Wolfram Language & System 10.0 (2014)|Legacy Documentation
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discretizes only the elements in g that match the pattern patt.
- BoundaryDiscretizeGraphics is also known as boundary evaluation.
- BoundaryDiscretizeGraphics discretizes full-dimensional graphics primitives into a boundary representation consisting of piecewise linear elements used in BoundaryMeshRegion.
- Only full-dimensional parts (areas in 2D and volumes in 3D) will be discretized.
- The graphic g can be Graphics, Graphics3D, or individual graphics primitives.
- BoundaryDiscretizeGraphics effectively treats multiple primitives in Graphics and Graphics3D as a union operation.
- Bounded piecewise linear primitives in Graphics (these can be represented exactly):
Triangle[…] filled triangle (2D) Polygon[…] filled polygon (2D) Rectangle[…] filled rectangle (2D) Parallelogram[…] filled parallelogram (2D) Simplex[…] simplex (2D)
- In addition SSSTriangle, SASTriangle, ASATriangle, and AASTriangle evaluate to Triangle and can be represented exactly.
- Unbounded piecewise linear primitives in Graphics (only a finite range can be represented):
HalfPlane[…] halfspace (2D) ConicHullRegion[…] linear cone (2D)
- Nonlinear primitives in Graphics (only an approximation can be represented):
Disk[…] disk, filled ellipse, sectors (2D) FilledCurve[…] filled closed curve (2D)
- Bounded piecewise linear primitives in Graphics3D (these can be represented exactly)
Cuboid[…] filled cuboid (3D) Parallelepiped[…] filled parallelepiped (3D) Tetrahedron[…] filled tetrahedron (3D) Hexahedron[…] filled hexahedron (3D) Pyramid[…] filled pyramid (3D) Prism[…] filled prism (3D) Simplex[…] simplex (3D)
- Unbounded piecewise linear primitives in Graphics3D (only a finite range can be represented):
ConicHullRegion[…] linear cone (3D)
- Nonlinear primitives in Graphics3D. Only an approximation can be represented.
Ball[…] ball or filled sphere (3D) Ellipsoid[…] filled ellipsoid (3D) Cylinder[…] filled cylinder (3D) Cone[…] filled cone (3D)
- The following options may be given:
AccuracyGoal Automatic digits of accuracy sought MaxCellMeasure Automatic maximum cell measure Method Automatic method to use PlotRange Automatic the range to include PerformanceGoal $PerformanceGoal whether to consider speed or quality PrecisionGoal Automatic digits of precision sought
- With AccuracyGoal->a and PrecisionGoal->p an attempt will be made to keep the maximum distance between the region reg or the discretized region dreg and any point in RegionSymmetricDifference[reg,dreg] to less than where is the length of the diagonal of the plot range.
Introduced in 2014