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**A marching method for parametric surface/surface intersection.**
*(English)*
Zbl 0716.65013

From the authors’ abstract: A general marching method for surface/surface intersection is described for smooth parametric surfaces defined over rectangular and triangular domains. Surface equations are not required explicitly - only evaluated surface positions and tangents. The algorithm is based on an extension of a marching method presented by the first author, G. Farin, M. Jordan and B. R. Piper [ibid. 4, 3-16 (1987; Zbl 0642.65010)]. The new algorithm permits the intersection of triangular surfaces, and the intersection of surfaces that generate tangent and branch points, and tangent tracks. A method for approximating step length, and methods for relaxing intersection points onto surface boundaries are included. These ideas are discussed and illustrative colour examples are also included.

Reviewer: C.Simerská

### MSC:

65D17 | Computer-aided design (modeling of curves and surfaces) |

### Keywords:

subdivision; bounding boxes; octrees; geometric modelling; marching method; surface/surface intersection; parametric surfaces; intersection of triangular surfaces### Citations:

Zbl 0642.65010
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\textit{R. E. Barnhill} and \textit{S. N. Kersey}, Comput. Aided Geom. Des. 7, No. 1--4, 257--280 (1990; Zbl 0716.65013)

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### References:

[1] | Barnhill, R.E., Geometry processing: curvature analysis and surface/surface intersection, (), 51-60 |

[2] | Barnhill, R.E.; Farin, G.; Jordan, M.; Piper, B.R., Surface⧸surface intersection, Computer aided geometric design, 4, 3-16, (1987) · Zbl 0642.65010 |

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[11] | Prakash, P.V.; Patrikalakis, N.M., Algebraic and rational polynomial surface intersections, MIT report, (1988) |

[12] | Pratt, M.J.; Geisow, A.D., Surface/surface intersection problems, () |

[13] | Sabharwal, C.L.; Factor, J.D., Cross intersections between any two C0 parametric surfaces, Ausgraph, (1988) |

[14] | Samet, H., Neighbor finding techniques for images represented by quadtrees, Computer graphics and image processing, 18, 37-57, (1982) · Zbl 0531.68041 |

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[16] | Von Herzon, B.; Barr, A.H., Accurate triangulations of deformed, intersecting surfaces, ACM computer graphics, 21, (1987), SIGGRAPH Proceedings. |

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