We present an interpretation of approximate subdivision surface evaluation in the language of linear algebra. Specifically, vertices in the refined mesh can be computed by left-multiplying the vector of control vertices by a sparse matrix we call the subdivision operator. This interpretation is rather general: it applies to any level of subdivision, it holds for many common subdivision schemes ...

In a recent paper (Computer Aided Geometric Design 23 (3), 243–260), Yang presented a novel kind of nonlinear and geometry driven subdivision scheme for curve interpolation. The author declared that this scheme was shape preserving when all free parameters were explicitly selected by some specific rules. In this note, we demonstrate that the author (a) ignored the consistency of the definition ...

It is of increasing contemporary interest to preserve ambient isotopy during geometric modeling. Bézier curves are pervasive in computer aided geometric design, as one of the fundamental computational representations for geometric modeling. For Bézier curves, subdivision algorithms create control polygons as piecewise linear (PL) approximations that converge under Hausdorff distance. A natural ...

A challenge in vector graphics is to define primitives that offer flexible manipulation of colour gradients. We propose a new primitive, called a shading curve, that supports explicit and local gradient control. This is achieved by associating shading profiles to each side of the curve. These shading profiles, which can be manually manipulated, represent the colour gradient out from their assoc...

This paper presents a Web based system for capturing outlines of 2D shapes using Matlab Web Server. From a simple user interface in HTML, any Web user can upload his data and view the results. Cubi c Bezier curve design is used to capture the outlines. In that, outline is divided into curve segments at corner points and curve approximation of each segment is performed by estimation of Bezier co...

The present paper provides a new definition of the dual interpolation curve in geometric-intuitive way based on adaptive refinement techniques. is an implementation interpolatory subdivision scheme for modeling, which comprises polynomial segments different degrees. Dual curves maintain various desirable properties conventional modeling methods, such as local subdivision, high accuracy and conv...

Subdivision schemes with matrix masks are a natural extension of the well studied case of subdivision schemes with scalar masks. Such schemes arise in the analysis of multivariate scalar schemes, in subdivision processes corresponding to shift-invariant spaces generated by more than one function, in geometric modeling where each component of the curve/surface is designed by a diierent linear co...