# A noniterative method for robustly computing the intersections between a line and a curve or surface

@article{Xiao2019ANM, title={A noniterative method for robustly computing the intersections between a line and a curve or surface}, author={Xiao Xiao and Laurent Bus{\'e} and Fehmi Cirak}, journal={International Journal for Numerical Methods in Engineering}, year={2019}, volume={120}, pages={382 - 390} }

The need to compute the intersections between a line and a high‐order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a noniterative method for computing intersections by solving a matrix singular value decomposition and an eigenvalue problem. That is, all intersection points and their parametric coordinates are determined in one‐shot using only standard linear algebra techniques…

## 4 Citations

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### Equiareal Parameterization of Triangular Bézier Surfaces

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The equiareal parameterization is extended to the triangular Bézier surface on the triangular domain for the first time and the iso-parametric curves from the new expression are more uniform than the original one, which is displayed by numerical examples.

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A new algebraic method is contributed for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space by means of fast and robust numerical linear algebra calculations.

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