We build a surface between two complex closed spatial spline curves. Our algorithm allows the input curves to have differing degree, parameterization, and shape. The construction of this surface is useful in geometric modeling including applications for filleting, hole filling methods, and generation of parting surfaces for injection mold constructions. Joel Daniels Elaine Cohen University of Utah Algorithm Overview Stage 1: Solving the navigation problem ACKNOWLEDGEMENTS This work was supported in part by NIH All opinions, findings, conclusions or recommendations expressed on this poster are those of the author and do not necessarily reflect the views of the sponsoring agencies. Stage 2: Building a planar mesh (step 1) Stage 3: Solving boundary continuity and parameterization challenges ( steps 2-8) we resolve the brown (overlapping) regions and white (void) regions) Stage 4: Computing height components (steps 9-12) 3.Assign these fields to projected curves’ skeleton (medial axis approximation) 4.Trace vertex trajectories from all control points through the new field without local minima! 5.Add path repulsion to avoid intersections with neighbor trajectories Results 1.Create surfaces between two spatial curves. A.Novel solution to the vertex trajectory problem within curve deformations. 1.Guarantees avoidance of local and global self-intersections. B.Novel solution to surface generation. 1.Approach considers surface generation as a constrained deformation to avoid intersections between two intermediate curve shapes. 2.Broader applications: A.Robot path planning, hole filling procedures, filleting for modeling by example applications, parting surface generation, and other geometric modeling challenges. 1. Standard repulsion fields trap vertex paths at local minima! 2.Define new local vector field functions: a. Attraction (blue) b. Flow (green) We develop an algorithm to generate a smooth surface between two closed spatial spline curves. It is assumed that the two input curves can be projected to a common plane so that the projections do not have any mutual or self intersections, and on projection completely encompasses the other. The algorithm generates a temporal deformation between the two input curves that can be thought of as sweeping a surface. Our approach does not address feature matching, as many planar curve deformation algorithms do; instead, the deformation method generates intermediate curves that behave like wave fronts, evolving from the shape of one boundary curve to that of a medial type curve, and then gradually taking on the characteristics of the second boundary curve. This is done without singularities in the parameterization, and without self- intersections in the projected surface. Abstract Stage 2Stage 3Stage 1 Stage 4 Research Challenges Navigational problems due to local minima in gradient descent algorithms. Quad mesh extraction without self-intersections. Continuous parameterization and degree changes across the boundary of two surfaces. Curve deformations without self-intersections. Curve deformations between curves with dissimilar degree, parameterization, and shape. Generation of a smooth height field surface from a planar parameterized spline surface. Deformations between spatial spline curves. Problem Statement