Question

I want to plot a triangular mesh, and color each edge with a different color. The matlab documentation for trimesh states there’s a color argument, but it doesn’t state what its structure should be – as the triangles share edges, how do I know where to position which color inside the vector C?

Answer 1

I was struggling with this problem yesterday, and I think I have the solution. It turns out that in general if you want to be very detailed with which edge is which color, you have to be very sneaky.

So you understand what the problem is, I’ll first review how the command trimesh(Tri,X,Y,Z,C) assigns colors in the first place. The argument C has be a vector of numbers with length equaling the number of vertices (not edges). The way it colors edges is as follows. If we have 4 vertices and we assign

Tri=[1 2 3; 3 2 4]

and

C=[10 20 30 40]

then the first edge found in Tri is 1 to 2 and it is colored using the color of point 1, which is 10. The next edge found is 2 to 3, which is colored using the color of point 2, which is 20. The next edge is 3 to 1, which has color 30. The next edge is 3 to 2 with color 30; notice this edge has already been colored 20 but this new color overwrites the old color. And then edge 2 to 4 is colored 20 and edge 4 to 3 is colored 40.

The problem is that without using a special trick, this coloring scheme can make it literally impossible to color the edges exactly as you want. Your case in point: if you have more edges than vertices (as in my example) and you want each edge to be colored differently, you are out of luck because the edges are colored according to the colors assigned to the vertices. But if we make multiple copies of each vertex (and, consequently, multiple copies of each edge), then we are back in business. Also, our lives are made easier by the fact that Tri accepts not just faces but also individual edges as well.

As an example of what I mean, suppose you wanted edge 2 to 3 to have the color 50 in the example above. To do this, make a new point, point 5, which is the same as point 2 (i.e., the same (x,y,z) coordinates). Redefine Tri and C as follows:

Tri=[1 2 3; 3 2 4;3 5 3]

C=[10 20 30 40 50]

Notice that the last three numbers in Tri do not define a face but rather an edge (the edge 3 to 5, which is the same as 2 to 3). This edge will be colored by whatever color point 5 is assigned. In this manner, you can overwrite the colors of every edge individually. Just be sure to put these edges at the end of the Tri matrix so that their colorings overwrite any previous undesired colorings. If you don’t care about having faces filled in, you can even have a Tri matrix with nothing but edges. Its a bit of a hack, but it works.