Offsetting operations in solid modelling
Computer Aided Geometric Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
3D Compression Made Simple: Edgebreaker with Zip&Wrap on a Corner-Table
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Curvature-based Energy for Simulation and Variational Modeling
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Equivolumetric offsets for 2D machining with constant material removal rate
Computer Aided Geometric Design
Equivolumetric offset surfaces
Computer Aided Geometric Design
Computer-Aided Design
Articulated swimming creatures
ACM SIGGRAPH 2011 papers
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Fast interactive visualization for multivariate data exploration
CHI '13 Extended Abstracts on Human Factors in Computing Systems
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We address three related problems. The first problem is to change the volume of a solid by a prescribed amount, while minimizing Hausdorff error. This is important for compensating volume change due to smoothing, subdivision, or advection. The second problem is to preserve the individual areas of infinitely small chunks of a planar shape, as the shape is deformed to follow the gentle bending of a smooth spine (backbone) curve. This is important for bending or animating textured regions. The third problem is to generate consecutive offsets, where each unit element of the boundary sweeps the same region. This is important for constant material-removal rate during numerically controlled (NC) machining. For all three problems, we advocate a solution based on normal offsetting, where the offset distance is a function of local or global curvature measures. We discuss accuracy and smoothness of these solutions for models represented by triangle or quad meshes or, in 2D, by spine-aligned planar quads. We also explore the combination of local distance offsetting with a new selective smoothing process that reduces discontinuities and preserves curvature sign.