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In solid modeling and computer-aided design, the Euler operators modify the graph of connections to add or remove details of a mesh while preserving its topology. They are named by Baumgart [1] after the Euler–Poincaré characteristic. He chose a set of operators sufficient to create useful meshes, some lose information and so are not invertible.
Mesh generation is deceptively difficult: it is easy for humans to see how to create a mesh of a given object, but difficult to program a computer to make good decisions for arbitrary input a priori. There is an infinite variety of geometry found in nature and man-made objects. Many mesh generation researchers were first users of meshes.
MeshLab an open source mesh processing tool that is able to accurately simplify 3D polygonal meshes. Polygon Cruncher a commercial software from Mootools that reduces the number of polygons of objects without changing their appearance. Simplygon a commercial mesh processing package for remeshing general input meshes into real-time renderable ...
Gouraud-shaded triangle mesh using the Phong reflection model. Gouraud shading (/ ɡ uː ˈ r oʊ / goo-ROH), named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes.
A coarse mesh may provide an accurate solution if the solution is a constant, so the precision depends on the particular problem instance. One can selectively refine the mesh in areas where the solution gradients are high, thus increasing fidelity there. Accuracy, including interpolated values within an element, depends on the element type and ...
Edge thinning is a technique used to remove the unwanted spurious points on the edges in an image. This technique is employed after the image has been filtered for noise (using median, Gaussian filter etc.), the edge operator has been applied (like the ones described above, Canny or Sobel) to detect the edges and after the edges have been ...
Polygon Mesh Processing by Mario Botsch et al. is a textbook on the topic of Geometry Processing. [1]Geometry processing is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of complex 3D models.
For the gradient amplitude calculation, the old Canny edge detection algorithm uses the center in a small 2×2 neighborhood window to calculate the finite difference mean value to represent the gradient amplitude. This method is sensitive to noise and can easily detect false edges and lose real edges.