This is the first one in a sequence of several papers dedicated to the development of applications of Euler Beta-function B-splines (BFBS) to Computer-aided Geometric Design (CAGD) and, in particular, for geometric modelling of parametric curves, surfaces and volume deformations. This study is an analogue of the study conducted in [12, 10] for the case of expo-rational Bsplines (ERBS). An impor...

The role of differential geometry in describing a curve can not be denied. The differential forms defined for Bézier curves which are widely used in computer aided geometric design, plays a significant role in classification and image processing of curves. For this reason, the definitions such as Serret-Frenet frame, curvature and torsion which are described for Bézier curves are very important...

For some applications of computer-aided geometric design it is important to maintain strictly monotone curvature along a curve segment. Here we analyze the curvature distributions of segments of conic sections represented as rational quadratic Bézier curves in standard form. We show that if the end points and the weight are fixed, then the curvature of the conic segment will be strictly monoton...

The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet–Serret (RF) curves for robot trajectory planning. RF curves distinguished by the...

The Pythagorean hodograph (PH) curves are characterized by certain Pythagorean n-tuple identities in the polynomial ring, involving the derivatives of the curve coordinate functions. Such curves have many advantageous properties in computer aided geometric design. Thus far, PH curves have been studied in 2or 3-dimensional Euclidean and Minkowski spaces. The characterization of PH curves in each...

This paper presents a service marketplace vision for enterprise-wide integrated design modeling. In this environment, expert participants and product development organizations are empowered to publish their geometric design, CAE, manufacturing, or marketing capabilities as live services that are operable over the Internet. These services are made available through a service marketplace. Product...

The paper presents the Surface Constructor (SC) 3D kinematical modelling and simulation program, which is intended for the development of new types of complex contacting kinematical surfaces, especially gear surfaces. This innovative application is based on an original theory of the author, named the Reaching Model. The paper summarises the theory and introduces the structure and capabilities o...

Developable strip is commonly used in product design due to its ease of manufacture. This paper proposes an algorithm for geometric design of strip using developable Bézier patches. It computes an aggregate of triangular and quadrilateral patches interpolate two given space curves defining a strip. The computation process selects optimal solutions in terms of surface assessment criteria specifi...

Using a new formulation of the Bézout matrix, we construct bivariate matrix polynomials expressed in a tensor-product Lagrange basis. We use these matrix polynomials to solve common tasks in computer-aided geometric design. For example, we show that these bivariate polynomials can serve as stable and efficient implicit representations of plane curves for a variety of curve intersection problems.

Transfinite surface interpolation is a classic topic of computer-aided geometric design (CAGD), and many non-quadrilateral schemes are known. Surfaces defined solely by means of their boundary curves and cross-tangent functions are needed, for example, in three-dimensional curve network-based design, and to fill complex irregular holes such as in vertex blending. This paper deals with interpola...