# A robust algorithm for geometric predicate by error-free determinant transformation

@article{Ozaki2012ARA, title={A robust algorithm for geometric predicate by error-free determinant transformation}, author={Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi Oishi}, journal={Inf. Comput.}, year={2012}, volume={216}, pages={3-13} }

## 5 Citations

Computing the exact sign of sums of products with floating point arithmetic

- Computer Science, MathematicsArXiv
- 2021

The algorithm is efficient and uses only of floating point arithmetic, which is much faster than exact arithmetic, and it is proved that the algorithm is correct and the efficient and tested C++ code for it is correct.

Improving the GJK algorithm for faster and more reliable distance queries between convex objects

- Computer ScienceTOGS
- 2017

A new version of the Gilbert-Johnson-Keerthi (GJK) algorithm is presented that circumvents the shortcomings introduced by degenerate geometries and is guided toward a shorter search path in less computing time by a distance subalgorithm that is faster and accurate to machine precision.

Improving the GJK Algorithm for Faster and More Reliable Distance Queries Between Convex Objects

- Computer ScienceACM Trans. Graph.
- 2017

A new version of the Gilbert-Johnson-Keerthi (GJK) algorithm is presented that circumvents the shortcomings introduced by degenerate geometries and is guided toward a shorter search path in less computing time by a distance subalgorithm that is faster and accurate to machine precision.

Floating-point filters towards floating-point exceptions

- Computer Science
- 2013

This talk simplifies the floating-point filters for the two dimensional orientation problem and ensures correctness of a numerical result when a problem is well-conditioned even if floating- point exceptions like overflow and underflow occur in floating-points evaluation.

Extension of floating-point filters to absolute and relative errors for numerical computation

- EngineeringJournal of Physics: Conference Series
- 2019

This paper extends floating-point filters to guarantee absolute and relative errors in order to verify the accuracy of approximate solutions in the computational geometry field.

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