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Direct Rendering of Boolean Combinations of Self-trimmed Surfaces

J. Rossignac, I. Fudos and A. Vasilakis
Computer Aided Design 45(2): 288-300 (2013), also presented in Symposium on Solid and Physical Modeling 2012, Dijon France

(a) The original magnifold surface (non self-crossing). (b) The result of carrying out a set of deformations on (a). The part of the surface tha should be trimmed off is illustrated in pink. (c) The self-trimmed surface (STS) shown using clipping. (d) The solid bounded by the STS inspected using capping. (e) and (f) illustrate the result of the solid bounded by the STS after being used as primitive in a substraction and an intersection operation with a parallelepiped.


We explore different semantics for the solid defined by a self-crossing surface (immersed sub-manifold). Specifically, we introduce rules for the interior/exterior classification of the connected components of the complement of a self-crossing surface produced through a continuous deformation process of an initial embedded manifold. We propose efficient GPU algorithms for rendering the boundary of the regularized union of the interior components, which is a subset of the initial surface and is called the trimmed boundary or simply the trim. This classification and rendering process is accomplished in realtime through a rasterization process without computing any self-intersection curve, and hence is suited to support animations of self-crossing surfaces. The solid bounded by the trim can be combined with other solids and with half-spaces using Boolean operations and hence may be capped (trimmed by a half-space) or used as a primitive in direct CSG rendering. Being able to render the trim in realtime makes it possible to adapt the tessellation of the trim in realtime by using view-dependent levels-of-details or adaptive subdivision.


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author = {Jarek Rossignac and
Ioannis Fudos and
Andreas Vasilakis},
title = {Direct rendering of Boolean combinations of self-trimmed
journal = {Computer-Aided Design},
volume = {45},
number = {2},
year = {2013},
pages = {288-300},
ee = {http://dx.doi.org/10.1016/j.cad.2012.10.012}


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