We present an adaptive tessellation scheme for surfaces consisting of parametric patches. The resulting tessellations are topologically uniform, yet consistent and watertight across boundaries of patches with different tessellation levels. Our scheme is simple to implement, requires little memory, and is well suited for instancing, a feature available on current GPUs that allows a substantial p...

Optimal transport from the volume measure to a convex combination of Dirac measures yields a tessellation of a Riemannian manifold into pieces of arbitrary relative size. This tessellation is studied for the cost functions cp(z, y) = 1 p d(z, y) and 1 ≤ p < ∞. Geometric descriptions of the tessellations for all p is obtained for compact subsets of the Euclidean space and the sphere. For p = 1 t...

The model of the torus as a parallelogram in the plane with opposite sides identiied enables us to deene two families of parallel lines and to tessellate the torus, then to associate to each tessellation a toroidal map with an upward drawing. It is proved that a toroidal map has a tessellation representation if and only if its universal cover is 2-connected. Those graphs that admit such an embe...

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological repres...

By a regular tessellation, we mean any hyperbolic 3-manifold tessellated by ideal Platonic solids such that the symmetry group acts transitively on oriented flags. A regular tessellation has an invariant we call the cusp modulus. For small cusp modulus, we classify all regular tessellations. For large cusp modulus, we prove that a regular tessellations has to be infinite volume if its fundament...

Interactive rendering of trimmed NURBS models is of great importance for CAD systems. For this the model needs to be transformed into a polygonal representation. This transformation can be either performed in a preprocessing step, at the cost of losing the capability to edit the surfaces, or on the fly during rendering. Since the number of frames per second is usually critical, efficient on the...

This paper describes enumeration of a class of topologically distinct periodic divisions of a stripe. Optimization of the geometry of these periodic tilings--optimization that yields minimum total perimeter of the tiles--gives a set of physically plausible periodic structures of monodisperse, two-dimensional foams bounded by two parallel walls. Evaluation of the minimum total perimeters of the ...