COMP 5411 Programming Assignment 1
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Tasks
1. Implement Explicit Laplacian smoothing: • Using uniform weights
• Using cotangent weights
2. Implement Implicit Laplacian smoothing: • Using uniform weights
• Using cotangent weights
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Tasks
1. Implement Explicit Laplacian smoothing: • Corresponding function in the code:
• Mesh::umbrellaSmooth()
2. Implement Implicit Laplacian smoothing:
• Corresponding function in the code: • Mesh::implicitUmbrellaSmooth()
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Explicit Laplacian Smoothing
• Fairing operator (uniform)
• In matrix form
Uniform Laplacian, where t is time stamp.
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Explicit Laplacian Smoothing
• Instead of uniform-weight Laplacian, use cotangent-weight Laplacian
• In matrix form
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Explicit Laplacian Smoothing
• The matrix element of L
• L is sparse and has the following elements:
• For sparse matrix construction in Eigen, please refer to http://eigen.tuxfamily.org/dox/group__TutorialSparse.html#title3
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Implicit Laplacian Smoothing
•
You need to solve a sparse linear system.
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Mesh Viewer
• Commands
Use uniform or cot. weights
Explicit or implicit smoothing
Perform one step smoothing
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