Implicit Surface Fitting Using Directional Constraints

A commonly used technique for fitting curves and surfaces to measured data is that known as orthogonal distance regression, where the sum of squares of orthogonal distances from the data points to the surface is minimized. An alternative has recently been proposed for curves and surfaces which are parametrically defined, which minimizes the sum of squares in given directions which depend on the measuring process. In addition to taking account of that process, it is claimed that this technique has the advantage of complying with traditional fixed-regressor assumptions, enabling standard inference theory to apply. Here we consider extending this idea to curves and surfaces where the only assumption made is that there is an implicit formulation. Numerical results are given to illustrate the algorithmic performance.This revised version was published online in October 2005 with corrections to the Cover Date.     

Smooth surface reconstruction via natural neighbour interpolation of distance functions

We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and accommodates non-uniform samples. The reconstructed surface interpolates the data points and is implicitly represented as the zero set of some pseudo-distance function. It can be meshed so as to satisfy a user-defined error bound, which makes the method especially relevant for small point sets. Experimental results are presented for surfaces in .     

Willmore Surfaces in S n

A surface x> : M S ⁿ is called a Willmore surface if it is a critical surface of the Willmore functional. It is well known that any minimal surface is a Willmore surface and that many nonminimal Willmore surfaces exists. In this paper, we establish an integral inequality for compact Willmore surfaces in S ⁿ and obtain a new characterization of the Veronese surface in S ⁴ as a Willmore surface. Our result reduces to a well-known result in the case of minimal surfaces.     

Construction of Surfaces with Parallelism Conditions

In this paper we define the notion of pseudo-parallel parameterized surfaces, extending that of offset surfaces. Then we consider the problem of fitting a set of scattered points with a surface pseudo-parallel to a given reference surface. We propose a method of solution based on a modified version of the classical smoothing D ^m -splines over a bounded domain. The convergence of the method is established and some numerical examples are given.     

The Compressibility of Checkerboard Surfaces of Link Diagrams

Consider the checkerboard surfaces defined by some link diagrams. When they are not orientable, one considers the boundary surfaces of small regular neighborhoods of them. This article studies the compressibility problem of these kinds of surfaces in the link complements. The problem is solved by devising a normalization theory for the compressing discs, which brings up an algorithm to read out compressibility directly from the link diagrams. As an application of the algorithm, the compressibility changes under Reidermeister moves are studied. Diagrams from the knot tables are also studied, and surprisingly, some of them are shown to define completely compressible surfaces of this kind. Infinitely many examples of non-alternating knot diagrams with incompressible surfaces of this kind are also constructed.     

基于层次T网格的分片孔斯曲面重构

本文提出一种基于任意层次T网格的多项式(PHT)样条空间$S(3,3,1,1,T)$的一个新的曲面重构算法.该算法由分片插值于层次T网格上每个小矩形单元对应4个顶点的16个参数的孔斯曲面形式给出.对于一个给定的T网格和相应基点处的几何信息(函数值,两个一阶偏导数和混合导数值),可得到与$S(3,3,1,1,T)$的PHT样条曲面相同的结果,且曲面表达形式更简单,同时,在离散数据点的曲面拟合中,我们给出了自适应的曲面加细算法.数值算例显示,该自适应算法能够有效的拟合离散数据点.     

Uniformly Distributed Circular Porous Pattern Generation on Surface for 3D Printing

We present an algorithm for uniformly distributed circular porous pattern generation on surface for three-dimensional (3D) printing using a phase-field model. The algorithm is based on the narrow band domain method for the nonlocal Cahn–Hilliard (CH) equation on surfaces. Surfaces are embedded in 3D grid and the narrow band domain is defined as the neighborhood of surface. It allows one can perform numerical computation using the standard discrete Laplacian in 3D instead of the discrete surface Laplacian. For complex surfaces, we reconstruct them from point cloud data and represent them as the zero-level set of their discrete signed distance functions. Using the proposed algorithm, we can generate uniformly distributed circular porous patterns on surfaces in 3D and print the resulting 3D models. Furthermore, we provide the test of accuracy and energy stability of the proposed method.     

Non-manifold surface reconstruction from high-dimensional point cloud data

We present an algorithm capable of reconstructing a non-manifold surface embedded as a point cloud in a high-dimensional space. Our algorithm extends a previously developed incremental method and produces a non-optimal triangulation, but will work for non-orientable surfaces, and for surfaces with certain types of self-intersection. The self-intersections must be ordinary double curves and are fitted locally by intersecting planes using a degenerate quadratic surface. We present the algorithm in detail and provide many examples, including a dataset describing molecular conformations of cyclo-octane.     

BOUNDING PYRAMIDS AND BOUNDING CONES FOR TRIANGULAR BEZIER SURFACES

1. IntroductionA 6ounding pyramid/cone of a rational B6zier surface patch is a pyramid/cone whichhas the property that if its vertex is translated to any point on the B6zier patch, thepatch will lie completely outside the pyramid/cone. These kinds of pyramids/conesare useful tools in detecting closed loops in surface/surface intersections[2, 3] and determining directions for which a surface is single valued[5]. While methods of finding bounding pyramids and bounding cones for rectangular B6zi…     

NURBS曲线曲面拟合数据点的迭代算法

本文推广了文献[1]的结果,将文献[1]中关于B样条曲线曲面拟合数据点的迭代算法推广至有理形式,给出了无需求解方程组反求控制点及权因子即可得到拟合NURBS曲线曲面的迭代方法．该算法和文献[1]的算法本质上是统一的,而后者恰是前者的一种退化形式．文章还给出了收敛性证明以及一些定性分析．文末的数值实例说明该算法简单实用．