Introduction to Solid Modeling
Introduction to Solid Modeling
Towards implementing robust geometric computations
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
A solid modelling system free from topological inconsistency
Journal of Information Processing
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
A set operation algorithm for sculptured solids modeled with trimmed patches
Computer Aided Geometric Design
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Precise computation using range arithmetic, via C++
ACM Transactions on Mathematical Software (TOMS)
Real algebraic number computation using interval arithmetic
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Exact arithmetic solid modeling
Exact arithmetic solid modeling
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Boundary representation modelling with local tolerances
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
Computing exact geometric predicates using modular arithmetic with single precision
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Computer Aided Geometric Design
Computer Aided Geometric Design
The synthesis of solids bounded by many faces
Communications of the ACM
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Efficient and accurate boundary evaluation algorithms for boolean combinations of sculptured solids
Efficient and accurate boundary evaluation algorithms for boolean combinations of sculptured solids
Exact boundary evaluation for curved solids
Exact boundary evaluation for curved solids
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
The reliable algorithmic software challenge RASC
Computer Science in Perspective
Blister: GPU-based rendering of Boolean combinations of free-form triangulated shapes
ACM SIGGRAPH 2005 Papers
Feature-Sensitive Subdivision and Isosurface Reconstruction
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Fast and accurate evaluation of regularized Boolean operations on triangulated solids
Computer-Aided Design
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We present a system, ESOLID, that performs exact boundary evaluation of low degree curved solids in reasonable amounts of time. ESOLID performs accurate Boolean operations using exact representations and exact computations throughout. The demands of exact computation require a different set of algorithms and efficiency improvements than those found in a traditional inexact floating point based modeler. We describe the system architecture, representations, and issues in implementing the algorithms. We also describe a number of techniques that increase the efficiency of the system based on lazy evaluation, use of floating point filters, arbitrary floating point arithmetic with error bounds, and lower dimensional formulation of subproblems. ESOLID has been used for boundary evaluation of many complex solids. These include both synthetic datasets and parts of a Bradley Fighting Vehicle designed using the BRL-CAD solid modeling system. It is shown that ESOLID can correctly evaluate the boundary of solids that are very hard to compute using a fixed-precision floating point modeler. In terms of performance, it is about an order of magnitude slower as compared to a floating point boundary evaluation system on most cases.