Showing papers on "Representation (systemics) published in 1978"

Planar Geometric Projections and Viewing Transformations

Abstract: In computer graphics one is often concerned with representing three-dimensional objects on a two-dimensional display surface. The choice of such a representation depends on several factors, including the purpose for which the representation is intended, the visual effects tha t are desired, and the shape of the object. This paper describes how twodimensional views can be obtained using planar geometric projections such as perspective and parallel projections. It discusses how these projections can be generated from a threedimensional representation of an object in a manner suitable for computer graphics systems. In particular, it shows how these projections can be generated using the viewing transformations of the Core Graphics System. The factors tha t affect the choice of projection are also discussed, and some guidelines for making such a choice are given.

Iteration of endomorphisms on the real axis and representation of numbers

Abstract: We study a class of endomorphisms of the set of real numbers x of the form: ~ 2014~ ~/M, ~ E [0, 2]. The function f is continuous, convex with a single maximum but otherwise arbitrary; A is a real parameter. We focus our attention on periodic points : x E [0, 2] is periodic if there exists an integer n such that the nth iterate of x by ~.f coincides with x. Because of their special importance, we restrict ourselves to periods involving the maximum. As shown by Metropolis et ul., for each mapping, one may represent in a non ambiguous way these periods by finite sequences of symbols Rand L [the i th iterate of the maximum is represented by R (right) or L (left) depending on its position relatively to maximum] and these sequences have many universal properties. For example they can be ordered in a way which does not depend on details of the mapping. In this paper, we prove two points : i~ the ordered set of all the symbolic sequences possesses a property of internal similarity : it is possible to find a monotonous application of the whole set into one of its subsets ; ii3 we give a simple criterion for recognizing whether a sequence is allowed or not and to know in which order two given sequences appear. For reasons of universality property, it will be sufficient to derive these results for the simplest case, namely the « linear )) transform, i. e. We are led to define an expansion of real numbers analogous to 03B2-expansion of Renyi. A few other properties of this peculiar case are briefly discussed. (*) Institut von Laue-Langevin, B. P. 156, 38042 Grenoble Cedex de l’lnstitut Poincaré Section A Vol. XXIX, nO 3 1978. 12 306 B. DERRIDA, A. GERVOIS, Y. POMEAU RESUME. 2014 On etudie une classe d’endomorphismes de 1’ensernble des nombres réels x, de la forme La fonction f est continue, convexe avec un seul maximum mais par ailleurs arbitraire ; A est un parametre reel. Nous nous interessons surtout aux points périodiques: x E [0,2] est periodique s’il existe un entier n tel que Ie nième itere de x par 03BBf coïncide avec x. En raison de leur importance particuliere, nous nous limitons aux periodes comprenant Ie maximum. Comme l’ont montre Metropolis et ses collaborateurs, ces periodes peuvent etre representees de maniere non ambigue par des sequences finies de symboles R et L [Ie itere du sommet est represente par R (« right ») ou L (« left ))) suivant sa position relative par rapport au maximum] et ces sequences ont des proprietes universelles. Par exemple, on peut les ordonner d’une maniere qui ne depend pas de 1’application. Dans cet article, on clarifie 2 points : i) 1’ensemble ordonné de toutes ces sequences symboliques presente une propriete d’homothetie interne : on peut trouver une application monotone de tout 1’ensemble dans l’une de ses parties, ii) on donne un critere simple pour decider si une sequence est autorisee et pour savoir dans quel ordre relatif deux sequences apparaissent. En raison de l’universalité, il suffit de montrer ces proprietes pour Ie cas Ie plus simple, 1’application « lineaire » On est amene a definir un developpement des nombres reels semblables au 03B2-développement de Renyi. Quelques proprietes supplementaires liees a ce cas particulier sont egalement discuses.

Graphical Representation of Multivariate Data

Abstract: • One difficulty with multivariate data is their visualization, in particular when p > 3. • At the very least, we can construct pairwise scatter plots of variables. Data from exercise 1.1 (transpose of Figure 1.1) 90

Planning Nets: A Representation for Formalizing Analogies and Semantic Models of Procedural Skills.

Abstract: : At some time in our lives, we have all been forced to learn the procedural skills which supposedly comprise mathematical literacy (e.g., place value addition) through the process of rote memorization, perhaps, enhanced by the use of models (e.g., the abacus). These models were intended to provide an intuitive basis for a given procedure. This formalizes the concept of an analogy between procedures based on a Sacerdoti-like representation called planning nets. A planning net represents the synthesis of a given procedure from a set of constraints that define the properties of the arithmetic operation being implemented and the representation of the objects (numbers) being manipulated. An analogy between procedures is represented as a maximal partial isomorphism between the planing nets of the two procedures. The planning net representation turns out to provide an elegant framework for defining the teleologic semantics of a procedure as well as for investigating how to construct a natural sequence of models (or microworlds) for a student to use in inventing his own procedure. Since both utilize the same framework, we have an extraordinarily powerful way to explain (or teach) the underlying teleology by showing how to relate it to a sequence of intuitively understood models.

A Conflict Resolution Choice Model

Abstract: A choice model incorporating the concept of multi-stage sequential conflict resolution is examined in terms of the model's cognitive representation. The sequential conflict resolution model is compared with other choice models such as the compensatory model and the lexicographic semi-order model, on effectiveness of prediction, with favorable results.

Linguistic Representation of Spatial and Temporal Orientation

Abstract: Proceedings of the 4th Annual Meeting of the Berkeley Linguistics Society (1978), pp. 524-538

Three-dimensional representations for computer graphics and computer vision

Abstract: Representing complex three-dimensional objects in a computer involves more than just evaluating its display capabilities. Other factors are the uses and costs of the representation, what operations...