Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Adaptive implicit modeling using subdivision curves and surfaces as skeletons
Proceedings of the seventh ACM symposium on Solid modeling and applications
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Warping as a Modelling Tool for CSG/Implicit Models
SMA '97 Proceedings of the 1997 International Conference on Shape Modeling and Applications (SMA '97)
Super-helices for predicting the dynamics of natural hair
ACM SIGGRAPH 2006 Papers
Convolution surfaces based on polygonal curve skeletons
Journal of Symbolic Computation
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Implicit modeling with skeleton-based primitives has been limited up to now to planar skeleton elements, since no closed-form solution was found for convolution along more complex curves. We show that warping techniques can be adapted to efficiently generate convolution-like implicit primitives of varying radius along helices, a useful 3D skeleton found in a number of natural shapes. Depending on a single parameter of the helix, we warp it onto an arc of circle or onto a line segment. For those latter skeletons closed-form convolutions are known for entire families of kernels. The new warps introduced preserve the circular shape of the normal cross section to the primitive.