This paper introduces the theoretical design of reconfigurable machine tools using modular design approach. First, the general concept of modular robot and its growing need is introduced. Second, the design of reconfigurable parallel kinematic machines is discussed and the geometric modeling of such figures is presented and explained, and potential applications are described. Finally, a case st...

We present efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given surface, we propose using higher-order approximation techniques developed for the field of computer-aided geometric design (CAGD). We use Bézier curves and triangles, fundamental objects i...

A clothoid has the property that its curvature varies linearly with arclength. This is a useful feature for the path of a vehicle whose turning radius is controlled as a linear function of the distance travelled. Highways, railways and the paths of car-like robots may be composed of straight line segments, clothoid segments and circular arcs. Control polylines are used in computer aided design ...

Parametric surface [Fari02] is a surface defined by a tensor-product of parametric curves, which are represented by parametric equations. As such surface comes with a well defined mathematical definition, it becomes one of the most common geometric tools for computer-aided geometric design and object modeling aids for many computer graphics applications. Typical examples of such surface include...

Freeform surfaces are commonly used in Computer Aided Geometric Design so accurate analysis of surface properties is becoming increasingly important In this paper we de ne surface slope and surface speed develop visualization tools and demonstrate that they can be useful in the design process Generally surface properties such as curvature and twist are evaluated at a nite set of predetermined s...

Laplace–Beltrami operator and its discretization play a central role in the fields of image processing, computer graphics, computer aided geometric design and so on. In this paper, a discrete scheme for Laplace–Beltrami operator over quadrilateral meshes is constructed based on a bilinear interpolation of the quadrilateral. Convergence results for the proposed discrete scheme are established un...

The ability to control boundary behaviors is critical for the subdivision surface to become a useful representation in computer aided geometric design. Previous methods achieve boundary control by extending the boundary vertices of the control mesh, or by applying different subdivision rules to the boundary edges and vertices. This paper presents an open uniform quadratic subdivision scheme der...

Even if Computer-Aided Geometric Design modelers are now based on powerful mathematical models for curves and surfaces, there are important needs for tools to create, analyze and modify these objects. Designing product shapes with free-form curves and surfaces is still a tedious task and modifying the shape obtained is even more difficult and, most of the time, needs recreating a part up to the...

Different approaches to the decomposition of a nonsingular totally positive matrix as a product of bidiagonal matrices are studied. Special attention is paid to the interpretation of the factorization in terms of the Neville elimination process of the matrix and in terms of corner cutting algorithms of Computer Aided Geometric Design. Conditions of uniqueness for the decomposition are also given.

A polygonisation algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects. The result is a surface definition (to be called Boolean Compound Soft Object, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference op...