We describe an algorithm for fitting a Catmull-Clark subdivision surface model to an unstructured, incomplete and noisy data set. We complete the large missing data regions with the a-priori shape information and produce a smooth, compact and structured data description. The result can be used for further data manipulation, compression, or visualisation. Our fitting algorithm uses a quasi-inter...

This paper presents a new method for embedding digital watermarks into Bézier polynomial patches. An object surface is supposed to be represented by multiple piecewise Bézier polynomial patches. A Bézier patch passes through its four-corner control points, which are called data points, and does not pass through the other control points. To embed a watermark, a Bézier patch is divided into two p...

We present a new approach to finding ray–patch intersections with triangular Bernstein–Bézier patches of arbitrary degree. This paper extends and complements on the short presentation 17. Unlike a previous approach which was based on a combination of hierarchical subdivision and a Newton–like iteration scheme 21, this work adapts the concept of Bézier clipping to the triangular domain. The prob...

In this paper, we present wide-ranging families of subdivision schemes for fitting data to subdivision models. These schemes are constructed by fitting multivariate polynomial functions of any degree to different types of data by least squares techniques. Moreover, we also present the closed analytic expressions of the families of schemes for fitting data in 2 and 3 dimensional spaces. The sche...

A technique has been designed for capturing outlines by exploiting the properties of cubic Bezier curves. The planar images are used to extract the outline. The outline is divided into curve segments at high curvature points and each segment is processed independently for piecewise curve approximation. The proposed algorithm avoids the traditional method of least square fitting which is time co...

During the last 20 years, the joint expansion of computing power, computer graphics, networking capabilities and multiresolution analysis have stimulated several research domains, and developed the need for new types of data such as 3D models, i.e. discrete surfaces. In the intersection between multiresolution analysis and computer graphics, subdivision methods, i.e. iterative refinement proced...

This paper introduces a novel method to convert trimmed NURBS surfaces to untrimmed subdivision surfaces with Bézier edge conditions. We take a NURBS surface and its trimming curves as input, from this we automatically compute a base mesh, the limit surface of which fits the trimmed NURBS surface to a specified tolerance. We first construct the topology of the base mesh by performing a cross-fi...

This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the iso-topic approximation of a simple arrangement of curves. The arrangement is “simple” in the sense thatany three curves have no common intersection, any two curves intersect transversally, and each curve isnon-singular. A curve is given as the zero set of an analytic function f : R → ...

The distance between a Be-....ier segment and its control polygon is bounded in terms of the second differences of the control point sequence and a constant that depends only on the degree of the polynomial. The constant derived here is the smallest possible and is sharp for the Hausdorff distance between control polygon and curve segment. The bound provides a straightforward proof of quadratic...

A popular model of human sensorimotor learning suggests that a fast process and a slow process work in parallel to produce the canonical learning curve (Smith et al., 2006). Recent evidence supports the subdivision of sensorimotor learning into explicit and implicit processes that simultaneously subserve task performance (Taylor et al., 2014). We set out to test whether these two accounts of le...