Differential techniques for scalable and interactive mesh editing

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

“…However, different from most existing energy-minimization type algorithms that depend on traditional heuristic search methods such as the Newton's method or Genetic Algorithm, our algorithm formulates the minimization as a continuous shape deformation process that starts from some developable mesh surface (e.g., a planar figure) and ends on the final mesh surface that satisfies both the interpolation and developability requirements. Our algorithm is motivated by recent progress in mesh editing that employs the Laplacian operator [3], [4]. In a mesh editing environment that relies on the Laplacian operation, a mesh surface is continuously deformed, while the Laplacian coordinates at all the vertices are being preserved as much as possible (see Fig.…”