Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
SIAM Journal on Scientific Computing
Guaranteed precision for transcendental and algebraic computation made easy
Guaranteed precision for transcendental and algebraic computation made easy
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
| Hi-index | 0.01 |
Expression-dag-based number-types are a very general and user-friendly way to achieve exact geometric computation, a widely accepted approach to the reliable implementation of geometric algorithms. Such number-types record the computation history of a numerical value in an expression dag in order to allow for recomputing the value or an approximation of it at a later stage. We describe how to defer dag construction by using error-free transformations into sums of floating-point numbers. We store a limited number of summands in statically allocated memory in order to postpone or avoid dag creation which involves expensive dynamic memory allocations. Furthermore we report on experiments where we compare different implementation strategies of our new approach. The experiments show that for small polynomial expressions typically arising in geometric applications our approach is superior to existing expression-dag-based number-types in the presence of degenerate and nearly degenerate configurations and competitive otherwise.