Energies of curves and surfaces together with their discrete variants play a prominent role as fairness functionals in geometric modeling and computer aided geometric design. This paper deals with a particular discrete surface energy which is expressible in terms of curve energies, and which occurs naturally in the problem of smoothing digital elevation data with tolerance zone constraints. We ...

This paper demonstrates how to apply the method of coupling from the past (CFTP) (Propp and Wilson, 1996) to the problem of sampling orthogonal predictors in the Bayes linear model. Using CFTP we construct a coupled Gibbs sampler that automatically determines its own run time to convergence. This removes the need to rely on approximate convergence diagnostics as in usual Markov chain Monte Carl...

In this work, a geometric invariant curve and surface normalization method is presented. Translation, scale and shear are normalized by Principal Component Analysis (PCA) whitening. Independent Component Analysis (ICA) and the third order moments are then employed for rotation and reflection normalization. By applying this normalization, curves and surfaces that are related by geometric transfo...

We present a new 3D surface modeling approach that enables curve-based creation and modification of smooth surfaces by sketching. The key feature of the proposed methods is a two-way communication between the user-designed curve networks and the generated surfaces. A user-drawn curve network serves as a control cage, from which a subdivision surface is generated. The subdivision surface is upda...

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using derivatives are presented. The combination tension, continuity, bias control is used as a very powerful type interpolation; they applied to curves. Surface construction utilizing studied explored several examples obtained by C1 surface given show usefulness method.