Geometric and Arithmetic Culling Methods for Entire Ray Packets
نویسندگان
چکیده
Recent interactive ray tracing performance has been mainly derived from the use of ray packets. Larger ray packets allow for significant amortization of both computations and memory accesses; however, the majority of primitives are still intersected by each ray in a packet. This paper discusses several methods to cull entire ray packets against common primitives (box, triangle, and sphere) that allows an arbitrary number of rays to be tested by a single test. This provides cheap “all miss” or “all hit” tests and may substantially improve the performance of an interactive ray tracer. The paper surveys current methods, provides details on three particular approaches using interval arithmetic, bounding planes, and corner rays, describes how the respective bounding primitives can be easily and efficiently constructed, and points out the relation among the different fundamental concepts.
منابع مشابه
A Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes
The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...
متن کاملSome remarks on the arithmetic-geometric index
Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.
متن کاملThe second geometric-arithmetic index for trees and unicyclic graphs
Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...
متن کاملOn Third Geometric-Arithmetic Index of Graphs
Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.
متن کاملOn Second Geometric-Arithmetic Index of Graphs
The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.
متن کامل