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More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Four sided polygons (generally referred to as quads) [1] [2] and triangles are the most common shapes used in polygonal modeling.
The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons . A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes. The study of polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling
Secondly, each of these triangles can be transformed into a right triangle and subsequently into a rectangle with one side of length 1. Alternatively, a triangle can be transformed into one such rectangle by first turning it into a parallelogram and then turning this into such a rectangle. By doing this for each triangle, the polygon can be ...
In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
In two dimensions, flipping and smoothing are powerful tools for adapting a poor mesh into a good mesh. Flipping involves combining two triangles to form a quadrilateral, then splitting the quadrilateral in the other direction to produce two new triangles. Flipping is used to improve quality measures of a triangle such as skewness.
Doo-Sabin (1978), Quads – The second subdivision scheme was developed by Doo and Sabin, who successfully extended Chaikin's corner-cutting method (George Chaikin, 1974 [5]) for curves to surfaces. They used the analytical expression of bi-quadratic uniform B-spline surface to generate their subdivision procedure to produce C 1 limit surfaces ...
In computer graphics, tessellation is the dividing of datasets of polygons (sometimes called vertex sets) presenting objects in a scene into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL 4.0 and Direct3D 11. [1] [2]
This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see affine texture mapping above ...