Skip to main content
Log in

Parameterization of Faceted Surfaces for Meshing using Angle-Based Flattening

  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract.

We propose a new method to compute planar triangulations of faceted surfaces for surface parameterization. In contrast to previous approaches that define the flattening problem as a mapping of the three-dimensional node locations to the plane, our method defines the flattening problem as a constrained optimization problem in terms of angles (only). After applying a scaling that derives from the ‘curvature’ at a node, we minimize the relative deformation of the angles in the plane with respect to their counterparts in the three-dimensional surface. This approach makes the method more stable and robust than previous approaches, which used node locations in their formulations. The new method can handle any manifold surface for which a connected, valid, two-dimensional parameterization exists, including surfaces with large curvature gradients. It does not require the boundary of the flat two-dimensional domain to be prede-fined or convex. We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sheffer, A., de Sturler, E. Parameterization of Faceted Surfaces for Meshing using Angle-Based Flattening. EWC 17, 326–337 (2001). https://doi.org/10.1007/PL00013391

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/PL00013391

Navigation