ABSTRACT
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We present methods to approximate given shapes with user-tunable number of spheres to balance between accuracy and simplicity: touching medial/scale-axis polar balls and k-means smallest enclosing circles. Our methods are easy to implement, run efficiently, and can approach quality similar to manual construction.
Supplemental Material
- Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. 2001. The Power Crust. In SMA ’01 (Ann Arbor, Michigan, USA). 249–266.Google Scholar
- Chen-Yuan Hsu, Li-Yi Wei, Lihua You, and Jian Jun Zhang. 2020. Autocomplete Element Fields. In CHI ’20. 1–13.Google Scholar
- Philip M. Hubbard. 1996. Approximating Polyhedra with Spheres for Time-Critical Collision Detection. ACM Trans. Graph. 15, 3 (1996), 179–210.Google ScholarDigital Library
- Alec Jacobson, Ilya Baran, Jovan Popović, and Olga Sorkine. 2011. Bounded Biharmonic Weights for Real-Time Deformation. ACM Trans. Graph. 30, 4, Article 78 (2011), 8 pages.Google ScholarDigital Library
- Project Nayuki. 2018. Smallest enclosing circle.Google Scholar
- Ankit Phogat, Matthew Fisher, Danny M. Kaufman, and Vineet Batra. 2019. Skinning Vector Graphics with GANs. In ACM SIGGRAPH 2019 Posters (Los Angeles, California). Article 70, 2 pages.Google Scholar
- Szymon Rusinkiewicz and Marc Levoy. 2000. QSplat: A multiresolution point rendering system for large meshes. In SIGGRAPH ’00. 343–352.Google Scholar
- Floris Steenkamp. 2019. Medial (and Scale) Axis Transform library - SVG focused.Google Scholar
- Svetlana Stolpner, Paul Kry, and Kaleem Siddiqi. 2012. Medial Spheres for Shape Approximation. IEEE Trans. Pattern Anal. Mach. Intell. 34, 6 (2012), 1234–1240.Google ScholarDigital Library
- Jean-Marc Thiery, Émilie Guy, and Tamy Boubekeur. 2013. Sphere-Meshes: Shape Approximation Using Spherical Quadric Error Metrics. ACM Trans. Graph. 32, 6, Article 178 (2013), 12 pages.Google ScholarDigital Library
- Rui Wang, Kun Zhou, John Snyder, Xinguo Liu, Hujun Bao, Qunsheng Peng, and Baining Guo. 2006. Variational Sphere Set Approximation for Solid Objects. Vis. Comput. 22, 9 (2006), 612–621.Google ScholarDigital Library
- Wikipedia. 2019. Smallest-circle problem.Google Scholar
- Cem Yuksel. 2015. Sample Elimination for Generating Poisson Disk Sample Sets. Comput. Graph. Forum 34, 2 (2015), 25–32.Google ScholarDigital Library
Recommendations
Smoothly deformable spheres: modeling, deformation, and interaction
SA '16: SIGGRAPH ASIA 2016 Technical BriefsExisting shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as NURBS. Polygon models and subdivision ...
Comparison of curve and surface skeletonization methods for voxel shapes
Surface and curve skeletons are important shape descriptors with applications in shape matching, simplification, retrieval, and animation. In recent years, many surface and curve skeletonization methods for 3D shapes have been proposed. However, ...
Comments