Utilize three.js to blend colors in a 3D space

My 3d mesh consists of 11 static points with predefined values assigned to them. These points are represented as an array of positions in 3d space along with their corresponding values:

 x: 0.3 y: 0.4, z: 0.5, value: 100,
 x: 0.6 y: 0.9, z: 0.66, value: 20,
 x: 0.4 y: 0.22, z: 0.35, value: 50,
 x: 0.11 y: 0.34, z: 0.65, value: 0,
 x: 0.35 y: 0.65, z: 0.5, value: 0,
 x: 0.22 y: 0.67, z: 0.5, value: 0,
 x: 0.43 y: 0.22, z: 0.5, value: 0,
 x: 0.67 y: 0.31, z: 0.5, value: 16,
 x: 0.84 y: 0.34, z: 0.5, value: 13,
 x: 0.22 y: 0.43, z: 0.5, value: 0,
 x: 0.13 y: 0.24, z: 0.5, value: 11,

To color the faces of my 3d mesh, I need to assign a value to each face based on its distance from these points. I have the position of each face, but I'm unsure how to determine their values. What interpolation method should I use? For example, for this face 

x: 0.34, y: 0.43, z: 0.18, value: ?
I am seeking a solution using JS/Three.js for frontend implementation or a Python library for backend processing.

https://i.sstatic.net/zkeYY.png

I have come across some methods that only work in 2D or support interpolation between two points. How can I apply this to an array of points?

javascriptmaththree.js

Answer №1

One approach to achieving this would involve converting a color matrix into 3D voxel maps, as described in this post on Stack Overflow. Instead of rendering triangles, the idea is to render filled voxelized tetrahedrons. This method creates a regular map of colors that can be used in conjunction with trilinear interpolation to determine the color at any given position.

Another alternative is to identify the four closest reference points to your current position, ensuring that they form a tetrahedron in which your point lies. Color interpolation can then be performed using techniques such as trilinear interpolation or barycentric coordinates on each face of the triangle.

If your mesh has UV mapping, you can project your reference points onto it and utilize 2D algorithms accordingly.

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