Discrete m-reps use tolerance-based, sampled medial skeleta as an underlying framework for boundaries defined by displaced subdivision surfaces. They provide local and global shape information, combining the strengths of multiscale skeletal modeling with the multi-resolution, deformation and shading properties afforded by subdivision surfaces. Hierarchically linked medial figures allow figural,...

The hemisphere subdivision technique is an importancedriven technique using a triangular adaptive subdivision of a hemisphere in order to guide the rays shot from a patch [17]. The purpose of this technique is to take advantage of the knowledge of an environment in order to optimise the space distribution of rays shot in radiosity algorithms. In this paper, we present a new approach of the hemi...

Hierarchical subdivision techniques remove the need for a-priori meshing of surfaces when approximating global illumination. In addition they allow progressive reenement of the solution. However, when subdivision is based upon Monte Carlo methods, due to the stochastic nature of such techniques, subdivision decisions cannot be made unless a suuciently large number of samples have been considere...

This paper presents approaches of incorporating subdivision techniques in the rendering process for computer-generated line drawings. A new method for accelerating silhouette detection is introduced. This “silhouette propagation” method gains its strength from being intertwined with the 3D subdivision process. Another technique reduces the number of 3D subdivision steps necessary for high-quali...

Hierarchical subdivision techniques remove the need for a-priori meshing of surfaces when approximating global illumination. In addition they allow progressive re nement of the solution. However, when subdivision is based upon Monte Carlo methods, due to the stochastic nature of such techniques, subdivision decisions cannot be made unless a su ciently large number of samples have been considere...

Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partition of the vertices of G\K5 into equivalence classes. As a result, we can reduce a projective planarity or toroidality algorithm to a small constant number of simple planarity checks [6] or to a K3,3-subdivision in the...

We investigate whether the eternal chaotic inflation can be achieved when the weak gravity conjecture is taken into account. We show that even the assisted chaotic inflation with potential λφ or mφ can not be eternal. The effective field theory description for the inflaton field breaks down before inflation reaches the eternal regime. We also find that the total number of e-folds is still bound...

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

In this paper we study the ability of convergent subdivision schemes to reproduce polynomials in the sense that for initial data, which is sampled from some polynomial function, the scheme yields the same polynomial in the limit. This property is desirable because the reproduction of polynomials up to some degree d implies that a scheme has approximation order d +1. We first show that any conve...