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 Novot...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.展开更多
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...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.展开更多
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)...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.展开更多
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 ...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.展开更多
Geodesic isolines derived from polylines constitute a crucial element within geographic information systems,playing a pivotal role in enhancing the understanding of geographical terrains.Current methods for delineatin...Geodesic isolines derived from polylines constitute a crucial element within geographic information systems,playing a pivotal role in enhancing the understanding of geographical terrains.Current methods for delineating isolines sourced from polylines on discrete meshes often rely on simplistic linear interpolation.However,these methods fall short in accuracy due to the complex,non-linear nature of geodesic distance fields,thereby inadequately capturing intricate topological features present in real isolines.To tackle this challenge,we demonstrate that Apollonius diagrams can effectively encode the geometric attributes of isolines on meshes and extract the isolines using the Apollonius diagrams with geodesic metric.Moreover,exact geodesic computation is computationally intensive and memory-demanding.In response,we introduce a graph-based approach enhanced by Steiner point insertion,offering a practical method for computing geodesic distances.Drawing on these strategies,we introduce an accurate and efficient algorithm for polyline-sourced isoline computation on triangle meshes.Comprehensive evaluations indicate that our approach yields significantly more accurate geodesic isolines compared to the commonly employed linear interpolation.展开更多
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 constr...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.展开更多
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 sp...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.展开更多
基金This work was supported by National Natural Science Foundation of PRC(No.60503058,No.60533080)the Science and Technology Fund of Huawei Technologies Co.,Ltd.
文摘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.
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China(Nos.61373054,61203105,61173078)Natural Science Foundation of Shandong Province,China(Nos.ZR2010FM047,ZR2011FL016)
文摘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.
基金supported in part by the National Natural Science Foundation of China(No.62302124)the Natural Science Foundation of Shandong Province(No.ZR2023QF122)the Youth Teacher Development Foundation of Harbin Institute of Technology(No.IDGA10002143).
文摘Geodesic isolines derived from polylines constitute a crucial element within geographic information systems,playing a pivotal role in enhancing the understanding of geographical terrains.Current methods for delineating isolines sourced from polylines on discrete meshes often rely on simplistic linear interpolation.However,these methods fall short in accuracy due to the complex,non-linear nature of geodesic distance fields,thereby inadequately capturing intricate topological features present in real isolines.To tackle this challenge,we demonstrate that Apollonius diagrams can effectively encode the geometric attributes of isolines on meshes and extract the isolines using the Apollonius diagrams with geodesic metric.Moreover,exact geodesic computation is computationally intensive and memory-demanding.In response,we introduce a graph-based approach enhanced by Steiner point insertion,offering a practical method for computing geodesic distances.Drawing on these strategies,we introduce an accurate and efficient algorithm for polyline-sourced isoline computation on triangle meshes.Comprehensive evaluations indicate that our approach yields significantly more accurate geodesic isolines compared to the commonly employed linear interpolation.
基金This research work is supported by the Fellowship of Hong Kong Polytechnic University and the NationalNatural Science Foundati
文摘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.
基金supported by the US Army Research Office under contract W911NF-05-1-0301the US National Science Foundation.
文摘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.
