Warp-based Helical Implicit Primitives

Implicit modeling with skeleton-based primitives has been limited up to now to planar skeletons 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.