Representação de formas por distância euclidiana truncada

Orientador: Jorge StolfDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta dissertação estudamos o uso da transformada de distância euclidiana com sinal truncada para representar a forma de objetos n-dimensionais, com ênfase em três dimen- sões, e para aplicações de projeto e manufatura assistidas por computador (CAD/CAM). A representação consiste de uma imagem digital onde cada pixel contém a distância de seu centro à fronteira do objeto, quantizada e truncada. Nós elaboramos ferramentas para geração dessa representação com garantias informativas sobre o interior e o exterior do objeto a ser representado, e também estudamos algoritmos para conversão de e para outras representações de formas, como imagens binárias e ternárias, polígonos e malhas de triângulos, e modelos procedurais. Por fim, investigamos os erros empíricos da extração da representação de borda através da representação de distância truncada e o impacto de seus parâmetros nessa tarefaAbstract: In this dissertation, we study the usage of the clipped signed distance transform to rep- resent shapes of n-dimensional objects, with emphasis in three dimensions and for ap- plications in computer-aided design and manufacting (CAD/CAM). The representation consists in a digital image where every pixel holds the value of its center to the boundary of the object, truncated and quantized. We elaborate tools for generating the representation with informative properties about the interior and exterior of the object being represented and examine algorithms for conversions from and to other common shape representations, like binary and ternary images, polygons, triangle meshes, and procedural models. Fi- nally, we investigate the empirical errors of the boundary representation extraction of the clipped distance representation and the impact of its parameters for this purposeMestradoCiência da ComputaçãoMestre em Ciência da Computação131045/2018-0CAPESCNP

A Morphological Approach to the Voxelization of Solids

In this paper we present a new, morphological criterion for determining whether a geometric solid is suitable for voxelization at a given resolution. The criterion embodies two conditions, namely that the curvature of the solid must be bounded and the critical points of the distance field must be at a certain distance from the boundary of the solid. For solids that fulfill this criterion, we present an analytic and an empirical bound for the trilinear reconstruction error. Additionally, we give a theoretical argument as to why the distance field approach to voxelization is more sound than the prefiltering technique. The essence of the argument is that while sampling and interpolation must always introduce some error, the latter method (but not the former) introduces an error in the surface position independently of the sampling

A Morphological Approach To The Voxelization Of Solids

In this paper we present a new, morphological criterion for determining whether a geometric solid is suitable for voxelization at a given resolution. The criterion embodies two conditions, namely that the curvature of the solid must be bounded and the critical points of the distance field must be at a certain distance from the boundary of the solid. For solids that fulfill this criterion, we present an analytic and an empirical bound for the trilinear reconstruction error. Additionally, we give a theoretical argument as to why the distance field approach to voxelization is more sound than the prefiltering technique. The essence of the argument is that while sampling and interpolation must always introduce some error, the latter method (but not the former) introduces an error in the surface position independently of the sampling. Keywords: Voxelization, Morphology, Geometric modeling, Curvature, Hesse normalform 1 INTRODUCTION Volume graphics is the broad term used to describe..