These equilateral polygons are a regular triangle, quadrilateral, pentagon, hexagon, octagon, and decagon, whose vertices are 60°, 90°, 108°, 120°, 135°, and 144°, respectively.
For the second example, we select the case in which Ω is a regular triangle with the vertices ((0,0)), ((1,0)), and ((1/2,sqrt {3}/2)).
Let T ℓ be a regular triangulation of Ω into triangles which is obtained by adaptive local refinement of an initial triangulation T 0. Then, E ℓ Γ = T ℓ | Γ denotes the induced partition of Γ, i.e. the set of all boundary edges.
It has already been proved in [37] that problem (2) is well-posed on the continuous level, i.e. it admits a unique solution u = (u, ϕ ) ∈ H. Let T ℓ be a regular triangulation of Ω into triangles T j ∈ T ℓ and E ℓ Γ a partition of the coupling boundary Γ into piecewise affine line segments E j ∈ E ℓ Γ. Throughout, the index ℓ ∈ N 0 indicates the current step of the adaptive loop considered below.
Let be a regular quasi-uniform subdivision of where is a triangle or a quadrilateral if and is a -simplex or -rectangle if.
Let τ h be a regular and quasi-uniform triangulation of Ω consisting of triangles of diameter less than h.
The circularity should be 1.654 for a regular triangle and should approach 1 for a perfect circle [13].
The point cloud is represented by a regular triangle mesh, with the per face textures.
Each is a regular polygon, a triangle or square or pentagon or figures with too many sides to count.
