Surface Approximation to Scattered Lines
نویسنده
چکیده
A global weighted-mean approximation to scattered lines is introduced. Rational Gaussian weights are stretched along lines and standard deviations of Gaussians are selected in such a way as to produce surfaces that closely follow data along lines. When the lengths of the lines approach zero, the proposed formulation converges to that of global weighted mean approximation to scattered points. Therefore, the traditional weighted mean approximation becomes a special case of the proposed approximation. Implementation strategies are presented and examples of surface approximation using range data and polygon meshes are given.
منابع مشابه
Surface Approximation to Scattered Lines
A method for fitting a surface to line data is introduced. A weighted-mean approach to the problem is described using rational Gaussian (RaG) weights. The Gaussians are stretched along the lines and their widths are selected to reproduce sharp edges and corners in the surface. When the length of the lines becomes zero, the formulation converges to a weighted sum of points. Therefore, traditiona...
متن کاملApproximation in Line Space { Applications
Combining classical line geometry with techniques from numerical approximation, we develop algorithms for approximation in line space. In particular, linear complexes, linear congruences and reguli are tted to given sets of lines or line segments. The results are applied to computation-ally robust detection of special robot conngurations and to reconstruction of fundamental surface shapes from ...
متن کاملEfficient approximation algorithms. Part I: approximation of unknown fault lines from scattered data
A method for the detection of fault lines of a surface only known at scattered data is presented. In particular, we use a technique for the detection of fault points, picking out and collecting in a set all the data points close to fault lines. To select these points we use a cardinal radial basis interpolation formula. Then, applying a powerful refinement technique, we discuss different method...
متن کاملScattered data approximation of fully fuzzy data by quasi-interpolation
Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$. In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...
متن کاملSubdivision Surfaces for Scattered-data Approximation
Abstract. We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. Starting with a triangulated set of scattered data with associated function values, our scheme applies linear, stationary subdivision rules resulting in a hierarchy of triangulations that converge rapidly to a smooth limit surface. The novelty of our scheme is that it applies su...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007