Is Delaunay triangulation always possible?
By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean distance. However, in these cases a Delaunay triangulation is not guaranteed to exist or be unique.
Can polygons have holes?
In geometry, a polygon with holes is an area-connected planar polygon with one external boundary and one or more interior boundaries (holes). An ordinary polygon can be called simply-connected, while a polygon-with-holes is multiply-connected.
Can all polygons be decomposed into triangles?
Triangulations. Theorem: Any polygon can be decomposed into triangles.
How many triangles do you need to triangulate a polygon with n edges?
Every triangulation of an n-gon has exactly n − 2 triangles. 3. Polygon in picture has n = 13, and 11 triangles.
How many ways can you triangulate a polygon?
The 42 possible triangulations for a convex heptagon (7-sided convex polygon).
Which is better shape preserving or Delaunay triangulation?
The better-known Delaunay triangulationis generally not shape-preserving as it works only on points, without knowledge of input line segments or polygon edges. Shape-preserving Delaunay or more commonly near-Delaunaytriangulation is performed on a set of edges rather than paths, and can be performed on multiple polygons at once.
Is there library for triangulation of polygons with holes?
Now I found a 2D constrained Delaunay triangulation library called poly2tri originally written in C++ and Java but already ported in AS3 which seems to work with holes. At the moment it needs some changes to perfectly fit to my needs, but it’s a great start to achieve my destructible terrain.
Can a path based Polygon be triangulated with ear clipping?
Ear clipping (or cutting) must be applied to a path-basedpolygon that consists of only one island, with zero or more holes. Any multiple island polygons must be triangulation separately by this method.
Can a hole be performed on multiple polygons at once?
Shape-preserving Delaunay or more commonly near-Delaunaytriangulation is performed on a set of edges rather than paths, and can be performed on multiple polygons at once. Holes require careful trimming of triangles after the decomposition is performed in this approach.