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.

This paper presents and compares two methods for checking if a box is included inside the solution set of an equality constraint with existential quantification of its parameters. We focus on distance constraints, where each existentially quantified parameter has only one occurrence, because of their usefulness and their simplicity. The first method relies on a specific quantifier elimination based on geometric considerations whereas the second method relies on computations with generalized intervals— interval whose bounds are not constrained to be ordered. We show that on two dimension problems, the two methods yield equivalent results. However, when dealing with higher dimensions, generalized intervals are more efficient.

In accordance with the ideas of Interval Analysis, a notion of interval-valued semimetric space is proposed. Also, the possibility of applying the resulting theory to some chapters of Computer Science is examined.

Many computational systems need to deal with various forms of imprecision and uncertainty in their data; it is also the case that many systems, especially mobile and distributed systems, must be able to trade off the precision of their data and operations against the cost of performing those operations. Unfortunately, for many applications, trying to make these tradeoffs severely complicates the program, because there does not yet exist a programming model that gives the programmer the ability to easily describe the relevant tradeoffs between precision and cost of operations or to express in an algorithm what tradeoffs are appropriate under what circumstances. This paper lays a solid foundation for exploring

This paper introduces a new framework for solving quantified constraint satisfaction problems (QCSP) defined by universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and technology. We introduce a generic branch and prune algorithm to tackle these continuous CSPs with parametric constraints, where the pruning and the solution identification processes are dedicated to universally quantified inequalities. Special rules are proposed to handle the parameter domains of the constraints. The originality of our framework lies in the fact that it solves the QCSP as a non-quantified CSP where the quantifiers are handled locally, at the level of each constraint. Experiments show that our algorithm outperforms the state of the art methods based on constraint techniques.

Fusion of imprecise, uncertain and conflicting beliefs with DSm rules of combination