We present a method for tuning primal stationary subdivision schemes to give the best possible behaviour near extraordinary vertices with respect to curvature variation. Current schemes lead to a limit surface around extraordinary vertices for which the Gaussian curvature diverges, as demonstrated by Karčiauskas et al. [KPR04]. Even when coefficients are chosen such that the subsubdominant eige...

Subdivision surface method is a series of iterative operation adopts a certain subdivision formula for an initial grid, obtains the smooth limits surface finally, and can dispose any arbitrary complex topology grid. At present most of the subdivision algorithm are 1-4 subdivisions and as the number of subdivision increase, the grid grow so toorapid in the number of patch that it is difficult fo...

and Applied Analysis 3 P 1 2i P 1 2i 1 P 1 2i 2 P i 1 P 1 2i 3 P 1 2i 4 P k i 2 P k i a P 1 3i P 1 3i 1 P 1 3i 2 P i 1 P 1 3i 3 P 1 3i 4 P 1 3i 5 P 1 3i 6 P k i 2 P k i b P 1 4i P 1 4i 1 P 1 4i 2 P k i 1 P 1 4i 3 P 1 4i 4 P 1 4i 5 P 1 4i 6 P 1 4i 7 P 1 4i 8 P k i 2 P k i c Figure 1: Solid lines show coarse polygons whereas doted lines are refined polygons. a – c represent binary, ternary, and q...

for any $k in mathbb{n}$, the $k$-subdivision of graph $g$ is a simple graph $g^{frac{1}{k}}$, which is constructed by replacing each edge of $g$ with a path of length $k$. in [moharram n. iradmusa, on colorings of graph fractional powers, discrete math., (310) 2010, no. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $g$ has been introduced as a fractional power of $g$, denoted by ...

Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...

We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametriza...