Surface Creation and Curve Deformations Between Two Complex Closed Spatial Spline Curves

Abstract

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.

Algorithms and tools for deriving editable models from cross-sectional data sets

“…Surface smoothing and remeshing are conducted to optimize the initial surface triangulations. [38] presented an algorithm for generating a smooth surface between two closed spatial spline curves that generates a temporal deformation between the input curves, which can be thought of as sweeping a surface. Their method 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.…”