triangualize - ObjectVision/GeoDMS GitHub Wiki

Geometric functions triangualize

The triangualize function creates a Delaunay triangulation from a set of points.

triangualize(points: E->Point) -> E->Sequence<Point>

Computes a Delaunay triangulation of the input points. The Delaunay triangulation is a triangulation where no point is inside the circumcircle of any triangle - this maximizes the minimum angle of all triangles.

The result is a sequence of points for each input point, representing the triangles that include that point as a vertex. This is organized as a triangle fan around each point.

The Delaunay triangulation has important properties:

• It is unique (except for degenerate cases with co-circular points)
• It maximizes the minimum angle (avoids thin triangles)
• It is the dual graph of the Voronoi diagram
• The number of triangles is approximately 2n-5 for n points

Time complexity: O(n × log n) expected for well-distributed points using sweep line algorithm.

Worst case can be O(n²) for pathological distributions, but this is rare in practice.

Memory usage is O(n) for the triangulation structure.

• At least 3 non-collinear points are required for a valid triangulation
• All points must be defined (non-null)
• Duplicate points may cause issues

unit<uint32> SamplePoints: nrofrows = 100;
attribute<DPoint> location (SamplePoints);  // random or measured points

// Create Delaunay triangulation
attribute<DPoint> triangles (poly, SamplePoints) := triangualize(location);

// The triangulation can be used for:
// - Terrain modeling (TIN)
// - Interpolation
// - Mesh generation

• Terrain modeling: Creating Triangulated Irregular Networks (TIN) from elevation samples
• Interpolation: Natural neighbor or linear interpolation over triangulated surfaces
• Mesh generation: Starting point for finite element meshes
• Spatial analysis: Identifying natural neighbors, computing Voronoi diagrams

• Geometric functions
• points2polygon - creates polygons from point sequences

5.0