We present a surface generation method which produces B-spline-like surfaces (or curves) in any dimension. We focus on the 2D quadratic case.

Spline knots based on Bézier curves or B-splines can exhibit a knot type that is different from that exhibited by its control polygon, i.e., the spline and its control polygon are not ambient isotopic. By forming composite knots from suitably designed building blocks the difference in knottedness of the two 1-manifolds can be made arbitrarily large.

GB-spline curves can be considered as the generalization of B-spline curve incorporating a shape parameter into the polynomial basis functions. The geometric effect of the alteration of the shape parameter is discussed in this paper, including constrained shape control of the curve.

We introduce a modeling constructor for micro-structures and porous geometry via curve-trivariate, surface-trivariate and trivariate-trivariate function (symbolic) compositions. By using 1-, 2and 3-manifold based tiles and paving them multiple times inside the domain of a 3-manifold deforming trivariate function, smooth, precise and watertight, yet general, porous/micro-structure geometry might...

B-spline curves and their rational generalizations (NURBS curves) play central role and are widely used in computer aided design today. A B-spline curve is uniquely defined by its degree, control points and knot values, while in terms of NURBS curves the weight vector has to be specified in addition. The modification of a curve is also an essential problem in CAD systems, hence numerous methods...

Computer-Aided Design and Applications is an international journal on the applications of CAD CAM. It publishes papers in general domain plus emerging fields like bio-CAD, nano-CAD, soft-CAD, garment-CAD, PLM, PDM, data mining, internet, education, genetic algorithms engines. The aimed at all developers users technology to ptovide solutions for various stages design manufacturing. about technol...

Filtering algorithms are the workhorse of spacecraft attitude estimation but recent research has shown that the use of batch estimation techniques can result in higher accuracy per unit of computational cost. This paper presents an approach for singularity-free batch estimation of attitude in continuous-time using B-Spline curves on unit-length quaternions. It extends existing theory of unitlen...

The skeleton, or medial axis, is an important attribute of 2-D shapes. disk B-spline curve (DBSC) a skeleton-based parametric freeform region representation, which defined in the form. DBSC describes not only region, suitable for describing heterogeneous materials but also center (skeleton) explicitly, animation, simulation, and recognition. In addition to being useful error estimation curve, c...