TriangulatedSurface2D Class

public sealed class TriangulatedSurface2D : Surface

Public NotInheritable Class TriangulatedSurface2D
	Inherits Surface

public ref class TriangulatedSurface2D sealed : public Surface

[<SealedAttribute>]
type TriangulatedSurface2D = 
    class
        inherit Surface
    end

Inheritance

Object  →  Surface  →  TriangulatedSurface2D

The TriangulatedSurface2D class performs interpolation on irregularly distributed 2D points by constructing a Delaunay triangulation and using piecewise linear (barycentric) interpolation within each triangle.

Delaunay triangulation: The input points are triangulated using the Delaunay criterion, which maximizes the minimum angle of all triangles and avoids sliver triangles. The triangulation partitions the convex hull of the data points into triangular regions.

Interpolation method: For a query point p inside a triangle with vertices (p₀, p₁, p₂) and corresponding values (z₀, z₁, z₂), the interpolated value is computed using barycentric coordinates:

z(p) = λ₀z₀ + λ₁z₁ + λ₂z₂

where λᵢ are the barycentric coordinates satisfying λ₀ + λ₁ + λ₂ = 1.

Domain and extrapolation: The interpolant is naturally defined only over the triangulation (typically the convex hull of the data points). Query points outside this region are handled according to the ExtrapolationMode parameter:

• Throw: Throws an exception for out-of-domain queries.
• Constant: Returns a fill value (typically NaN) for out-of-domain queries.
• Clamp: Projects the query point to the triangulation boundary and interpolates there.

Performance characteristics:

• Construction: O(N log N) for Delaunay triangulation of N points.
• Evaluation: O(log N) per query using efficient point location in the triangulation.
• The interpolant is continuous but has discontinuous gradients at triangle edges.

Triangulated linear interpolation is well-suited for general 2D scattered data and is commonly used in computer graphics, GIS applications, and terrain modeling. It provides a good balance of smoothness, accuracy, and computational efficiency.

The TriangulatedSurface2D class inherits from Surface and is explicitly 2D-only. Create instances using the ScatteredLinear2DInterpolator factory method.

Reference