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 Hegarty, James Steven (Author)
 201006
 Description
 Book
 Summary

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 quadfragment merging, which reduces redundant shading work by buffering and selectively merging rasterized fragments prior to shading. The prototype quadfragment merger is described in detail, and evidence is presented that it is amenable to implementation in fixedfunction 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.
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 quadfragment merging, which reduces redundant shading work by buffering and selectively merging rasterized fragments prior to shading. The prototype quadfragment merger is described in detail, and evidence is presented that it is amenable to implementation in fixedfunction 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.  Collection
 Undergraduate Theses, School of Engineering
 Bayro Corrochano, Eduardo.
 London ; New York : Springer, c2010.
 Description
 Book — xxviii, 622 p. : ill. (some col.) ; 24 cm.
 Summary

 Part I: Fundamentals of Geometric Algebra Introduction to Geometric Algebra Geometric Algebra for Modeling in Robot Physics Part II: Euclidean, PseudoEuclidean, 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 BodySensors Calibration Tracking, Grasping and Object Manipulation 3D Maps, Navigation and Relocalization Modeling and Registration of Medical Data Part VII: Appendix.
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(source: Nielsen Book Data) 9781848829282 20160605
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3. Linear geometry with computer graphics [1993]
 Loustau, John, 1943
 New York : Marcel Dekker, ©1993.
 Description
 Book — x, 440 pages : illustrations ; 24 cm + 1 computer disc (3 1/2 in.).
 Summary

 Part 1 Preliminaries: fields vector spaces linear transformations cosets of a vector space invariant subspaces.
 Part 2 Symmetric bilinear forms: symmetric bilinear forms congruence orthogonal complements orthogonal bases Witt's cancellation theorem isotropic and anisotropic spaces functions on inner product spaces.
 Part 3 Plane geometries: the affine plane the affine group postulates for the Euclidean plane inner product planes projective planes conic sections.
 Part 4 Homogeneous spaces in Rn: topological groups homogeneous spaces geometry on homogeneous spaces the Riemann sphere the Poincare upper halfplane differentiable manifolds.
 Part 5 Topics in computer graphics: a first graphics programme a computer graphics system overview geometric mappings in a CG system the linedrawing algorithm the wingedge object representation the conic sections Bezier curves and Bsplines hidden surface removal texture mapping quadric intermediate surfaces Koch systems. Appendices: equivalence relations  basics the Jordan canonical form  proof of Jordan's theorem GraphLib documentation  types, procedures and functions.
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(source: Nielsen Book Data) 9780824788988 20160528
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QA448 .D38 L68 1993  Available 
 Washington, D.C. : United States. Dept. of Energy. ; Oak Ridge, Tenn. : distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2006
 Description
 Book — 1 online resource (108 p. ) : digital, PDF file.
 Summary

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.
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 Washington, D.C. : United States. Dept. of Energy. ; Oak Ridge, Tenn. : distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2004
 Description
 Book — 1 online resource (50 p. ) : digital, PDF file.
 Summary

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 asis 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 MPIbased 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 ACISbased engine is available to ACIS licensees on request.
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 Cox, David A.
 New York : SpringerVerlag, ©1992.
 Description
 Book — xi, 513 pages : illustrations ; 25 cm.
 Summary

 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.
(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
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QA564 .C688 1992  Available 
 EGC 2011 (2011 : Spain)
 Heidelberg ; New York : Springer, c2012.
 Description
 Book — 1 online resource (x, 281 p.)
 Summary

 On 5Gons and 5Holes. On Reversibility among Parallelohedra. A History of Flips in Combinatorial Triangulations. Open Guard Edges and Edge Guards in Simple Polygons. StringWrapped 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 1Center and 1Highway 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. StringWrapped 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 1Center and 1Highway 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.
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(source: Nielsen Book Data) 9783642341908 20160609
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8. Discrete and computational geometry [2011]
 Devadoss, Satyan L., 1973
 Princeton, N.J. : Princeton University Press, c2011.
 Description
 Book — xi, 255 p. : col. ill. ; 27 cm.
 Summary

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applicationsdriven 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 cuttingedge 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 realworld 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 fullcolor 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 email: Vickie_Kearn@press.princeton.edu.
(source: Nielsen Book Data) 9780691145532 20160609
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QA448 .D38 D48 2011  Unknown 
 Rovenskii, Vladimir Y., 1953
 New York : Springer, c2010.
 Description
 Book — xv, 452 p. : ill. ; 27 cm.
 Summary

 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)
(source: Nielsen Book Data) 9780387712772 20160604
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QA448 .D38 R69 2010  Unknown 
 3rd ed.  Berlin : Springer, c2008.
 Description
 Book — xii, 386 p. : ill. ; 25 cm.
 Summary

 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: NonUniform Mesh Generation. Visibility Graphs: Finding the Shortest Route. Simplex Range Searching: Windowing Revisited. Bibliography. Index.
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(source: Nielsen Book Data) 9783540779735 20160528
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QA448 .D38 C65 2008  Unknown 
 3rd ed.  Berlin : Springer, c2008.
 Description
 Book — xii, 386 p. : ill.
12. Computational line geometry [2001]
 Pottmann, Helmut.
 Berlin ; New York : Springer, 2001.
 Description
 Book — ix, 563 p. : ill. ; 24 cm.
 Summary

 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.
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(source: Nielsen Book Data) 9783540420583 20160528
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QA608 .P68 2001  Unknown 
 2nd, rev. ed.  Berlin ; New York : Springer, c2000.
 Description
 Book — xii, 367 p. : ill. ; 25 cm.
 Summary

 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: NonUniform Mesh Generation. Visibility Graphs: Finding the Shortest Route. Simplex Range Searching: Windowing Revisited. Bibliography. Index.
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(source: Nielsen Book Data) 9783540656203 20160527
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QA448 .D38 C65 2000  Unknown 
QA448 .D38 C65 2000  Unknown 
14. Algorithmic geometry [1998]
 Géometrie algorithmique. English
 Boissonnat, J.D. (JeanDaniel), 1953
 Cambridge, U.K. ; New York : Cambridge University Press, 1998.
 Description
 Book — xx, 519 p. : ill. ; 26 cm.
 Summary

 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. NonEuclidean metrics
 19. Diagrams in the plane References Notation Index.
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(source: Nielsen Book Data) 9780521563222 20160528
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QA448 .D38 B6513 1998  Unknown 
 Berlin ; New York : Springer, c1997.
 Description
 Book — xii, 365 p. : ill. ; 25 cm.
 Summary

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
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QA448 .D38 C65 1997  Unknown 
 Berlin ; New York : Springer, c1996.
 Description
 Book — viii, 222 p. : ill. ; 24 cm.
 Summary

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 stateoftheart 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
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QA448 .D38 A635 1996  Available 
 Canadian Conference on Computational Geometry (7th : 1995 : Québec, Québec)
 Quebec : Universite Laval, 1995.
 Description
 Book — 1 v.
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QA447 .C36 1995  Available 
 Mulmuley, Ketan.
 Englewood Cliffs, N.J. : PrenticeHall, 1994.
 Description
 Book — xv, 447 p.
 Summary

 I. BASICS.
 1. Quicksort and Search. Quicksort. Another view of quicksort. 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. Topdown sampling. Bottomup sampling. Dynamic sampling. Average conflict size. More dynamic algorithms. Range spaces and Enets. 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. Halfspace range queries. Decomposable search problems. Parametric search.
 9. Computer Graphics. Hidden surface removal. Binary Space Partitions. Moving viewpoint.
 10. How Crucial Is Randomness? Pseudorandom sources. Derandomization. Appendix: Tail Estimates. Chernoff's technique. Chebychev's technique. Bibliography. Index.
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(source: Nielsen Book Data) 9780133363630 20160527
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QA448 .D38 M85 1994  Available 
19. Geometric concepts for geometric design [1994]
 Boehm, Wolfgang, 1928
 Wellesley, Mass. : A.K. Peters, c1994.
 Description
 Book — xvii, 393 p. : ill. ; 24 cm.
 Summary

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
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QA445 .B63 1994B  Available 
 Canadian Conference on Computational Geometry (5th : 1993 : University of Waterloo, Waterloo, Ontario)
 [Waterloo? : s.n., 1993?]
 Description
 Book — vii, 492 p. : ill. ; 27 cm.
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QA447 .C36 1993  Available 
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