Geometry-Processing

幾何形状処理関連のいろいろ

mygp(old version) -> kika(refactored version(unfinished))

• algebraic topology

  • Tree-Cotree Decomposition
  • Minimum Cycle Basis
  • Minimum Homology Basis
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• chaos maps

  • ロジスティク写像
  • 池田写像
  • ティンカーベル写像
  • ボグダノフ写像
  • Thomas' cyclically symmetric attractor
  • ジンジャーブレッドマン写像
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• geodesic distance

  • Dijkstra最短経路
  • A*
  • Fast Marching Method
  • 熱拡散による測地距離計算 (The Heat Method for Distance Computation. Crane, K. et al. 2017)
  • 仮想頂点を利用した測地距離計算（Geodesic Distance Computation via Virtual Source Propagation. Trettner, P. et al. 2021）
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• intrinsic features

  • mean curvature
  • gaussian curvature
  • Heat Kernel Signature ( A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion. Sun, J. et al. 2009)
  • Wave Kernel Signature (The Wave Kernel Signature: A Quantum Mechanical Approach to Shape Analysis. Aubry, M. et al. 2011)
  • Wavelet-based Heat Kernel (Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis. Krigo, M. et al. 2020）
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  • Salient Feature Extraction
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  • principal curvature (Efficient Multi-scale Curvature and Crease Estimation. D. Panozzo, et al. 2010)
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• halfedge data structure

• iterative closest point

• coherent point drift ( Myronenko, Andriy and Song, Xubo. Point Set Registration: Coherent Point Drift. IEEE Transactions on Pattern Analysis and Machine Intelligence. 32. 2262-75, 2010.; O. Hirose. A Bayesian Formulation of Coherent Point Drift. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 2269-2286, 2021.;O. Hirose. Acceleration of Non-Rigid Point Set Registration With Downsampling and Gaussian Process Regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 2858-2865, 2021.)

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• vector field

  • trivial connection (Trivial Connections on Discrete Surfaces. Crane, K. et al.2010.)
  • vector heat (The Vector Heat Method. Sharp, N. et al. 2019.)
  • hodge decomposition
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• differential geometry

  • cotangent weight laplacian
  • polygonal laplacian（Discrete Differential Operators on Polygonal Meshes. Goes D. F., et al. 2020.)
  • polygonal laplacian (Polygon Laplacian Made Simple. Bunge A., et al. 2020.)
  • diamond laplacian (The Diamond Laplace for Polygonal and Polyhedral Meshes. Bunge A., et al. 2021.)

• signed distance function

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  • marching cubes

• sspace partitioning

  • kd木
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• spherization

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• simplification

  • Quadric Error Metrices
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• shape correspondences

  • functional maps
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dog-bear-trim_Q0G9238e.mp4

wolf-cat-trim_xIJD7kAC.mp4