Analogous to the quadratic B-spline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has C2 continuity, while the quadratic B-spline curve has C1 continuity. The quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic B-spline curve.

By simulating motion and deformation of a set of 3D characteristic curves defining surfaces, we introduce a new skin deformation technique to animate skin deformation of character models. This technique consists of two parts, representation of characteristic curves and dynamic skin deformation. The first part is to extract characteristic curves of an existing model, that is a polygon model or a...

This paper presents a new kind of splines, called non-uniform algebraic-trigonometric B-splines (NUAT B-splines), generated over the space spanned by {1, t, . . . , tk−3, cos t, sin t} in which k is an arbitrary integer larger than or equal to 3. We show that the NUAT B-splines share most properties of the usual polynomial B-splines. The subdivision formulae of this new kind of curves are given...

This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

In this paper, we present an e cient algorithm for contact determination between spline models. We make use of a new hierarchy, called ShellTree, that comprises of spherical shells and oriented bounding boxes. Each spherical shell corresponds to a portion of the volume between two concentric spheres. Given large spline models, our algorithm decomposes each surface into B ezier patches as part o...

A growing body of work has shown that deep neural networks are susceptible to adversarial examples. These take the form small perturbations applied model's input which lead incorrect predictions. Unfortunately, most literature focuses on visually imperceivable be digital images often are, by design, impossible deployed physical targets. We present Adversarial Scratches: a novel L0 black-box att...

We present a new approach for simplifying models composed of spline patches. Given an input model, the algorithm computes a new approximation of the model in terms of cubic triangular B ezier patches. It performs a series of geometric operations, consisting of patch merging and swapping diagonals, and makes use of patch connectivity information to generate C-LODs (curved levelsof-detail). Each ...

In this work a family of tension trigonometric curves analogous to those of cubic Bézier curves is presented. Some properties of the proposed curves are discussed. We propose an efficient interpolating method based on the tension trigonometric splines with various properties, such as partition of unity, geometric invariance and convex hull property, etc. This new interpolating method is applied...