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Undergraduate Theses, School of Engineering
Current graphics cards (GPUs) shade small polygons inefficiently. When surfaces are represented using micropolygons of less than a pixel in size, many shading computations performed by a GPU are redundant. Since shading is typically the most expensive operation in a graphics pipeline, this leads to poor rendering performance. This thesis presents a prototype implementation of quad-fragment merging, which reduces redundant shading work by buffering and selectively merging rasterized fragments prior to shading. The prototype quad-fragment merger is described in detail, and evidence is presented that it is amenable to implementation in fixed-function hardware. Performance results indicate that our implementation decreases shader executions by a factor of eight when rendering micropolygons, and effectively makes use of a number of optimizations to yield high performance. Finally, an early prototype of a corollary technique that shades scenes with motion blur is described, and preliminary results are presented.
Book
xxviii, 622 p. : ill. (some col.) ; 24 cm.
  • Part I: Fundamentals of Geometric Algebra Introduction to Geometric Algebra Geometric Algebra for Modeling in Robot Physics Part II: Euclidean, Pseudo-Euclidean, Lie and Incidence Algebras and Conformal Geometries 2D, 3D and 4D Geometric Algebras Kinematics of the 2D and 3D Spaces Lie Algebras and Algebra of Incidence Using The Null Cone and Affine Plane Conformal Geometric Algebra Programming Issues Part III: Geometric Computing for Image Processing, Computer Vision and Neurocomputing Clifford Fourier and Wavelet Transforms Geometric Algebra of Computer Vision Geometric Neuralcomputing Part IV: Geometric Computing of Robot Kinematics and Dynamics Kinematics Dynamics Part V: Applications I: Image Processing, Computer Vision, Neurocomputing Applications of Lie Filters, Quaternion Fourier and Wavelet Transforms Invariants Theory in Computer Vision and Omnidirectional Vision Registration of 3D Points Using GA and Tensor Voting Applications in Neuralcomputing Neural Computing for 2D Contour and 3D Surface Reconstruction Part VI: Applications II: Robotics and Medical Robotics Rigid Motion Estimation Using Line Observations Tracker Endoscope Calibration and Body-Sensors Calibration Tracking, Grasping and Object Manipulation 3D Maps, Navigation and Relocalization Modeling and Registration of Medical Data Part VII: Appendix.
  • (source: Nielsen Book Data)9781848829282 20160605
This study offers an introduction to Clifford geometric algebra, an advanced mathematical framework, for applications in perception action systems. Topics and features include theory and application of the quaternion Fourier and wavelet transforms, discussion on geometric computing under uncertainty and much more.
(source: Nielsen Book Data)9781848829282 20160605
dx.doi.org SpringerLink
Book
1 online resource (108 p. ) : digital, PDF file.
Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.
Book
1 online resource (50 p. ) : digital, PDF file.
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
Book
xi, 513 pages : illustrations ; 25 cm.
  • Ch. 1. Geometry, Algebra, and Algorithms. 1. Polynomials and Affine Space. 2. Affine Varieties. 3. Parametrizations of Affine Varieties. 4. Ideals. 5. Polynomials of One Variable
  • Ch. 2. Groebner Bases. 2. Orderings on the Monomials in [actual symbol not reproducible]. 3. A Division Algorithm in [actual symbol not reproducible]. 4. Monomial Ideals and Dickson's Lemma. 5. The Hilbert Basis Theorem and Groebner Bases. 6. Properties of Groebner Bases. 7. Buchberger's Algorithm. 8. First Applications of Groebner Bases. 9. (Optional) Improvements on Buchberger's Algorithm.
This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960s. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years and new algorithms, coupled with the power of fast computers, have led to some interesting applications, for example in robotics and in geometric theorem proving. This book is an introduction to algebraic geometry and commutative algebra aimed primarily at undergraduates. Emphasizing applications and the computational and algorithmic aspects of the subject, the text has less abstract flavour than standard treatments. With few prerequisites, it should also a useful introduction to the subject for computer scientists.
(source: Nielsen Book Data)9783540978473 20160802
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
(source: Nielsen Book Data)9780387978475 20160802
SAL3 (off-campus storage)
Book
1 online resource (x, 281 p.)
  • On 5-Gons and 5-Holes.- On Reversibility among Parallelohedra.- A History of Flips in Combinatorial Triangulations.- Open Guard Edges and Edge Guards in Simple Polygons.- String-Wrapped Rotating Disks.- The Chromatic Number of the Convex Segment Disjointness Graph.- Continuous Flattening of Convex Polyhedra.- Convexifying Monotone Polygons while Maintaining Internal Visibility.- On the Number of Radial Orderings of Colored Planar Point Sets.- Notes on the Twisted Graph.-Locating a Service Facility and a Rapid Transit Line.- Simultaneously Flippable Edges in Triangulations.- Spiral Serpentine Polygonization of a Planar Point Set.- The 1-Center and 1-Highway Problem.- Compact Grid Representation of Graphs.- On the Heaviest Increasing or Decreasing Subsequence of a Permutation, and Paths and Matchings on Weighted Point Sets.- A Generalization of the Source Unfolding of Convex Polyhedra.- Large Angle Crossing Drawings of Planar Graphs in Subquadratic Area.- Connecting Red Cells in a Bicolour Voronoi Diagram.- Covering Islands in Plane Point Sets.- Rectilinear Convex Hull with Minimum Area.- Separated Matchings and Small Discrepancy Colorings.- A Note on the Number of Empty Triangles.- Meshes Preserving Minimum Feature Size.- Geometric Graphs in the Plane Lattice. On Reversibility among Parallelohedra.- A History of Flips in Combinatorial Triangulations.- Open Guard Edges and Edge Guards in Simple Polygons.- String-Wrapped Rotating Disks.- The Chromatic Number of the Convex Segment Disjointness Graph.- Continuous Flattening of Convex Polyhedra.- Convexifying Monotone Polygons while Maintaining Internal Visibility.- On the Number of Radial Orderings of Colored Planar Point Sets.- Notes on the Twisted Graph.-Locating a Service Facility and a Rapid Transit Line.- Simultaneously Flippable Edges in Triangulations.- Spiral Serpentine Polygonization of a Planar Point Set.- The 1-Center and 1-Highway Problem.- Compact Grid Representation of Graphs.- On the Heaviest Increasing or Decreasing Subsequence of a Permutation, and Paths and Matchings on Weighted Point Sets.- A Generalization of the Source Unfolding of Convex Polyhedra.- Large Angle Crossing Drawings of Planar Graphs in Subquadratic Area.- Connecting Red Cells in a Bicolour Voronoi Diagram.- Covering Islands in Plane Point Sets.- Rectilinear Convex Hull with Minimum Area.- Separated Matchings and Small Discrepancy Colorings.- A Note on the Number of Empty Triangles.- Meshes Preserving Minimum Feature Size.- Geometric Graphs in the Plane Lattice.
  • (source: Nielsen Book Data)9783642341908 20160609
This Festschrift volume is published in honor of Ferran Hurtado on the occasion of his 60th birthday; it contains extended versions of selected communications presented at the XIV Spanish Meeting on Computational Geometry, held at the University of Alcala, Spain, in June 2011. Ferran Hurtado has played a central role in the Spanish community of Computational Geometry since its very beginning, and the quantity and quality of the international participants in the conference is an indisputable proof of his relevance in the international level. The 26 revised full papers were carefully reviewed and selected from numerous submissions. The papers present original research in computational geometry, in its broadest sense. Topics included are discrete and combinatorial geometry, linear programming applied to geometric problems, geometric algorithms and data structures, theoretical foundations of computational geometry, questions of interest in the implementation of geometric algorithms, and applications of computational geometry.
(source: Nielsen Book Data)9783642341908 20160609
dx.doi.org SpringerLink
Book
xi, 255 p. : col. ill. ; 27 cm.
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincare conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: Vickie_Kearn@press.princeton.edu.
(source: Nielsen Book Data)9780691145532 20160609
Science Library (Li and Ma)
Book
xv, 452 p. : ill. ; 27 cm.
  • Functions and Transformations.- Functions and Graphs.- Rigid Motions (Isometries).- Affine and Projective Transformations.- Mobius Transformations.- Curves and Surfaces.- Examples of Curves.- Geometry of Curves.- Geometry of Surfaces.- Examples of Surfaces.- Piecewise Curves and Surfaces.
  • (source: Nielsen Book Data)9780387712772 20160604
This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB(R) including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.
(source: Nielsen Book Data)9780387712772 20160604
dx.doi.org SpringerLink
Science Library (Li and Ma)
Book
xii, 386 p. : ill. ; 25 cm.
  • Computational Geometry: Introduction.- Line Segment Intersection: Thematic Map Overlay.- Polygon Triangulation: Guarding an Art Gallery.- Linear Programming: Manufacturing with Molds.- Orthogonal Range Searching: Querying a Database.- Point Location: Knowing Where You Are.- Voronoi Diagrams: The Post Office Problem.- Arrangements and Duality: Supersampling in Ray Tracing.- Delaunay Triangulations: Height Interpolation.- More Geometric Data Structures: Windowing.- Convex Hulls: Mixing Things.- Binary Space Partitions: The Painter's Algorithm.- Robot Motion Planning: Getting Where You Want to Be.- Quadtrees: Non-Uniform Mesh Generation.- Visibility Graphs: Finding the Shortest Route.- Simplex Range Searching: Windowing Revisited.- Bibliography.- Index.
  • (source: Nielsen Book Data)9783540779735 20160528
This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In this third edition, besides revisions to the second edition, new sections discussing Voronoi diagrams of line segments, farthest-point Voronoi diagrams, and realistic input models have been added.
(source: Nielsen Book Data)9783540779735 20160528
Science Library (Li and Ma)
Book
ix, 563 p. : ill. ; 24 cm.
  • Preface.- 1. Fundamentals.- 2. Models of Line Space.- 3. Linear Complexes.- 4. Approximation in Line Space.- 5. Ruled Surfaces.- 6. Developable Surfaces.- 7. Line Congruences and Line Complexes.- 8. Linear Line Mappings - Computational Kinematics.- References.- List of Symbols.- Index.- Color Plates.
  • (source: Nielsen Book Data)9783540420583 20160528
The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geometrical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from various viewpoints and aims towards computation and visualization. Besides applications, it contains a tutorial on projective geometry and an introduction into the theory of smooth and algebraic manifolds of lines. It will be useful to researchers, graduate students, and anyone interested either in the theory or in computational aspects in general, or in applications in particular.
(source: Nielsen Book Data)9783540420583 20160528
Science Library (Li and Ma)
Book
xii, 367 p. : ill. ; 25 cm.
  • Computational Geometry: Introduction.- Line Segment Intersection: Thematic Map Overlay.- Polygon Triangulation: Guarding an Art Gallery.- Linear Programming: Manufacturing with Molds.- Orthogonal Range Searching: Querying a Database.- Point Location: Knowing Where You Are.- Voronoi Diagrams: The Post Office Problem.- Arrangements and Duality: Supersampling in Ray Tracing.- Delaunay Triangulations: Height Interpolation.- More Geometric Data Structures: Windowing.- Convex Hulls: Mixing Things.- Binary Space Partitions: The Painter's Algorithm.- Robot Motion Planning: Getting Where You Want to Be.- Quadtrees: Non-Uniform Mesh Generation.- Visibility Graphs: Finding the Shortest Route.- Simplex Range Searching: Windowing Revisited.- Bibliography.- Index.
  • (source: Nielsen Book Data)9783540656203 20160527
This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students, this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.
(source: Nielsen Book Data)9783540656203 20160527
Science Library (Li and Ma)
Book
xx, 519 p. : ill. ; 26 cm.
  • Preface-- Part I. Algorithmic Tools: 1. Notions of complexity-- 2. Basic data structures-- 3. Deterministic methods used in geometry-- 4. Random sampling-- 5. Randomized algorithms-- 6. Dynamic randomized algorithms-- Part II. Convex Hulls: 7. Polytopes-- 8. Incremental convex hulls-- 9. Convex hulls in 2 and 3 dimensions-- 10. Linear programming-- Part III. Triangulations: 11. Complexes and triangulations-- 12 Triangulations in dimension 2-- 13. Triangulations in dimension 3-- Part IV. Arrangements: 14. Arrangements of hyperplanes-- 15. Arrangements of line segments in the plane-- 16. Arrangements of triangles-- Part V. Voronoi Diagrams: 17. Euclidean metrics-- 18. Non-Euclidean metrics-- 19. Diagrams in the plane-- References-- Notation-- Index.
  • (source: Nielsen Book Data)9780521563222 20160528
The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.
(source: Nielsen Book Data)9780521563222 20160528
Cambridge Core Access limited to one user.
Science Library (Li and Ma)
Book
xii, 365 p. : ill. ; 25 cm.
In this introduction to computational geometry the the text focuses on algorithms. All solutions and techniques described in the text are from computational geometry and are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
(source: Nielsen Book Data)9783540612704 20160527
Science Library (Li and Ma)
Book
viii, 222 p. : ill. ; 24 cm.
This anthology is based on the First ACM Workshop on Applied Computational Geometry, WACG '96, held in Philadelphia, PA, USA, in May 1996, as part of the FCRC Conference.Today, CG is in transition and applied computational geometry has established itself as a fertile meeting ground for theorists from core computational geometry and practitioners from the potential application areas to exchange their ideas and identify issues of common interest. The book presents 11 invited contributions and state-of-the-art reports by leading experts together with 12 refereed full papers selected from 32 submissions. It points the way towards geometrical engineering and addresses researchers and professionals sharing an interest in geometric algorithms and techniques and their use in computational sciences and engineering.
(source: Nielsen Book Data)9783540617853 20160528
dx.doi.org SpringerLink
SAL3 (off-campus storage)
Book
1 v.
SAL3 (off-campus storage)
Book
xv, 447 p.
  • I. BASICS. 1. Quick-sort and Search. Quick-sort. Another view of quick-sort. Randomized binary trees. Skip lists. 2. What Is Computational Geometry? Range queries. Arrangements. Trapezoidal decompositions. Convex polytopes. Voronoi diagrams. Hidden surface removal. Numerical precision and degeneracies. Early deterministic algorithms. Deterministic vs. randomized algorithms. The model of randomness. 3. Incremental Algorithms. Trapezoidal decompositions. Convex polytopes. Voronoi diagrams. Configuration spaces. Tail estimates. 4. Dynamic Algorithms. trapezoidal decompositions. Voronoi diagrams. History and configuration spaces. Rebuilding history. Deletions in history. Dynamic shuffling. 5. Random Sampling. Configuration spaces with bounded valence. Top-down sampling. Bottom-up sampling. Dynamic sampling. Average conflict size. More dynamic algorithms. Range spaces and E-nets. Comparisons. II. APPLICATIONS. 6. Arrangements of Hyperplanes. Incremental construction. Zone Theorem. Canonical triangulations. Point location and ray shooting. Point location and range queries. 7. Convex Polytopes. Linear Programming. The number of faces. Incremental construction. The expected structural and conflict change. Dynamic maintenance. Voronoi diagrams. Search problems. Levels and Voronoi diagrams of order k. 8. Range Search. Orthogonal intersection search. Nonintersecting segments in the plane. Dynamic point location. Simplex range search. Half-space range queries. Decomposable search problems. Parametric search. 9. Computer Graphics. Hidden surface removal. Binary Space Partitions. Moving viewpoint. 10. How Crucial Is Randomness? Pseudo-random sources. Derandomization. Appendix: Tail Estimates. Chernoff's technique. Chebychev's technique. Bibliography. Index.
  • (source: Nielsen Book Data)9780133363630 20160527
This introduction to computational geometry is designed for beginners. It emphasizes simple randomized methods, developing basic principles with the help of planar applications, beginning with deterministic algorithms and shifting to randomized algorithms as the problems become more complex. It also explores higher dimensional advanced applications and provides exercises.
(source: Nielsen Book Data)9780133363630 20160527
SAL3 (off-campus storage)
Book
xvii, 393 p. : ill. ; 24 cm.
Often a solution to a problem lies simply in uncovering its correct description. It is this underlying concept that consolidates the text of this survey of geometric ideas. The aim of this book is to provide a way in which to visualize a variety of geometric problems and present the tools for their accurate representation. Disassociating fundamental ideas and methods from special applications, they clarify these concepts for the reader and allow for applying the material to other problems of a geometric nature. They also provide a foundation of applied geometry as used in geometric design and geometric modelling.
(source: Nielsen Book Data)9781568810041 20160528
SAL3 (off-campus storage)
Book
vii, 492 p. : ill. ; 27 cm.
SAL3 (off-campus storage)
Book
156 p.
Computational geometry concerns itself with designing andanalyzing algorithms for solving geometric problems. Thefield has reached a high level of sophistication, and verycomplicated algorithms have been designed. However, it isalso useful to develop more practical algorithms, so long asthey are based on rigorous methods. One such method is theuse of randomized algorithms. These algorithms have becomemore and more popular, turning into one of the hottest areasof recent years. Dynamic algorithms are particularlyinteresting because in practice the data of a problem areoften acquired progressively. In this monograph the authorstudies the theoretical complexity and practical efficiencyof randomized dynamic algorithms.
(source: Nielsen Book Data)9783540575030 20160528
dx.doi.org SpringerLink
SAL3 (off-campus storage)

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