A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Meshing Skin Surfaces with Certified Topology
CAD-CG '05 Proceedings of the Ninth International Conference on Computer Aided Design and Computer Graphics
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Approximating polygonal objects by deformable smooth surfaces
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
3D ball skinning using PDEs for generation of smooth tubular surfaces
Computer-Aided Design
Variational skinning of an ordered set of discrete 2D balls
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Skinning of circles and spheres
Computer Aided Geometric Design
Enclosing surfaces for point clusters using 3d discrete voronoi diagrams
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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We construct a class of envelope surfaces in Rd, more precisely envelopes of balls. An envelope surface is a closed C1 (tangent continuous) manifold wrapping tightly around the union of a set of balls. Such a manifold is useful in modeling since the union of a finite set of balls can approximate any closed smooth manifold arbitrarily close.The theory of envelope surfaces generalizes the theoretical framework of skin surfaces [5] developed by Edelsbrunner for molecular modeling. However, envelope surfaces are more flexible: where a skin surface is controlled by a single parameter, envelope surfaces can be adapted locally.We show that a special subset of envelope surfaces is piecewise quadratic and derive conditions under which the envelope surface is C1. These conditions can be verified automatically. We give examples of envelope surfaces to demonstrate their flexibility in surface design.