93,507 research outputs found
Science, Art and Geometrical Imagination
From the geocentric, closed world model of Antiquity to the wraparound
universe models of relativistic cosmology, the parallel history of space
representations in science and art illustrates the fundamental role of
geometric imagination in innovative findings. Through the analysis of works of
various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the
present author, it is shown how the process of creation in science and in the
arts rests on aesthetical principles such as symmetry, regular polyhedra, laws
of harmonic proportion, tessellations, group theory, etc., as well as beauty,
conciseness and emotional approach of the world.Comment: 22 pages, 28 figures, invited talk at the IAU Symposium 260 "The Role
of Astronomy in Society and Culture", UNESCO, 19-23 January 2009, Paris,
Proceedings to be publishe
Schrodinger Evolution for the Universe: Reparametrization
Starting from a generalized Hamilton-Jacobi formalism, we develop a new
framework for constructing observables and their evolution in theories
invariant under global time reparametrizations. Our proposal relaxes the usual
Dirac prescription for the observables of a totally constrained system
(`perennials') and allows one to recover the influential partial and complete
observables approach in a particular limit. Difficulties such as the
non-unitary evolution of the complete observables in terms of certain partial
observables are explained as a breakdown of this limit. Identification of our
observables (`mutables') relies upon a physical distinction between gauge
symmetries that exist at the level of histories and states (`Type 1'), and
those that exist at the level of histories and not states (`Type 2'). This
distinction resolves a tension in the literature concerning the physical
interpretation of the partial observables and allows for a richer class of
observables in the quantum theory. There is the potential for the application
of our proposal to the quantization of gravity when understood in terms of the
Shape Dynamics formalism.Comment: 25 pages (including title page and references), 1 figur
Shape computations without compositions
Parametric CAD supports design explorations through generative methods which compose and transform geometric elements. This paper argues that elementary shape computations do not always correspond to valid compositional shape structures. In many design cases generative rules correspond to compositional structures, but for relatively simple shapes and rules it is not always possible to assign a corresponding compositional structure of parts which account for all operations of the computation. This problem is brought into strong relief when design processes generate multiple compositions according to purpose, such as product structure, assembly, manufacture, etc. Is it possible to specify shape computations which generate just these compositions of parts or are there additional emergent shapes and features? In parallel, combining two compositions would require the associated combined computations to yield a valid composition. Simple examples are presented which throw light on the issues in integrating different product descriptions (i.e. compositions) within parametric CAD
GRASS: Generative Recursive Autoencoders for Shape Structures
We introduce a novel neural network architecture for encoding and synthesis
of 3D shapes, particularly their structures. Our key insight is that 3D shapes
are effectively characterized by their hierarchical organization of parts,
which reflects fundamental intra-shape relationships such as adjacency and
symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a
flat, unlabeled, arbitrary part layout to a compact code. The code effectively
captures hierarchical structures of man-made 3D objects of varying structural
complexities despite being fixed-dimensional: an associated decoder maps a code
back to a full hierarchy. The learned bidirectional mapping is further tuned
using an adversarial setup to yield a generative model of plausible structures,
from which novel structures can be sampled. Finally, our structure synthesis
framework is augmented by a second trained module that produces fine-grained
part geometry, conditioned on global and local structural context, leading to a
full generative pipeline for 3D shapes. We demonstrate that without
supervision, our network learns meaningful structural hierarchies adhering to
perceptual grouping principles, produces compact codes which enable
applications such as shape classification and partial matching, and supports
shape synthesis and interpolation with significant variations in topology and
geometry.Comment: Corresponding author: Kai Xu ([email protected]
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