A unified approach to blending of constant and varying parametric surfaces with curvature continuity

In this paper, we develop a new approach to blending of constant and varying parametric surfaces with curvature continuity. We propose a new mathematical model consisting of a vector-valued sixth-order partial differential equation (PDE) and time-dependent blending boundary constraints, and develop an approximate analytical solution of the mathematical model. The good accuracy and high computational efficiency are demonstrated by comparing the new approximate analytical solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on the continuity at trimlines, and apply the new approximate analytical solution in blending of constant and varying parametric surfaces with curvature continuit

Tangent-ball techniques for shape processing

Shape processing defines a set of theoretical and algorithmic tools for creating, measuring and modifying digital representations of shapes.  Such tools are of paramount importance to many disciplines of computer graphics, including modeling, animation, visualization, and image processing.  Many applications of shape processing can be found in the entertainment and medical industries. In an attempt to improve upon many previous shape processing techniques, the present thesis explores the theoretical and algorithmic aspects of a difference measure, which involves fitting a ball (disk in 2D and sphere in 3D) so that it has at least one tangential contact with each shape and the ball interior is disjoint from both shapes. We propose a set of ball-based operators and discuss their properties, implementations, and applications.  We divide the group of ball-based operations into unary and binary as follows: Unary operators include: * Identifying details (sharp, salient features, constrictions) * Smoothing shapes by removing such details, replacing them by fillets and roundings * Segmentation (recognition, abstract modelization via centerline and radius variation) of tubular structures Binary operators include: * Measuring the local discrepancy between two shapes * Computing the average of two shapes * Computing point-to-point correspondence between two shapes * Computing circular trajectories between corresponding points that meet both shapes at right angles * Using these trajectories to support smooth morphing (inbetweening) * Using a curve morph to construct surfaces that interpolate between contours on consecutive slices The technical contributions of this thesis focus on the implementation of these tangent-ball operators and their usefulness in applications of shape processing. We show specific applications in the areas of animation and computer-aided medical diagnosis.  These algorithms are simple to implement, mathematically elegant, and fast to execute.Ph.D.Committee Chair: Jarek Rossignac; Committee Member: Greg Slabaugh; Committee Member: Greg Turk; Committee Member: Karen Liu; Committee Member: Maryann Simmon

Blending using ODE swept surfaces with shape control and C1 continuity

Surface blending with tangential continuity is most widely applied in computer aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: 1). exact satisfaction of 1C continuous blending boundary constraints, 2). effective shape control of blending surfaces, 3). high computing efficiency due to explicit mathematical representation of blending surfaces, and 4). ability to blend multiple (more than two) primary surfaces

Intuitive procedure for constructing geometrically complex objects using cyclides

In the past, cyclide surfaces have been used effectively for the variable radius blending of natural quadric intersections. However, attempts to use cyclides for constructing realistic, freeform composite surfaces met with rather limited success. The paper presents a simple procedure for creating and manipulating geometrically complex objects using tubular cyclide pieces. The method described is intuitive from the designer's point of view, and it is based on the fundamental definitions and properties of the cyclide. Various practical issues involved in this design procedure are discussed, several extensions of the basic technique are described, and implemented examples are provided.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31678/1/0000614.pd

The Maunakea Spectroscopic Explorer Book 2018

(Abridged) This is the Maunakea Spectroscopic Explorer 2018 book. It is intended as a concise reference guide to all aspects of the scientific and technical design of MSE, for the international astronomy and engineering communities, and related agencies. The current version is a status report of MSE's science goals and their practical implementation, following the System Conceptual Design Review, held in January 2018. MSE is a planned 10-m class, wide-field, optical and near-infrared facility, designed to enable transformative science, while filling a critical missing gap in the emerging international network of large-scale astronomical facilities. MSE is completely dedicated to multi-object spectroscopy of samples of between thousands and millions of astrophysical objects. It will lead the world in this arena, due to its unique design capabilities: it will boast a large (11.25 m) aperture and wide (1.52 sq. degree) field of view; it will have the capabilities to observe at a wide range of spectral resolutions, from R2500 to R40,000, with massive multiplexing (4332 spectra per exposure, with all spectral resolutions available at all times), and an on-target observing efficiency of more than 80%. MSE will unveil the composition and dynamics of the faint Universe and is designed to excel at precision studies of faint astrophysical phenomena. It will also provide critical follow-up for multi-wavelength imaging surveys, such as those of the Large Synoptic Survey Telescope, Gaia, Euclid, the Wide Field Infrared Survey Telescope, the Square Kilometre Array, and the Next Generation Very Large Array.Comment: 5 chapters, 160 pages, 107 figure

A feature-based approach to the Computer-Aided Design of sculptured products

Computer-Aided Design systems offer considerable potential for improving design process efficiency. To reduce the 'ease of use' barrier hindering full realisation of this potential amongst general mechanical engineering industries, many commercial systems are adopting a Feature-Based Design (FBD) metaphor. Typically the user is allowed to define and manipulate the design model using interface elements that introduce and control parametric geometry clusters, with engineering meaning, representing specific product features (such as threaded holes, slots, pockets and bosses). Sculptured products, such as golf club heads, shoe lasts, crockery and sanitary ware, are poorly supported by current FBD systems and previous research, because their complex shapes cannot be accurately defined using the geometrically primitive feature sets implemented. Where sculptured surface regions are allowed for, the system interface, data model and functionality are little different from that already provided in many commercial surface modelling systems, and so offer very little improvement in ease of use, quality or efficiency. This thesis presents research to propose and develop an FBD methodology and system suitable for sculptured products. [Continues.