Theoretical Foundations of Computer Graphics and CAD

Front Matter....Pages I-18
Front Matter....Pages 19-19
Geometric data structures for computer graphics: an overview....Pages 21-49
An Overview of Quadtrees, Octrees, and Related Hierarchical Data Structures....Pages 51-68
Front Matter....Pages 69-69
Computational Geometry — Then and Now....Pages 71-109
Ruler, Compass and Computer....Pages 111-165
Computational geometry on a grid an overview....Pages 167-184
Geometric Computing Environments:....Pages 185-197
Algorithms for High Dimensional Stabbing Problems....Pages 199-210
The Representation and Manipulation of Convex Polygons....Pages 211-252
Davenport-Schinzel Sequences and their Geometric Applications....Pages 253-278
A New Point Containment Algorithm for B_Regions in the Discrete Plane....Pages 279-306
Reporting and Counting Intersections Between Two Sets of Line Segments....Pages 307-325
Front Matter....Pages 327-327
Anomalies in Incremental Line Rastering....Pages 329-358
Hardware aspects of algorithm generation....Pages 359-379
The High Precision DDA for Ellipse-Generatiom....Pages 381-396
Grid Geometries Which Preserve Properties of Euclidean Geometry: A Study of Graphics Line Drawing Algorithms....Pages 397-432
Front Matter....Pages 433-433
New Mathematics for Computer Graphics....Pages 435-448
Specification, Derivation and Verification of Concurrent Line Drawing Algorithms and Architectures....Pages 449-516
A Model for Graphical Interaction....Pages 517-541
Formal Specification of Graphics Software....Pages 543-574
The Visible Surface Problem Under Abstract Graphic Models....Pages 575-586
Front Matter....Pages 433-433
A family of algorithms for generating discrete embeddings of continuous objects....Pages 587-597
Node Placement Algorithms to Display Communications Topology to Network Controllers....Pages 599-616
Front Matter....Pages 617-617
Geometry and Graphics Applied to Robotics....Pages 619-638
Some Collision Avoidance Problems in the Plane....Pages 639-672
Front Matter....Pages 673-673
An Introduction to Pixel-planes and other VLSI-Intensive Graphics Systems....Pages 675-688
CUBE — An Architecture Based on a 3D Voxel Map....Pages 689-701
Distributed Ray Tracing Using an SIMD Processor Array....Pages 703-725
Fine Grain Parallel Architectures and the Creation of High-Quality Images....Pages 727-754
Front Matter....Pages 755-755
Béziers and B-splines as Multiaffine Maps....Pages 757-776
Smoothing Digitized Contours....Pages 777-793
Efficient Raster-Graphing of Bivariate Functions by Incremental Methods....Pages 795-803
A Simple, General Method for Ray Tracing Bicubic Surfaces....Pages 805-820
Spline Curve Fitting for an Interactive Design Environment....Pages 821-832
Approximation of Digitized Contours....Pages 833-855
The Circle-Brush Algorithm....Pages 857-878
Front Matter....Pages 879-879
The role of different levels of modelling in CAD systems....Pages 881-898
The Problem of Form Feature Classification and Recognition in CAD/CAM....Pages 899-918
Representation and Extraction of Shape Features in a Solid Model....Pages 919-940
Relational Algebra, Relational Calculus and Computational Solid Geometry....Pages 941-951
Industrial Design Based on Geometric Intentions....Pages 953-963
Front Matter....Pages 965-965
Constructing 3D Objects from 2D Information....Pages 967-996
Ray Tracing Algorithms — Theory and Practice....Pages 997-1030
Representation of 3D objects, reconstructed from series of parallel 2D slices....Pages 1031-1038
An Introduction to Ray Tracing....Pages 1039-1060
Front Matter....Pages 1061-1061
The use of Modularity and Configurability in the Comparison of Graphics Systems Designs....Pages 1063-1081
Definitive Principles for Interactive Graphics....Pages 1083-1097
Algorithms and Data Structures for Windowing on Raster Graphics Devices....Pages 1099-1108
A Relational Database Interface to a GKS Like Graphics Package....Pages 1109-1118
Front Matter....Pages 1119-1119
Models and Tools for the Designers of User-Computer Interfaces....Pages 1121-1151
Graphics, Design and Artificial Intelligence....Pages 1153-1174
Front Matter....Pages 1175-1175
Image Analysis and Graphics....Pages 1177-1195
Computer Image Generation Using Elementary Functions Matched to Human Vision....Pages 1197-1241
Back Matter....Pages 1243-1244