Proceedings on Mathematics of surfaces II
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
International Journal of Computer Vision
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
Intrinsic scale space for images on surfaces: The Geodesic Curvature Flow
Graphical Models and Image Processing
On harmonic and biharmonic Bézier surfaces
Computer Aided Geometric Design
Surface blending with curvature continuity
CAD-CG '05 Proceedings of the Ninth International Conference on Computer Aided Design and Computer Graphics
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Constrained design of polynomial surfaces from geodesic curves
Computer-Aided Design
Cubic polynomial patches through geodesics
Computer-Aided Design
Two C1-methods to generate Bézier surfaces from the boundary
Computer Aided Geometric Design
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Technical Section: PDE blending surfaces with C2 continuity
Computers and Graphics
Construction and smoothing of triangular Coons patches with geodesic boundary curves
Computer Aided Geometric Design
Construction of rational surface patches bounded by lines of curvature
Computer Aided Geometric Design
Advances in Computational Mathematics
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In order to explore a new approach to construct surfaces bounded by geodesics or lines of curvature, a method of surface modeling based on fourth-order partial differential equations (PDEs) is presented. Compared with the free-form surface modeling based on finding control points, PDE-based surface modeling has the following three advantages. First, the corresponding biharmonic surface can naturally be derived under some degenerative conditions; second, the parameters in the PDE implicate some physical meaning, such as elasticity or rigidity; third, there are only a few parameters that need to be evaluated, and hence the computation is simple. In addition, this paper constructs two adjacent surfaces with C^1 continuity whose common boundary is the same given curve as well as respective geodesic (or line of curvature). Examples show that this method to construct PDE-based surfaces bounded by geodesics or lines of curvature is easy and effective.