Lehrveranstaltungsinhalt aus - Institute for Computer Graphics and ...
Lehrveranstaltungsinhalt aus - Institute for Computer Graphics and ...
Lehrveranstaltungsinhalt aus - Institute for Computer Graphics and ...
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CONTENTS 7<br />
9.19.1 Presenting a Curve by Samples <strong>and</strong> an Interpolation Scheme . . . . . . . . 182<br />
9.19.2 Parametric Representations of Curves . . . . . . . . . . . . . . . . . . . . . 183<br />
9.19.3 Introducing Piecewise Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
9.19.4 Rearranging Entities of the Vector Function Q . . . . . . . . . . . . . . . . 183<br />
9.19.5 Showing Examples: Three methods of Defining Curves . . . . . . . . . . . . 184<br />
9.19.6 Hermite’s Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184<br />
9.20 Bezier’s Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184<br />
9.21 Subdividing Curves <strong>and</strong> Using Spline Functions . . . . . . . . . . . . . . . . . . . . 185<br />
9.22 Generalization to 3 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187<br />
9.23 Graz <strong>and</strong> Geometric Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187<br />
10 Data Structures 195<br />
10.1 Two-Dimensional Chain-Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195<br />
10.2 Two-Dimensional Polygonal Representations . . . . . . . . . . . . . . . . . . . . . 196<br />
10.3 A Special Data Structure <strong>for</strong> 2-D Morphing . . . . . . . . . . . . . . . . . . . . . . 197<br />
10.4 Basic Concepts of Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 197<br />
10.5 Quadtree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198<br />
10.6 Data Structures <strong>for</strong> Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199<br />
10.7 Three-Dimensional Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200<br />
10.8 The Wire-Frame Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200<br />
10.9 Operations on 3-D Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201<br />
10.10Sweep-Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201<br />
10.11Boundary-Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201<br />
10.12A B-Rep Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202<br />
10.13Spatial Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202<br />
10.14Binary Space Partitioning BSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203<br />
10.15Constructive Solid Geometry, CSG . . . . . . . . . . . . . . . . . . . . . . . . . . . 204<br />
10.16Mixing Vectors <strong>and</strong> Raster Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205<br />
10.17Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205<br />
11 3-D Objects <strong>and</strong> Surfaces 211<br />
11.1 Geometric <strong>and</strong> Radiometric 3-D Effects . . . . . . . . . . . . . . . . . . . . . . . . 211<br />
11.2 Measuring the Surface of An Object (Shape from X) . . . . . . . . . . . . . . . . . 211<br />
11.3 Surface Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213<br />
11.4 Representing 3-D Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214<br />
11.5 The z-Buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215<br />
11.6 Ray-tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216<br />
11.7 Other Methods of Providing Depth Perception . . . . . . . . . . . . . . . . . . . . 218
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