Object representation by means of nonminimal division quadtrees and octrees
ACM Transactions on Graphics (TOG)
Geometric modeling
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Introduction to algorithms
Boundary integration over linear polyhedra
Computer-Aided Design
An adaptive subdivision algorithm for crack prevention in the display of parametric surfaces
Proceedings on Graphics interface '90
Graphics gems IV
Large mesh generation from boundary models with parametric face representation
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Hierarchical triangulation for multiresolution surface description
ACM Transactions on Graphics (TOG)
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Computing moments of objects enclosed by piecewise polynomial surfaces
ACM Transactions on Graphics (TOG)
Simplifying surfaces with color and texture using quadric error metrics
Proceedings of the conference on Visualization '98
New quadric metric for simplifiying meshes with appearance attributes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
A unified approach for hierarchical adaptive tesselation of surfaces
ACM Transactions on Graphics (TOG)
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Computational Geometry in C
Piecewise Linear Approximation of Trimmed Surfaces
Geometric Modelling, Dagstuhl, Germany, 1993
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
Shape sensitivity of constructive representations
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Shape sensitivity of constructively represented geometric models
Computer Aided Geometric Design
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Boundary representation (B-rep) is a popular representation scheme for mechanical objects due to its ability to accurately represent piecewise smooth surfaces bounding solids. However, non-trivial topology and geometry of the surface patches hinder point generation, classification, searching, and other algorithms. We propose a new hybrid representation that addresses these shortcomings by imposing on the boundary representation an additional simplicial structure. The simplicial structure applies a triangle-mesh metaphor to the usual boundary representation, allowing access to points on the exact solid boundary or its many approximations. The resulting simplicially enhanced boundary representation (B-rep SE) simplifies and accelerates the usual boundary representation queries. We discuss full implementation of B-rep SE with the Parasolid kernel and demonstrate the advantages of B-rep SE in applications that integrate and visualize arbitrary fields on a solid's boundary.