https://github.com/111116/sphere-set-approximation
approximate a mesh with a set of spheres
https://github.com/111116/sphere-set-approximation
mesh-processing
Last synced: 10 months ago
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approximate a mesh with a set of spheres
- Host: GitHub
- URL: https://github.com/111116/sphere-set-approximation
- Owner: 111116
- Created: 2020-06-24T08:04:05.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2021-05-17T03:47:59.000Z (over 4 years ago)
- Last Synced: 2025-03-29T03:51:15.206Z (11 months ago)
- Topics: mesh-processing
- Language: C++
- Homepage:
- Size: 1.87 MB
- Stars: 22
- Watchers: 2
- Forks: 4
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Sphere Set Approximation
**WORK IN PROGRESS**
Approximate a mesh by bounding it with a set of spheres, which can be used for collision detection, shadowing, etc.
The program requires an original mesh and a simplified manifold version of the mesh, which can be generated from the original mesh using [hjwdzh/Manifold](https://github.com/hjwdzh/Manifold). The original mesh is used for surface constraint, while the manifold mesh is used for volume constraint & redundant volume optimization.
You may try with different seeds to get better result.
## Usage
```bash
cd src
make
./main -i ../armadillo.obj -m ../armadillo_manifold.obj -n 64
```
It outputs to `stdout` and logs to `stderr`.
The algorithm runs quite slow (proportional to number of triangular faces of the manifold).
The manifold must be closed and orientable.
## Algorithm
We use method described in
[*Variational Sphere set Approximation for Solid Objects*](http://dx.doi.org/10.1007/s00371-006-0052-0)
with several minor changes:
- bugfixes SOTV, which in this paper is overestimated in some cases
- provides an analytic algorithm to solve swing volume
- voxel size doesn't have to be manually specified
- better sample quality of surface points
- other minor strategy optimizations
#### paper abstract
We approximate a solid object represented as a triangle mesh by a bounding set of spheres having minimal summed volume outside the object. We show how outside volume for a single sphere can be computed using a simple integration over the object’s triangles. We then minimize the total outside volume over all spheresin the set using a variant of iterative Lloyd clustering which splits the mesh points into sets and bounds each with an outside volume-minimizing sphere. The resulting sphere sets are tighter than those of previous methods. In experiments comparing against a state-of-the-art alternative (adaptive medial axis), our method often requires half or fewer as many spheres to obtain the same error, under a variety of error metrics including total outside volume, shadowing fidelity, and proximity measurement.
#### Optimization steps
1. Fix the centers of spheres. Greedily assign points to them, minimizing SOV
2. Fix the point clusters. Adjust the spheres using Powell's method, minimizing SOV
3. Teleportation: Remove the most redundant sphere. Split the sphere with most SOV