How is vertex normal defined for 3-D surface triangulation?

Bruce Elliott

2020 3 17

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Does the vertexNormal method of a triangulation object return the normalized numerical average of the adjacent face normal vectors? I believe that's a common definition, but I'd like to confirm it.

Thanks.

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darova 2020-3-18

You can check this with norm()

Bruce Elliott 2020-3-18

在 MATLAB Online 中打开

Well yes, that's true!

I did it, and found that the differences between the built-in vertexNormal vectors and those I computed by averaging the normal vectors of the adjacent faces were at the level of machine precision. In other words, they were the same, as expected.

For the curious, here is the code I used:

[F,P] = freeBoundary(delaunayTriangulation(rand(50,1),rand(50,1),rand(50,1)));
TR = triangulation(F,P);
normVecsBuiltIn = vertexNormal(TR);
vtxAtt = vertexAttachments(TR);
fprintf('\n');
for vertIdx = 1:size(TR.Points,1)
  adjFaces = vtxAtt{vertIdx};
  meanNorm = mean(faceNormal(TR,adjFaces'));
  meanNorm = meanNorm/norm(meanNorm);
  diffVec = normVecsBuiltIn(vertIdx,:)-meanNorm;
  fprintf('Vert. ID: %2u - Vect. Diff: %e\n',vertIdx,norm(diffVec));
end