In this paper, we present a novel non-uniform rational B-spline (NURBS) muscle system for the simulation of human facial expressions and talking animation based on features extracted from video sequences. We construct the facial muscles based on anatomical knowledge and NURBS models. We use 43 feature points to represent facial expressions and apply a lip contour extraction technique to determi...

We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial order, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates....

According to the need of canopy visualization calculation in the digital plant research, we introduced a method, using Non-Uniform Rational B-Splines (NURBS) interpolation and multi-line segment splitting algorithm, to reconstruct the 3D morphological structure of maize leaf with a complexity controllable mesh. Using the data cloud obtained by digitizer, construct the surface of maize leaf by c...

Quadratic Powell-Sabin splines and their rational extension, the socalled NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a Bspline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to conve...

This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offe...

We present functional-type a posteriori error estimates in isogeometric analysis (IGA). These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the true error in the energy norm. By exploiting the properties of non-uniform rational B-splines (NURBS), we present efficient computation of these error estimates. The numerical realization and the quality of the c...

A parameter-uniform numerical method based on Shishkin mesh is constructed and analyzed for a weakly coupled system of singularly perturbed second order reaction-diffusion equations. A B-spline collocation method is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound (independent of the perturbation parameter ε) in the maximum norm is established theoretically. To illustr...

Geometric constraints have proved to be helpful for shape modeling. Moreover, they are efficient aids in controlling deformations and enhancing animation realism. The present paper addresses the deformation of B-spline surfaces while constraining the volume enclosed by the surface. Both uniform and non-uniform frameworks are considered. The use of level-of-detail (LoD) editing allows the preser...

A fast convergent optimization algorithm is proposed in this paper to calculate sequential optimal trajectories for pursuing a moving target or under dynamically changing environments. The changing boundary conditions or perturbations in such problems require an efficient algorithm to update the optimal trajectories with appropriate time steps. Concepts of a uniform B-spline and differentially ...