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Three Step Geometric Pipeline

This tool enables grid sampling, surface generation using zero-crossing interpolation, and triangle generation based on the Marching Cubes algorithm. It also includes outlier computation, consensus surface algorithm, and octree-based voxel splitting for efficient volumetric modeling.

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Three Step Geometric Pipeline

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  1. Three Step Geometric Pipeline

  2. VolumetricModeling • Grid sampling of an implicit surface • Generate surface by zero-crossing interpolation inside surface outside surface surface

  3. Marching Cubes Algorithm • Lorensen and Cline（’87） • f(x) given to each vertex x: • if , vertex x is outside of the object. • if , vertex x is inside of the object. • Generate triangles to meet the above rule

  4. f(x) f(x) f(x’) f(x’) signed distance Outlier Compute Scalar Value • Naive Algorithm • Compute the magnitude: compute the distance f(x), to the nearest object surface from x • Compute the sign: determine whether the point is inside or outside of the object

  5. Consensus Surface Algorithm • Compute consensus surface: comparing using the location and surface normal • Compute f(x) by averaging signed-distances

  6. Octree-based Voxel Splitting • If subdivide the current octant • The octree reduces the computation O(n3) to O(n2)

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