Generating fair meshes with G/sup 1/ boundary conditions

Abstract

In this paper we present a new algorithm to create fair discrete surfaces satisfying prescribed ½ boundary constraints. All surfaces are built by discretizing a partial differential equation based on pure geometric intrinsics. The construction scheme is designed to produce meshes that are partitioned into regular domains. Using this knowledge in advance we can develop a fast iterative algorithm resulting in surfaces of high aesthetic quality that have no local mean curvature extrema in the interior.

A level set formulation for Willmore flow

“…A further potential application of Willmore flow is in image processing and related to image inpainting or restoration of implicit surfaces. Methods based on similar ideas can be found in the works of Kobbelt and Schneider [29,30] and Yoshizawa and Belyaev [35]. In the restoration of flat 2D images-known as the inpainting problem-variational methods have proved to be successful tools.…”

Interactive mesh deformation using equality-constrained least squares

“…This is because matrix AQ 2 in Eq. (20) becomes less sparse in such a case. In future work, we would like to investigate methods for stably and efficiently solving a large number of hard constraints with two or more variables.…”

“…Nonlinear methods solve Laplacian or Poisson equations using non-linear iterative solvers [17][18][19][20][21]. These methods produce fair surfaces, but they are time-consuming and it is difficult to deform shapes interactively.…”

Higher-order nonlinear priors for surface reconstruction

“…This exact solution is also computationally expensive. A two-step approximate solution to the intrinsic Laplacian of mean curvature flow for meshes is proposed in [31]. However, that approach can only be applied to meshes and relies on analytic properties of the steady-state solutions for that specific surface flow, ÁH ¼ 0, by fitting surface primitives that have such properties.…”

“…They propose several new numerical schemes, but none are satisfactory due to their slow computation and inability to handle singularities. In related works [30], [31], approximations of higher-order geometric surface flows have been applied to surface fairing in computer graphics.…”