Search results for " Computer-Aided design"
showing 10 items of 232 documents
Semi-Regular Triangle Remeshing: A Comprehensive Study
2014
Semi-regular triangle remeshing algorithms convert irregular surface meshes into semi-regular ones. Especially in the field of computer graphics, semi-regularity is an interesting property because it makes meshes highly suitable for multi-resolution analysis. In this paper, we survey the numerous remeshing algorithms that have been developed over the past two decades. We propose different classifications to give new and comprehensible insights into both existing methods and issues. We describe how considerable obstacles have already been overcome, and discuss promising perspectives.
From A Medial Surface To A Mesh
2012
Medial surfaces are well-known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. The link between an object and its medial surface is also intuitively understood by people. We want to exploit such skeletons to use them in applications like shape creation and shape deformation. For this purpose, we need to define medial surfaces as Shape Representation Models (SRMs). One of the very first task of a SRM is to offer a visualization of the shape it describes. However, achieving this with a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh that approximates an object only described by …
On harmonic and biharmonic Bézier surfaces
2004
We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bezier surfaces. The main result we report here is that any biharmonic Bezier surface is fully determined by the boundary control points. We compare the new method, by way of practical examples, with some related methods such as surfaces generation using discretisation masks and functional minimisations.
MESH COMPARISON USING ATTRIBUTE DEVIATION METRIC
2004
We propose a mesh comparison method using a new attribute deviation metric. The considered meshes contain geometrical and appearance attributes (material color, texture, temperature, etc.). The proposed deviation metric computes local differences between the attributes of two meshes. A mesh comparison assessment can be done easily and quickly using this metric. The techniques proposed are applicable in a number of ways, e.g. 3D matching and registration, and the example described in the paper is the simplification of a surface by iteratively reducing its complexity according to an error metric. The results are presented showing the success of the algorithm through comparisons with other me…
A general 4th-order PDE method to generate Bézier surfaces from the boundary
2006
In this paper we present a method for generating Bezier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bezier surfaces whereby we studied the Bezier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bezier solutions of the Euler-Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bezier solutions exist and hence we show that such operators can be utilised to generate Bezier surfaces from the boundary information. As part of this work we present a general method…
Boolean operations with implicit and parametric representation of primitives using R-functions
2005
We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a constructive solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition …
Another defence of enumerated types
1991
I claim that enumerations, while of course not strictly necessary, are an elegant and useful facility in modern programming languages. I try to show that arguments recently given against them are weak at best and bogus a t worst, for general-purpose programming. Some related issues on types in programming languages are touched as well. These make it even more questionable whether Oberon marks progress or regress in language design.
A Viscoelastic Model for the Long-Term Deflection of Segmental Prestressed Box Girders
2017
Most of segmental prestressed concrete box girders exhibit excessive multidecade deflections unforeseeable by past and current design codes. To investigate such a behavior, mainly caused by creep and shrinkage phenomena, an effective finite element (FE) formulation is presented in this article. This formulation is developed by invoking the stationarity of an energetic principle for linear viscoelastic problems and relies on the Bazant creep constitutive law. A case study representative of segmental prestressed concrete box girders susceptible to creep is also analyzed in the article, that is, the Colle Isarco viaduct. Its FE model, based on the aforementioned energetic formulation, was succ…
On the problem of visualizing point distributions in high dimensional spaces
1995
Abstract Exploring dynamical systems with the aid of computer graphics requires that the relevant structures can be seen and be noticed. This poses special problems if the system is multidimensional, and it has to be decided which kind of projection serves the purpose. I propose using the mathematical frame of categories and functors to describe the process of visualization. This allows detecting and analyzing possible sources of misinterpretation in a formal way. The distribution of distances of embedded electroencephalographic data from a fixed reference point is used as an example for discussing some aspects of the visualization process. The multidimensional p-norms are an example of a p…
Building Construction Sets by Tiling Grammar Simplification
2016
This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammars such that we obtain physically manufacturable building blocks of controllable granularity while retaining variability, i.e., the ability to construct many different, related shapes. Simplification is performed by sequences of two types of elementary operations: non-local joint edge collapses in the tile graphs reduce the gra…