# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# 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.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

A ConicHullRegion in 2D:

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And in 3D:

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Different styles applied to a conic hull region:

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Determine if points belong to a given conic hull region:

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