Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Algorithms for computer algebra
Algorithms for computer algebra
Fourier analysis and applications: filtering, numerical computation, wavelets
Fourier analysis and applications: filtering, numerical computation, wavelets
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 Modelling with Skeleton Curves: Controlled Blending in Contact Situations
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
Symbolic Integration I: Transcendental Functions (Algorithms and Computation in Mathematics)
Symbolic Integration I: Transcendental Functions (Algorithms and Computation in Mathematics)
Implicit modeling from polygon soup using convolution
The Visual Computer: International Journal of Computer Graphics
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
SMI 2011: Full Paper: Warp-based helical implicit primitives
Computers and Graphics
Convolution surfaces based on polygonal curve skeletons
Journal of Symbolic Computation
Matisse: painting 2D regions for modeling free-form shapes
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
Convolution surfaces based on polygonal curve skeletons
Journal of Symbolic Computation
| Hi-index | 0.01 |
We provide formulae to create 3D smooth shapes fleshing out a skeleton made of line segments and planar polygons. The boundary of the shape is a level set of the convolution function obtained by integration along the skeleton. The convolution function for a complex skeleton is thus the sum of the convolution functions for the basic elements of the skeleton. Providing formulae for the convolution of a polygon is the main contribution of the present paper. We improve on previous results in several ways. First we do not require the prior triangulation of the polygon. Then, we obtain formulae for families of kernels, either with infinite or compact supports. Last, but not least, in the case of compact support kernels, the geometric computations needed are restricted to intersections of spheres with line segments.