Laplacian smoothing代写 COMP 5411 Programming Assignment 1

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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