These iterators are all built on the same scheme. Operator are retrieved by the mean of iterators, one iterator per object type: generated object Represents a 3D twisted area, and fails to be expressed in terms ofĪs many tessellation objects can be generated, the results of a tessellation In case of some perturbed surface, the tessellation can lead In some rare cases, polygons can be returned if theĪlgorithm failed to tessellate them. But it happens that it returns them as isolated triangles, although itĬould find strips or fans. The algorithm tries, as far as possible, to return the triangles as strips orįans. The list with any two consecutive points define a triangle.Ī strip of triangles is a list of points, such that any three 3: The Various Result FormatsĪn isolated triangle is defined by its three points (V1,V2,V3).Ī fan of triangles is a list of triangles, such that the first point of In peculiar, if you tessellate a cube, no isolated triangles are In other words, the tessellation process outputs as few trianglesĪs possible. Last two being provided for minimizing the memory size. The results for surfaces, topological faces and bodiesĪre given as isolated triangles, strips of triangles, fans of triangles, the The results for curves and topological edges are given by the means of anĪrray of computed points. Optionally, add new curves, surfaces, cells to tessellate.They are built on the same scheme, which is the general scheme of a CGM CATCellTessellator to tessellate one or several topological edges.
The curves and topological edges are discretized
The surfaces, faces, and the skin of the topological bodiesĪre paved with triangles. 1: The Tessellation of a Quarter of Hemisphere Work with discretized data, such as visualization, mesh, or numerical controlĪpplications. The results of their tessellation can then be used by applications which need to Surfaces, or topological bodies, edges, or faces. The tessellation computes a geometric discretization from geometric curves ,
Process, then explains how to use a tessellation operator to tessellate an TheĪrticle first recalls the parameters that are used to tune the tessellation This use case is intended to help you use the tessellation classes. This article discusses the CAATesBody use case. Using (a) and (b), find all possible pairs $(m,n)$įor a regular tessellation of the plane.Tessellation A way to discretize the geometry Show that for any such tesselation, we must have $m \geq 3$ and, using part (a), that $n \leq 6$. In this problem you will discover some very strong restrictions on possible tesselations of the plane, stemming from the fact that that each interior angle of an $n$ sided regular polygon measures $\frac\right) = 360. Of a regular tessellation which can be continued indefinitely in all directions:
The checkerboard pattern below is an example If any two polygons in the tessellation either do not meet, share a vertex only, If all polygons in the tessellation are congruent regular polygons and For example, part of a tessellation with rectangles is A tessellation of the plane is an arrangement of polygons which cover the plane without gaps or overlapping.