This paper presents a generalization of Catmull-Clark-variant Doo-Sabin surfaces and non-uniform biquadratic B-spline surfaces called NURDSes (Non-Uniform Recursive Doo-Sabin Surfaces). One step of NURDS refinement can be factored into one non-uniform linear subdivision step plus one dual step. Compared to the prior non-uniform Doo-Sabin surfaces (i.e., quadratic NURSSes), NURDSes are convergen...

Basis functions of biquadratic polynomial spline spaces over hierarchical T-meshes are constructed. The basis functions are all tensor-product B-splines, which are linearly independent, nonnegative and complete. To make basis functions more efficient for geometric modeling, we also give out a new basis with the property of unit partition. Two preliminary applications are given to demonstrate th...

Deformable surfaces have many applications in surface reconstruction, tracking and segmentation of range or volumetric data. Many existing deformable surfaces connect control points in a predefined and inflexible way. This means that the surface topology is fixed in advance, and also imposes severe limitations on how a surface can be described. For example a rectangular grid of control points c...

This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key strategy is linear space embedding with the operator of mixed partial derivative. The dimension of the original space equals the difference between the dimension o...

Michaelis-Menten equation is a basic equation of enzyme kinetics and gives an acceptable approximation of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to MichaelisMenten curve (15). This curve is derived from Quasi-Steady-State Assumption(QSSA), which has been proved always t...

New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ‘modern’ treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. A conceptual proof is presented of a result of Rohn concerning curves in P × P of bi-degree (2, 2). The string model...

By making use of the duality transformation, gauge field correlators of the Abelian Higgs Model are studied in the London limit. The obtained results are in a good agreement with the dual Meissner scenario of confinement and with the Stochastic Model of QCD vacuum. The nontrivial contribution to the quartic correlator arising due to accounting for the finiteness of the coupling constant is disc...

Given an odd surjective Galois representation ̺ : GQ → PGL2(F3) and a positive integer N, there exists a twisted modular curve X(N, 3)̺ defined over Q whose rational points classify the quadratic Q-curves of degree N realizing ̺. The paper gives a method to provide an explicit plane quartic model for this curve in the genus-three case N= 5.