Traditionally schematized maps make extensive use of curves. However, automated methods for schematization are mostly restricted to straight lines. We present a generic framework for topology-preserving curved schematization that allows a choice of quality measures and curve types. Our fully-automated approach does not need critical points or salient features. We illustrate our framework with B...

Article history: Received 21 May 2009 Received in revised form 25 June 2010 Accepted 22 August 2010 Available online 16 September 2010

In this paper, we present our approach of face and lip detection, lip modeling, and tracking. A new lip model based on Bézier Curves is used to capture the dynamics of the lips efficiently. The model is defined only through few points which are modeled using the Active Shape Model (ASM). Accurate detection of lip details is implemented using multiple independent feature templates. The method de...

[AinAD11] Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures, SIAM J. Scient.

We present a model for the lips using the Active Shape Model (ASM) based on Bézier Curves which can capture the dynamics of the lips efficiently. The curves are defined only by a few points that can be used as visual speech features. Using some measured feature points, we can recover the full model of the lips especially for those features which are difficult to be detected. Accurate detection ...

In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bézier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real projective plane RP into four and six triangles respectively. The third method applies to surfaces specified by rectangular control nets and partitions the torus RP ...

Strip approximation with Bézier patches in conical form for design and manufacturing of developable materials Chih-Hsing Chu a , Charlie C.L. Wang b & Chi-Rung Tsai a a Department of Industrial Engineering and Engineering Management , National Tsing Hua University , Hsinchu, Taiwan b Department of Mechanical and Automation Engineering , The Chinese University of Hong Kong , Shatin N.T., Hong Ko...

The aim of this article is to focus on the investigation of such rationally parametrized hypersurfaces which admit rational convolution (RC) generally, or in some special cases. Examples of such hypersurfaces are presented and their properties are discussed. We also aim to examine links between well-known curves and surfaces (PH/PN or LN) and general objects defined and explored in this article...

The stretching energy functional and the bending energy functional are widely used for approximating the solution of the Plateau-Béizer Problem. This paper presents another two simple methods by using the extended stretching energy functional and the extended bending energy functional. The resulting surface obtained by the new methods will have a smaller area. Comparisons are made with both the...

We study polynomial solutions in the Bézier form of the wave equation in dimensions one and two. We explicitly determine which control points of the Bézier solution at two different times fix the solution.