This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with 1 continuity around a common corner vertex. A 1 continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with 1 continuity around a corner is then developed. Our approach is easy and fast with the...

The microscopic origin of compact triangular islands on close-packed surfaces is identified using kinetic Monte Carlo simulations with energy barriers obtained from density-functional calculations. In contrast to earlier accounts, corner diffusion anisotropy is found to control the shape of compac$ ~ islands at intermediate temperatures. -CEIVEE We rationalize the correlation between the orient...

This paper presents a piecewise cubic approximation method with approximate G1 continuity. For a given triangular mesh of points with arbitrary topology, one cubic triangular Bézier patch surface is constructed. The resulting surfaces have G1 continuity at the vertex points, but only requires approximate G1 continuity along the macro-patch boundaries so as to lower the patch degree. While our s...

The directional solidification of the transparent binary alloy succinonitrile-poly(ethylene oxide) was studied in an experiment in which solidification speeds of about 2 mm/sec could be reached without loss of the linear temperature gradient. The low diffusivity of the polymer solute allowed the study of the dynamics of rapid solidification using an optical microscope. For both normal and doubl...

We present a derivation of exponential shape functions for the convection diffusion problem. The shape functions are defined for triangular elements and can be regarded as an extension of the one-dimensional Scharfetter-Gummel discretization scheme to two dimensions. The shape function varies exponentially in the direction of the element field vector and linearly in the direction orthogonal to ...

A new region-based approach to nonrigid motion tracking is described. Shape is defined in terms of a deformable triangular mesh that captures object shape plus a color texture map that captures object appearance. Photometric variations are also modeled. Nonrigid shape registration and motion tracking are achieved by posing the problem as an energy-based, robust minimization procedure. The appro...

This paper tackles a particular shape matching problem: given a data base of shapes (described as triangular meshes), we search for all shapes which describe a human. We do so by applying a 3D face detection approach on the mesh which consists of three steps: first, a local symmetry value is computed for each vertex. Then, the symmetry values in a certain neighborhood of each vertex are analyze...

We study parametrized dynamics of the Weierstrass elliptic ℘ function by looking at the underlying lattices; that is, we study parametrized families ℘Λ and let Λ vary. Each lattice shape is represented by a point τ in a fundamental period in modular space; for a fixed lattice shape Λ = [1, τ ] we study the parametrized space kΛ. We show that within each shape space there is a wide variety of dy...