The ocean, is fundamentally important to many areas of modern society and thus improved knowledge of the ocean is essential. Ocean scientists have made remarkable progress in observation technology, modeling and assimilation in physical oceanography, acoustics, and biology. To some extent, such advances have been confined to each discipline. Therefore a great demand has arisen for a modern distributed computing and networking infrastructure within which we bring together advanced modeling, observation tools and field estimation methods. The paper describes a knowledge network of distributed heterogeneous data and software resources for multidisciplinary ocean research.

We present an unstructured triangular mesh generation algorithm that approximates a set of mutually non-intersecting simple trimmed rational B-spline surface patches within a user specified geometric tolerance. The proposed method uses numerically robust interval geometric representations/computations and also addresses the problem of topological consistency (homeomorphism) between the exact geometry and its approximation. Those are among the most important outstanding issues in geometry approximation problems. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is utilized to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed. Unstructured triangular meshes for free-form surfaces frequently involve triangles with high aspect ratio and accordingly, result in ill-conditioned meshing. Our proposed algorithm constructs 2D triangulation domains which sufficiently preserve the shape of triangles when mapped into 2D space and furthermore, the algorithm provides an efficient method that explicitly controls the aspect ratio of the triangular elements.

We present an efficient and reliable method for computing the unit-in-the-last-place (ulp) of a double-precision floating-point number, taking advantage of the standard binary representation for floatingpoint numbers defined by IEEE Std 754-1985. The ulp is necessary to perform software rounding for robust rounded-interval arithmetic (RIA) operations. Hardware rounding, using two of the standard rounding modes defined by IEEE-754, may be more efficient. RIA has been used to produce robust software systems for the solution of systems of nonlinear equations, interrogation of geometric and differential properties of curves and surfaces, curve and surface intersections, and solid modeling.