Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Computing exact geometric predicates using modular arithmetic with single precision
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
MAPC: a library for efficient and exact manipulation of algebraic points and curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A strong and easily computable separation bound for arithmetic expressions involving square roots
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Computer Aided Geometric Design
Algebraic methods and arithmetic filtering for exact predicates on circle arcs
Proceedings of the sixteenth annual symposium on Computational geometry
A Fortran Multiple-Precision Arithmetic Package
ACM Transactions on Mathematical Software (TOMS)
A modified Newton method for polynomials
Communications of the ACM
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
PRECISE: Efficient Multiprecision Evaluation of Algebraic Roots and Predicates for Reliable Geometric Computation
ESOLID---A System for Exact Boundary Evaluation
Proceedings of the seventh ACM symposium on Solid modeling and applications
Efficient max-norm distance computation and reliable voxelization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Hi-index | 0.00 |
Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitives like curves and surfaces. The algorithms designed for these problems make decisions based on signs of geometric predicates or on the roots of polynomials characterizing the problem. The reliability of the algorithm depends on the accurate evaluation of these signs and roots. In this paper, we present a {\em naive precision-driven computational model} to perform these computations reliably and demonstrate its effectiveness on a certain class of problems like sign of determinants with rational entries, boundary evaluation and curve arrangements. We also present a novel algorithm to compute all the roots of a univariate polynomial to any desired accuracy. The computational model along with the underlying number representation, precision-driven arithmetic and all the algorithms are implemented as part of a stand-alone software library, PRECISE.