Barnhill, R. E.; Kersey, S. N. A marching method for parametric surface/surface intersection. (English) Zbl 0716.65013 Comput. Aided Geom. Des. 7, No. 1-4, 257-280 (1990). 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 Cited in 1 ReviewCited in 20 Documents 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 PDF BibTeX XML Cite \textit{R. E. Barnhill} and \textit{S. N. Kersey}, Comput. Aided Geom. Des. 7, No. 1--4, 257--280 (1990; Zbl 0716.65013) Full Text: DOI OpenURL 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 [3] Barnhill, R.E., Geometry processing, September 14-16, St. Louis, MO, AIAA/AHS/ASEE aircraft design, systems and operations meeting, (1987) [4] DeMontaudouin, Y.; Tiller, W.; Vold, H., Applications of power series in computational geometry, Computer aided design, 18, (1986) [5] Faux, I.D.; Pratt, M.J., Computational geometry for design and manufacture, (1979), Ellis Horwood Chichester, UK · Zbl 0395.51001 [6] Gregory, J.A. (1989), Private communications, Arizona State University, March-April. [7] Houghton, E.G.; Emnett, R.F.; Factor, J.D.; Sabharwal, C.L., Implementation of a divide-and-conquer method for intersection of parametric surfaces, Computer aided geometric design, 2, 173-183, (1985) · Zbl 0613.65143 [8] Marchant, P., A numerical method for intersections of parametric surfaces, () [9] Mortenson, M.E., Geometric modeling, (1985), Wiley New York [10] Mullenheim, G., Convergence of a surface/surface intersection algorithm, Computer aided geometric design, (1990), to appear. · Zbl 0704.65009 [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 [15] Samet, H., The quadtree and related hierarchical data structures, Computing surveys, 16, 187-260, (1984) [16] Von Herzon, B.; Barr, A.H., Accurate triangulations of deformed, intersecting surfaces, ACM computer graphics, 21, (1987), SIGGRAPH Proceedings. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.