2/28/07

3D Graph Interpolation

Rhino Labs
This plugin creates a smooth colour distribution over a 3D mesh based on spatial relationships of sample points. A sample point is a combination of a 3D coordinate and a sample value. When multiple sample points occupy the same space, the sample value at any given coordinate can be guessed (interpolated). The diagram below is a one-dimensional representation of this algorithm:

In this case only two sample points are specified; A and B. The null-effect line represents the zero-influence line. Let's assume that Sample A has a value of 2.0 and Sample B a value of -0.5. When we calculate the value at point 2, the resulting value is the exact average of A and B; +0.75. In a 3D environment, every vertex of a mesh is interpolated and the local value mapped to a colour gradient which gives the following result for three Sample-points:

No comments: