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Publication# Reviving the Roman Odeon of Aphrodisias: Dynamic Animation and Variety Control of Crowds in Virtual Heritage

Daniel Thalmann, Jonathan Maim, Pablo Stanislaw De Heras Ciechomski, Sébastien Schertenleib

2005

Conference paper

2005

Conference paper

Abstract

In this paper we propose a new method for rendering crowds of virtual humans with dynamicallydeformed skeletons with levels of detail using two simple caching schemes for animations and geometry. Weshow how the virtual heritage project ERATO pushed for these innovations as we did not find any off-theshelfproducts for the purpose. We also show how to create a large variety in appearance using graphicsalgorithm techniques that run on graphics cards with a fixed function pipeline support like the one ofOpenGL 1.1

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In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.

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Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.

Projective variety

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .

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