Abstract
This paper presents an algorithm to generate a smooth surface between two closed spatial spline curves. With the assumption that the two input curves can be projected to a single plane so that the projections do not have any mutual or self intersections, and so that one projection completely encloses the other. We describe an algorithm that generates a temporal deformation between the input curves, one which can be thought of as sweeping a surface. Instead of addressing feature matching, as many planar curve deformation algorithms do, the deformation method described generates intermediate curves that behave like wavefronts as they evolve from the shape of one boundary curve to a medial type curve, and then gradually take on the characteristics of the second boundary curve. This is achieved in a manner that assures there will be neither singularities in the parameterization nor self-intersections in the projected surface.
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Daniels, J., Cohen, E. (2006). Surface Creation and Curve Deformations Between Two Complex Closed Spatial Spline Curves. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_16
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DOI: https://doi.org/10.1007/11802914_16
Publisher Name: Springer, Berlin, Heidelberg
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