The present authors have introduced polynomial splines over T-meshes (PHT-splines) and provided the theories and applications for PHT-splines over hierarchical T-meshes. This paper generalizes PHT-splines to arbitrary topology over general T-meshes with any structures. The general PHT-spline surfaces can be constructed through an unified scheme to interpolate the local geometric information at ...

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness f...

The dynamic characteristics of an axisymmetrical linear actuator with axially magnetized moving permanent magnet are obtained using combined field and circuit approach. The magnetic field of the actuator has been analysed using the finite element method over a current-displacement sampling grid. Two field analyses are carried out for each point of the grid one for the real system and one for th...

New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify thèbad' data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorith...

Several efficient constructions of smooth surfaces following the outlines of a polyhedral mesh are based on three-sided patches. To demonstrate that these constructions arc compatible with existing software based on tensor-product patches, the particular scheme in [3] is expressed in terms of linearly-trimmed bicubic patches. Explicit formulas relating the coefficients of the patches to the ver...

A VLSI chip for ray tracing bicubic patches in Bezier form is explored. The purpose of the chip is to calculate the intersection point of a ray with the bicubic patch to a specified level of accuracy, returning the location of the intersection on the patch and on the ray. This is done by computing the intersection of the ray with a bounding volume of the patch and repeatedly subdividing the pat...

Determining the least m such that one m×m bi-cubic macropatch per quadrilateral offers enough degrees of freedom to construct a smooth surface by local operations regardless of the vertex valences is of fundamental interest; and it is of interest for computer graphics due to the impending ability of GPUs to adaptively evaluate polynomial patches at animation speeds. We constructively show that ...