Texture mapping is a common operation to increase the realism of three-dimensional meshes at low cost. We propose a new texture optimization algorithm based on the reduction of the physical space allotted to the texture image. Our algorithm optimizes the use of texture space by computing a warping function for the image and new texture coordinates. Neither the mesh geometry nor its connectivity are modified by the optimization. Our method uniformly distributes frequency content of the image in the spatial domain. In other words, the image is stretched in high frequency areas, whereas low frequency regions are shrunk. We also take into account distortions introduced by the mapping onto the model geometry in this process. The resulting image can be resampled at lower rate while preserving its original details. The unwarping is performed by the texture mapping function. Hence, the spaceoptimized texture is stored as-is in texture memory and is fully supported by current graphics hardware. We present several examples showing that our method significantly decreases texture memory usage without noticeable loss in visual quality.

We study the algorithmic complexity of the discrete fixed point problem and develop an asymptotic matching bound for a cube in any constantly bounded finite dimension. To obtain our upper bound, we derive a new fixed point theorem, based on a novel characterization of boundary conditions for the existence of fixed points. In addition, exploring a linkage with the approximation problem of the continuous fixed point problem, we obtain asymptotic matching bounds for complexity of the approximate Brouwer fixed point problem in the continuous case for Lipschitz functions that close a previous exponential gap. It settles a fifteen years old open problem of Hirsch, Papadimitriou and Vavasis by improving both the upper and lower bounds. Our new characterization for existence of a fixed point is also applicable to functions defined on non-convex domain and makes it a potentially useful tool for design and analysis of algorithms for fixed points in general domain.

this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functions f :

A new metric domain of processes is presented. This domain is located in between two metric process domains introduced by De Bakker and Zucker. The new process domain characterizes the collection of image finite processes. This domain has as advantages over the other process domains that no complications arise in the definitions of operators like sequential composition and parallel composition, and that image finite language constructions like random assignment can be modelled in an elementary way. As in the other domains, bisimilarity and equality coincide in this domain. The three domains are obtained as unique (up to isometry) solutions of equations in a category of 1-bounded complete metric spaces. In the case the action set is finite, the three domains are shown to be equal (up to isometry). For infinite action sets, e.g., equipollent to the set of natural or real numbers, the process domains are proved not to be isometric. AMS Subject Classification (1991): 68Q55 CR Subject Classification (1991): D.3.1, F.3.2 Keywords & Phrases: process, complete metric space, bisimulation, finitely branching, image finite, sequential composition Note: This work was partially supported by the Netherlands Nationale Faciliteit Informatica programme, project Research and Education in Concurrent Systems (REX). This paper will appear in Proceedings of the Ninth Conference on the Mathematical Foundations of Programming Semantics, New Orleans, LA, USA, April 7-10, 1993.

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Various results appear in the literature for deriving existence and uniqueness of fixed points for endofunctors on categories of complete metric spaces. All these results are proved for contracting functors which satisfy some further requirements, depending on the category in question. Following a new kind of approach, based on the notion of η-isometry, we show that the sole hypothesis of contractivity is enough for proving existence and uniqueness of fixed points for endofunctors on the category of compact metric spaces and embedding-projection pairs. 1

Abstract. We investigate the computable content of the Uniform Boundedness Theorem and of the closely related Banach-Steinhaus Theorem. The Uniform Boundedness Theorem states that a pointwise bounded sequence of bounded linear operators on Banach spaces is also uniformly bounded. But, given the sequence, can we also effectively find the uniform bound? It turns out that the answer depends on how the sequence is “given”. If it is just given with respect to the compact open topology (i.e. if just a sequence of “programs ” is given), then we cannot even compute an upper bound of the uniform bound in general. If, however, the pointwise bounds are available as additional input information, then we can effectively compute an upper bound of the uniform bound. Additionally, we prove an effective version of the contraposition of the Uniform Boundedness Theorem: given a sequence of linear bounded operators which is not uniformly bounded, we can effectively find a witness for the fact that the sequence is not pointwise bounded. As an easy application of this theorem we obtain a computable function whose Fourier series does not converge. §1. Introduction. In this paper we want to study the computational content of some theorems of functional analysis. The Uniform Boundedness Theorem is one of the central theorems of functional analysis and it has first been published in Banach’s thesis [1].

This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation.

Labelled transition systems are useful for giving semantics to programming languages. Kok and Rutten have developed some theory to prove semantic models defined by means of labelled transition systems to be equal to other semantic models. Metric labelled transition systems are labelled transition systems with the configurations and actions endowed with metrics. The additional metric structure allows us to generalize the theory developed by Kok and Rutten. Introduction The classical result due to Banach [Ban22] that a contractive function from a nonempty complete metric space to itself has a unique fixed point plays an important role in the theory of metric semantics for programming languages. Metric spaces and Banach's theorem were first employed by Nivat [Niv79] to give semantics to recursive program schemes. Inspired by the work of Nivat, De Bakker and Zucker [BZ82] gave semantics to concurrent languages by means of metric spaces. The metric spaces they used were defined as solutio...