A Torus Patch Approximation Approach for Point Projection on Implicit Surfaces
Point projection on an implicit surface is essential for the geometric modeling and graphics applications of it. This paper presents a method for computing the principle curvatures and principle directions of an implicit surface. Using the principle curvatures and principle directions, we construct a torus patch to approximate the implicit surface locally. The torus patch is second order osculating to the implicit surface. By taking advantage of the approximation torus patch, this paper develops a second order geometric iterative algorithm for point projection on the implicit surface. Experiments illustrate the efficiency and less dependency on initial values of our algorithm.
X. M. Liu et al., "A Torus Patch Approximation Approach for Point Projection on Implicit Surfaces", Advanced Materials Research, Vol. 346, pp. 259-265, 2012