gives the sphere that can be inscribed in the simplex defined by points pi in .
gives the insphere of a polyhedron or polygon poly.
- Insphere is also known as incircle, inscribed circle, or inscribed disk.
- Insphere gives the Sphere of largest measure (arc length, area, etc.) that can be inscribed in the simplex (triangle, tetrahedron, etc.) defined by points pi.
- Insphere evaluates to a Sphere[c,r], where the center c is known as the incenter and radius r is known as the inradius for the related simplex.
- Insphere is defined for and affinely independent.
- For polyhedra, Insphere[poly] returns a sphere that is contained within the polyhedron poly and tangent to each of the polyhedron faces.
- For polygons, Insphere[poly] returns a sphere that is contained within the polygon poly and tangent to each of the polygon edges.
- Insphere can be used with symbolic points in GeometricScene.
Examplesopen allclose all
Basic Examples (2)
Insphere works in any number of dimensions:
Solve equations over an Insphere:
Use Insphere to generate a circle packing for a triangulated region. First triangulate the region:
Use Insphere to compute a circle for each triangle:
Use Insphere to generate a sphere packing for a triangulated region. First discretize and triangulate the region:
Use Insphere to compute spheres for each tetrahedron: