)

Introduced in 2014
(10.0)