We define a new graph invariant called the scramble number. show that number of is lower bound for gonality and an upper treewidth. Unlike treewidth, not minor monotone, but it subgraph monotone under subdivision. compute several families graphs which these invariants are strictly greater than

In this paper we present a new framework, based on subdivision surface approximation, for efficient compression and coding of 3D models represented by polygonal meshes. Our algorithm fits the input 3D model with a piecewise smooth subdivision surface represented by a coarse control polyhedron, near optimal in terms of control points number and connectivity. Our algorithm, which remains independ...

The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate ...

Although regular subdivision has been shown to be efficient at ray tracing scenes where objects are evenly distributed, such algorithms perform poorly when objects are concentrated in a small number of voxels. In this paper, a method is presented where voxels in a regular grid are examined and recursively subdivided depending on object density. This integration of regular and adaptive spatial s...

Efficient electromagnetic analysis of the composite metallic and dielectric structures in the frequency domain based on the Method of Moments applied to the Surface Integral Equations is provided, if building blocks have the form of bilinear surfaces (in particular, flat quads), and if analysis is supported by the higher order basis functions. Heterogenous surfaces of many 3D structures can be ...

We present a new I/O-efficient index structure for storing planar subdivisions. This so-called guard-quadtree is a compressed linear quadtree, which is provably efficient for map overlay, point location, and range queries in low-density subdivisions. In particular, we can preprocess a lowdensity subdivision with n edges, in O(sort(n)) I/Os, to build a guard-quadtree that allows us to: (i) compu...