Wonjoon Cho

A dithering algorithm for local composition control with three-dimensional printing

A dithering algorithm is presented for application to local composition control (LCC) with three-dimensional printing (3D printing) to convert continuous-tone representation of objects with LCC into discrete (pointwise) version of machine instructions. The algorithm presented effectively reduces undesirable low frequency textures of composition for individual 3D layers and also for 3D volumes. Peculiarities of the 3D printing machine, including anisotropic geometry of its picture elements (PELs) and uncertainties in droplet placement, are addressed by adapting a standard digital halftoning algorithm. Without loss of generality, our algorithm also accounts for technical limitations in the printing device, only generating lattices that can be represented within the finite memory limits of the hardware.

Efficient and reliable methods for rounded-interval arithmetic

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.

Computation of Self-Intersections of Offsets of Bézier Surface Patches

Self-intersection of offsets of regular Bezier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Bezier surface patches. Examples illustrate the principal features and robustness characteristics of the method.

Approximate development of trimmed patches for surface tessellation

Abstract This paper presents a method for constructing an auxiliary planar domain of triangulation for tessellating trimmed parametric surface patches. By minimizing a mapping error function, an approximate locally isometric mapping between a given trimmed parametric surface patch and its triangulation domain is constructed. In this way the shape of triangular elements on the triangulation domain is approximately preserved when mapped into three-dimensional space. We also provide an efficient method to achieve a good initial guess for the minimization of the mapping error function. Furthermore, our proposed method guarantees a homeomorphism between a triangulation domain and parametric space/given surface patch by robustly removing the possibility of self-intersection on the developed surface net. Practical application of the proposed algorithm can include the formation of ship hulls, ducts, shoes, clothing and automobile parts as well as the surface meshing procedure.

Topologically reliable approximation of composite Bézier curves

We present an efficient method of approximating a set of mutually nonintersecting simple composite planar and space Bezier curves within a prescribed tolerance using piecewise linear segments and ensuring the existence of a homeomorphism between the piecewise linear approximating segments and the actual nonlinear curves. Equations and a robust solution method relying on the interval projected polyhedron algorithm to determine significant points of planar and space curves are described. Preliminary approximation is obtained by computing those significant points on the input curves. This preliminary approximation, providing the most significant geometric information of input curves, is especially valuable when a coarse approximation of good quality is required such as in finite element meshing applications. The main approximation, which ensures that the approximation error is within a user specified tolerance, is next performed using adaptive subdivision. A convex hull method is effectively employed to compute the approximation error. We prove the existence of a homeomorphism between a set of mutually non-intersecting simple composite curves and the corresponding heap of linear approximating segments which do not have inappropriate intersections. For each pair of linear approximating segments, an intersection check is performed to identify possible inappropriate intersections. If these inappropriate intersections exist, further local refinement of the approximation is performed. A bucketing technique is used to identify the inappropriate intersections, which runs in O(n) time on the average where n is the number of linear approximating segments. Our approximation scheme is also applied to interval composite Bezier curves.

Topologically Reliable Approximation of Trimmed Polynomial Surface Patches

We present an unstructured triangular mesh generation algorithm that approximates a set of mutually nonintersecting simple trimmed polynomial parametric 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. We also extract important differential geometric features of input geometry for use in the approximation. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is introduced to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed and furthermore, an efficient method to compute a tight upper bound of the approximation error is proposed. 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 3D space and, furthermore, the algorithm provides an efficient method that explicitly controls the aspect ratio of the triangular elements.

The digital ocean

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.

Memory Analysis of Solid Model Representations for Heterogeneous Objects

Methods to represent and exchange parts consisting of Functionally Graded Material (FGM) for Solid Freeform Fabrication (SFF) with Local Composition Control (LCC) are evaluated based on their memory requirements. Data structures for representing FGM objects as heterogeneous models are described and analyzed, including a voxel-based structure, finite-element mesh-based approach, and the extension of the Radial-Edge and Cell-Tuple-Graph data structures with Material Domains representing spatially varying composition properties. The storage cost for each data structure is derived in terms of the number of instances of each of its fundamental classes required to represent an FGM object. In order to determine the optimal data structure, the storage cost associated with each data structure is calculated for several hypothetical models. Limitations of these representation schemes are discussed and directions for future research also recommended.

Robust tessellation of trimmed rational B-spline surface patches

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.

Design of Field Experiments for Adaptive Sampling of the Ocean with Autonomous Vehicles

Due to the highly non‐linear and dynamical nature of oceanic phenomena, the predictive capability of various ocean models depends on the availability of operational data. A practical method to improve the accuracy of the ocean forecast is to use a data assimilation methodology to combine in‐situ measured and remotely acquired data with numerical forecast models of the physical environment. Autonomous surface and underwater vehicles with various sensors are economic and efficient tools for exploring and sampling the ocean for data assimilation; however there is an energy limitation to such vehicles, and thus effective resource allocation for adaptive sampling is required to optimize the efficiency of exploration. In this paper, we use physical oceanography forecasts of the coastal zone of Singapore for the design of a set of field experiments to acquire useful data for model calibration and data assimilation. The design process of our experiments relied on the oceanography forecast including the current sp...