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Hello, I am working on generating a vertex mapping file that identifies corresponding vertices across different levels of an icosahedral mesh. Specifically, for ico6, I want to determine which vertices contribute to each vertex in ico5 when downsampling is performed. Currently, I approximate this mapping using Euclidean distance: for each vertex in ico5, I find the n closest vertices in ico6 based on their (x, y, z) coordinates, then average across these. However, I’m wondering if there is a more formal or standard approach to defining these vertex correspondences—perhaps one based on the hierarchical structure of icosahedral refinement. Would you have any suggestions for a more principled method to determine vertex equivalence across levels? Thanks, Sam
I think what you are doing is fine. Those meshes were made over 25 years ago, so the details you seek are probably lost
On 2/5/2025 7:26 PM, Samuel D Anderson wrote:
External Email - Use Caution
Hello, I am working on generating a vertex mapping file that identifies corresponding vertices across different levels of an icosahedral mesh. Specifically, for ico6, I want to determine which vertices contribute to each vertex in ico5 when downsampling is performed. Currently, I approximate this mapping using Euclidean distance: for each vertex in ico5, I find the /n/ closest vertices in ico6 based on their (x, y, z) coordinates, then average across these. However, I’m wondering if there is a more formal or standard approach to defining these vertex correspondences—perhaps one based on the hierarchical structure of icosahedral refinement. Would you have any suggestions for a more principled method to determine vertex equivalence across levels? Thanks, Sam
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Douglas N. Greve -
Samuel D Anderson