Algorithms for computer algebra
Algorithms for computer algebra
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Adaptive implicit modeling using subdivision curves and surfaces as skeletons
Proceedings of the seventh ACM symposium on Solid modeling and applications
Convolution surfaces for line skeletons with polynomial weight distributions
Journal of Graphics Tools
Interactive Shape Design with Convolution Surfaces
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Subdivision-Curve Primitives: A New Solution for Interactive Implicit Modeling
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Implicit modeling from polygon soup using convolution
The Visual Computer: International Journal of Computer Graphics
Matisse: painting 2D regions for modeling free-form shapes
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
SMI 2011: Full Paper: Warp-based helical implicit primitives
Computers and Graphics
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This paper reviews and generalizes convolution surfaces, a technique used in computer graphics to generate smooth 3D volumes around skeletons that are lower dimensional or simpler geometric models of the shape to be created. Convolution surfaces are defined as level sets of a function obtained by integrating a kernel function along this skeleton. To allow interactive modeling, the technique has relied on closed form formulas for integration obtained through symbolic computation software. This paper provides new qualitative results and generalizations on the topic when the skeleton is a polygonal line. It is also an opportunity for us to introduce the field of convolution surfaces to the symbolic computation community, hoping that researchers well versed into integration techniques can bring additional contributions to this appealing shape representation.