Software Testbed for Selective Laser Sintering

Computer software plays an important role in the implementation of Solid Freeform Fabrication (SFF) technologies. This paper describes a software testbed for processing part geometry for a particular SFF technology, selective laser sintering (SLS), that is built around the separation of the slicing and rasterization operations to accommodate geometric information from a variety of sources. The paper also discusses the process control software being developed for a new high-temperat rkstation for SLS of metal powders. This program features a high-resolution data rmat, the ability to interpolate to achieve a desired resolution, and a menu-driven user interface with graphical feedback and process simulation capabilities.Mechanical Engineerin

Curvature estimation for meshes via algebraic quadric fitting

We introduce the novel method for estimation of mean and Gaussian curvature and several related quantities for polygonal meshes. The algebraic quadric fitting curvature (AQFC) is based on local approximation of the mesh vertices and associated normals by a quadratic surface. The quadric is computed as an implicit surface, so it minimizes algebraic distances and normal deviations from the approximated point-normal neighbourhood of the processed vertex. Its mean and Gaussian curvature estimate is then obtained as the respective curvature of its orthogonal projection onto the fitted quadratic surface. Experimental results for both sampled parametric surfaces and arbitrary meshes are provided. The proposed method AQFC approaches the true curvatures of the reference smooth surfaces with increasing density of sampling, regardless of its regularity. It is resilient to irregular sampling of the mesh, compared to the contemporary curvature estimators. In the case of arbitrary meshes, obtained from scanning, AQFC provides robust curvature estimation.Comment: 14 page

A recursive Taylor method for algebraic curves and surfaces

This paper examines recursive Taylor methods for multivariate polynomial evaluation over an interval, in the context of algebraic curve and surface plotting as a particular application representative of similar problems in CAGD. The modified affine arithmetic method (MAA), previously shown to be one of the best methods for polynomial evaluation over an interval, is used as a benchmark; experimental results show that a second order recursive Taylor method (i) achieves the same or better graphical quality compared to MAA when used for plotting, and (ii) needs fewer arithmetic operations in many cases. Furthermore, this method is simple and very easy to implement. We also consider which order of Taylor method is best to use, and propose that second order Taylor expansion is generally best. Finally, we briefly examine theoretically the relation between the Taylor method and the MAA method

Digital Analytical Geometry: How do I define a digital analytical object?

International audienceThis paper is meant as a short survey on analytically de-ned digital geometric objects. We will start by giving some elements on digitizations and its relations to continuous geometry. We will then explain how, from simple assumptions about properties a digital object should have, one can build mathematical sound digital objects. We will end with open problems and challenges for the future

www.elsevier.com/locate/cagd A local fitting algorithm for converting planar curves to B-splines

In this paper we present a local fitting algorithm for converting smooth planar curves to B-splines. For a smooth planar curve a set of points together with their tangent vectors are first sampled from the curve such that the connected polygon approximates the curve with high accuracy and inflexions are detected by the sampled data efficiently. Then, a G1 continuous Bézier spline curve is obtained by fitting the sampled data with shape preservation as well as within a prescribed accuracy. Finally, the Bézier spline is merged into a C2 continuous B-spline curve by subdivision and control points adjustment. The merging is guaranteed to be within another error bound and with no more inflexions than the Bézier spline. In addition to shape preserving and error control, this conversion algorithm also benefits that the knots are selected automatically and adaptively according to local shape and error bound. A few experimental results are included to demonstrate the validity and efficiency of the algorithm

Modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting

This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than standard affine arithmetic when evaluating trivariate polynomials

Interactive ray tracing of arbitrary implicits with SIMD interval arithmetic

Journal ArticleWe present a practical and efficient algorithm for interactively ray tracing arbitrary implicit surfaces. We use interval arithmetic (IA) both for robust root computation and guaranteed detection of topological features. In conjunction with ray tracing, this allows for rendering literally any programmable implicit function simply from its definition. Our method requires neither special hardware, nor preprocessing or storage of any data structure. Efficiency is achieved through SIMD optimization of both the interval arithmetic computation and coherent ray traversal algorithm, delivering interactive results even for complex implicit functions

Renderização de curvas implícitas discretizadas no domínio da imagem

A representação gráfica de curvas implícitas continua a ser um tópico de investigação importante em computação gráfica e geometria computacional, e tem aplicações em várias áreas de interesse como sejam, por exemplo, representação de símbolos em tipografia digital, delimitação de contornos em imagem médica gerada por tomografia axial, bem como na definição de trajetórias para a simulação de movimento de personagens em animação computacional e jogos de vídeo. De forma sumária, pode dizer-se que esta dissertação propõe um algoritmo de pixelização de curvas implícitas que, ao que parece, não tem paralelo na literatura, a não ser nos algoritmos de rasterização de linhas retas e circunferências que incorporavam os sistemas gráficos primitivos, como por exemplo o algoritmo de Bresenham. De alguma maneira, o referido algoritmo de pixelização pode ser visto como uma generalização daqueles algoritmos primitivos no sentido de que se aplica a qualquer curva implícita, mesmo que ela apresente singularidades, pontos isolados, e outros pontos críticos.The graphical representation of implicit curves remains a major research topic in computer graphics and computational geometry, and has applications in several areas of interest such as, for example, representation of symbols in digital typography, delineation of contours in medical images generated by computerized axial tomography, as well as the definition of trajectories for the simulation of movement of characters in computer animation and video games. Briefly speaking, it can be said that this dissertation proposes a pixelization algorithm for implicit curves that apparently has no parallel in literature, except in the rasterization algorithms of straight lines and circles incorporated in primitive graphics systems, such as Bresenham's algorithm. Somehow, this algorithm pixelization can be seen as a generalization of those primitive algorithms in that it applies to any curve implied, even if it presents singularities, isolated points, and other critical points

An evolutionary approach to the extraction of object construction trees from 3D point clouds

In order to extract a construction tree from a finite set of points sampled on the surface of an object, we present an evolutionary algorithm that evolves set-theoretic expressions made of primitives fitted to the input point-set and modeling operations. To keep relatively simple trees, we use a penalty term in the objective function optimized by the evolutionary algorithm. We show with experiments successes but also limitations of this approach