CSGRegion
CSGRegion[{reg1,reg2,…}]
represents the solid region corresponding to the union of solid regions reg1,reg2,….
CSGRegion["op",{reg1,reg2,…}]
represents the solid region corresponding to the Boolean combination "op" of regions reg1,reg2,….
CSGRegion["op",{…,wi[regi],…}]
represents the solid region defined by regions regi transformed by a geometric transformation wi.
Details and Options
- CSGRegion is also known as constructive solid geometry (CSG) object.
- CSGRegion is typically used to construct solid geometric regions by using nested combinations of union, intersection and subtraction of simple geometric primitives.
- CSGRegion[…] displays in a notebook as a plot of a solid region in 2D and 3D.
- In CSGRegion["op",{reg1,reg2,…}], "op" are Boolean operations and regions regi are other CSGRegion objects or geometric regions.
- The following Boolean operators "op" can be used:
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"Intersection" smallest solid containing the intersection of two regions "Difference" smallest solid containing the difference of two regions "Union" smallest solid containing the union of two regions - The following 2D solid regions regi are supported:
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Disk disk Ellipsoid ellipsoid Parallelogram parallelogram Rectangle rectangle Triangle triangle Simplex simplex - The following 3D solid regions regi are supported:
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Ball ball Cone cone Cube cube Cuboid cuboid Cylinder cylinder Dodecahedron dodecahedron Ellipsoid ellipsoid Icosahedron icosahedron Octahedron octahedron Parallelepiped parallelepiped Prism prism Pyramid pyramid Simplex simplex Tetrahedron tetrahedron - The following n‐dimensional solid regions regi are supported:
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Ball ball Cuboid axis-aligned cuboid Ellipsoid ellipsoid Parallelepiped parallelotope Simplex simplex - In CSGRegion["op",{…,wi[regi],…}], wi are geometric transformations or wrappers for regions regi.
- The following geometric transformations wi can be used:
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GeometricTransformation[regi,…] geometric affine transformation Rotate[regi,…] rotation Scale[regi,…] scaling Translate[regi,…] translation - CSGRegion[{reg1,reg2,…}] is equivalent to CSGRegion["Union",{reg1,reg2,…}].
- CSGRegion takes the same options as Region.
- CSGRegion can be used with functions such as RegionMember, RegionDistance, RegionMeasure and NIntegrate.
Examples
open allclose allBasic Examples (3)
Scope (5)
Applications (7)
Basic Applications (4)
CSGRegion using multiple operations:
Properties & Relations (4)
Compute the union of two regions:
CSG regions can be represented as Boolean regions:
A CSGRegion object is solid:
The embedding dimension of a CSG region is the same as its geometry dimension:
Possible Issues (1)
CSGRegion with transparency does not show occluded regions:
Use Graphics3D to show all regions:
Interactive Examples (3)
Text
Wolfram Research (2021), CSGRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/CSGRegion.html (updated 2024).
CMS
Wolfram Language. 2021. "CSGRegion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/CSGRegion.html.
APA
Wolfram Language. (2021). CSGRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CSGRegion.html