Fast Approximate Geodesic Paths on Triangle Mesh

We present a new algorithm to compute a geodesic path over a triangle mesh. Based on Novotni＇s propagating wavefront method which is similar to the well known Dijkstra algorithm, we made some improvements which Novotni had missed and we also gave the method to find out the geodesic path which Novotni had not. It can handle both convex and non-convex surfaces or even with boundaries. Experiment results show that our method works very well both in efficiency and precision.

Discrete Differential Geometry of Triangles and Escher-Style Trick Art

This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles) on a triangular mesh consisting of congruent isosceles triangles. As an example, we perform global analysis of an Escher-style trick art, i.e., a simpler version of “Ascending and Descending”. After defining the local structure on the trick art, we analyze its global structure and attribute its paradox to a singular point (i.e., a singular triangle) at the center. Then, the endless “Penrose stairs” is described as a closed trajectory around the isolated singular point. The approach fits well with graphical projection and gives a simple and intuitive example of the interaction between global and local structures. We could deal with higher dimensional objects as well by considering n-simplices (n > 2) instead of triangles.

An Evaluation Method for Distortion Energy Parameterization of Triangular Meshes

Parameterization of triangle meshes is a fundamental problem for texture mapping, surface fitting, surface reconstruction, and mesh editing. The deformation of triangular meshes caused by the parameterized process is the measurement of parameterization Traditional standard method has its limitation when evaluating mixture distortion energy parameterizations. Thus an evaluation method bases on distortion energy parameterization of triangular meshes is introduced for the limitation. The novel method employs an adaptive expression form to the mixture energy, and uses a weight factor to represent distortion energy distribution. By using this method, we can evaluate all kinds ofparameterization in a uniform measurement and acquire a more intuitive and clear evaluation.

Generation of triangle mesh surface from the disparity map for telerobotic welding

3D reconstruction of environment and weld workpiece can provide geometrical model for telerobotic welding and improve its intelligence. A novel framework of spacetime stereo is employed to overcome the lack of texture of the weld workpiece and obtain subpixel disparity map of the scene. Anisotropic diffusion is adopted to smooth the original subpixel disparity map in order to reduce the noise while preserving the depth discontinuity. A simple algorithm of generation triangle mesh surface from the disparity map of the spucetime stereo is presented. The experimental results of real weld scenes are shown.

A New Mesh Simplification Algorithm Based on Triangle Collapses

In this paper a new mesh simplification algorithm based on triangle collapses is presented. The algorithm can provide efficient error management and simplify the original mesh greatly. Progressive meshes may be constructed with triangle collapsing operation. To make continuous transition between level of detail (LOD) models possible, a method for interpolating is also presented. Examples illustrate the efficiency of the algorithm.

Spherical Parameterization of Marching Cubes IsoSurfaces Based upon Nearest Neighbor Coordinates

We present some new methods for parameterizing the triangle mesh surface （TMS） which result from the Marching Cubes （MC） algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equations which are solved iteratively. Examples and comparisons are presented.