We focus on the implicitization of parametric CAGD entities which are supposed to be of tensor product type. The presented approach is featured by its ability to treat polynomial or rational splines having a great number of control points. For B-splines, we describe a method of exactly obtaining the Fourier coefficients without using quadrature rules. As for NURBS, a preprocessing step is neces...

Design using free-form developable surfaces plays an important role in the manufacturing industry. Currently most commercial systems can only support converting free-form surfaces into approximate developable surfaces. Direct design using developable surfaces by interpolating descriptive curves is much desired in industry. In this paper, by enforcing a propagation scheme and observing its nesti...

In this paper we describe Persian floral patterns and explore techniques for animating them. We present several approaches for this dynamic recreation: visualizing pattern symmetries, illustrating their design process, and simulating plant growth. For creating a pleasant illusion of a never-ending movie, we also explore an infinitely cycling effect for self-similar patterns. The construction of...

This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant speci…cation involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identi…cation and estimation of both the nonparametric shapes of the Engel curves and the parametric speci…cation of the demographic scal...

Human figures have been animated using a variety of geometric models including stick figures, polygonal models, and NURBS-based models with muscles, flexible skin, or clothing. This paper reports on experimental results indicating that a viewer’s perception of motion characteristics is affected by the geometric model used for rendering. Subjects were shown a series of paired motion sequences an...

This paper shows that ROC curves, as a method of visualizing classifier performance, are inadequate for the needs of Artificial Intelligence researchers in several significant respects, and demonstrates that a different way of visualizing performance – the cost curves introduced by Drummond and Holte at KDD’2000 – overcomes these deficiencies.

We prove that a generic canonically or bicanonically embedded smooth curve has semistable m Hilbert points for all m ≥ 2. We also prove that a generic bicanonically embedded smooth curve has stable m Hilbert points for all m ≥ 3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with Gm-action, namely the canonically embedded balanced...