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| Preface | |
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| Introduction to Computer Graphics | |
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| What is Computer Graphics? | |
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| Where Computer Generated Pictures are Used | |
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| Art, Entertainment, and Publishing | |
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| Computer Graphics and Image Processing | |
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| Monitoring a Process | |
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| Displaying Simulations | |
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| Computer-aided Design | |
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| Scientific Analysis and Visualization | |
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| Elements of Pictures created in Computer Graphics | |
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| Polylines | |
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| Text | |
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| Filled Regions | |
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| Raster Images | |
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| Representation of Gray Shades and Color for Raster Graphics | |
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| Graphics Display Devices | |
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| Line Drawing Displays | |
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| Raster Displays | |
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| Indexed Color and the LUT | |
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| Other Raster Display Devices | |
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| Hard Copy Raster Devices | |
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| Graphics Input Primitives and Devices | |
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| Types of Input Graphics Primitives | |
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| Types of Physical Input Devices | |
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| Summary | |
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| Further Reading | |
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| Getting Started Drawing Figures | |
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| Getting Started Making Pictures | |
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| Device-independent Programming, and OpenGL | |
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| Windows-based Programming | |
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| Opening a Window for Drawing | |
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| Drawing Basic Graphics Primitives | |
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| Examples of Drawing Dot Constellations | |
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| Making Line Drawings | |
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| Drawing Polylines and Polygons | |
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| Line Drawing using moveto() and lineto() | |
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| Drawing Aligned Rectangles | |
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| Aspect Ratio of an Aligned Rectangle | |
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| Filling Polygons | |
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| Other Graphics Primitives in OpenGL | |
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| Simple Interaction with the Mouse and Keyboard | |
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| Mouse Interaction | |
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| Keyboard Interaction | |
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| More Drawing Tools | |
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| Introduction | |
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| World Windows and Viewports | |
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| The Mapping from the Window to the Viewport | |
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| Setting the Window and Viewport Automatically | |
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| Clipping Lines | |
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| Clipping a Line | |
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| The Cohen-Sutherland Clipping Algorithm | |
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| Developing the Canvas Class | |
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| Some useful Supporting Classes | |
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| Declaration of Class Canvas | |
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| Implementation of Class Canvas | |
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| Relative Drawing | |
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| Developing moveRel() and lineRel() | |
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| TurtleGraphics | |
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| Figures Based on Regular Polygons | |
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| The Regular Polygons | |
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| Variations on n-Gons | |
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| Drawing Circles and Arcs | |
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| Drawing arcs | |
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| Using the Parametric Form of a Curve | |
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| Parametric Forms for Curves | |
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| Drawing Curves Represented Parametrically | |
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| Superellipses | |
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| Polar Coordinate Shapes | |
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| 3D Curves | |
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| Vector Tools for Graphics | |
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| Introduction | |
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| Review of Vectors | |
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| Operations with Vectors | |
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| Linear Combinations of Vectors | |
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| The Magnitude of a Vector, and Unit Vectors | |
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| The Dot Product | |
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| Properties of the Dot Product | |
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| The Angle Between two Vectors | |
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| The Sign of b-c; Perpendicularity | |
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| The 2D "Perp" Vector | |
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| Orthogonal Projections, and the Distance from a Point to a Line | |
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| Applications of Projection: Reflections | |
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| The Cross Product of Two Vectors | |
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| Geometric Interpretation of the Cross Product | |
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| Finding the Normal to a Plane | |
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| Representations of Key Geometric Objects | |
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| Coordinate Systems and Coordinate Frames | |
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| Affine Combinations of Points | |
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| Linear Interpolation of Two Points | |
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| "Tweening" for Art and Animation | |
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| Preview: Quadratic and Cubic Tweening, and Bezier Curves | |
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| Representing Lines and Planes | |
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| Finding the Intersection of Two Line Segments | |
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| Application of Line Intersections: the Circle Through Three Points | |
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| Intersections of Lines with Planes, and Clipping | |
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| Polygon Intersection Problems | |
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| Working with Convex Polygons and Polyhedra | |
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| Ray Intersections and Clipping for Convex Polygons | |
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| The Cyrus-Beck Clipping Algorithm | |
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| Clipping against Arbitrary Polygons | |
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| More Advanced Clipping | |
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| Transformations of Objects | |
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| Introduction | |
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| Introduction to Transformations | |
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| Transforming Points and Objects | |
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| The Affine Transformations | |
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| Geometric Effects of elementary 2D Affine Transformations | |
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| The Inverse of an Affine Transformation | |
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| Composing Affine Transformations | |
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| Examples of Composing 2D Transformations | |
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| Some Useful Properties of Affine Transformations | |
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| 3D Affine Transformations | |
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| The Elementary 3D Transformations | |
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| Composing 3D Affine Transformations | |
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| Combining Rotations | |
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| Summary of Properties of 3D Affine Transformations | |
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| Changing Coordinate Systems | |
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| Using Affine Transformations in a Program | |
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| Saving the CT for Later Use | |
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| Drawing 3D Scenes with OpenGL | |
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| An Overview of the Viewing Process and the Graphics Pipeline | |
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| Some OpenGL tools for Modeling and Viewing | |
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| Drawing Elementary Shapes Provided by OpenGL | |
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| Reading a Scene Description from a File | |
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| Modeling Shapes with Polygonal Meshes | |
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| Introduction | |
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| Introduction to Solid Modeling with Polygonal Meshes | |
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| Defining a Polygonal Mesh | |
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| Finding the Normal Vectors | |
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| Properties of Meshes | |
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| Mesh Models for Nonsolid Objects | |
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| Working with Meshes in a Program | |
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| Polyhedra | |
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| Prisms and Antiprisms | |
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| The Platonic Solids | |
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| Other Interesting Polyhedra | |
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| Extruded Shapes | |
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| Creating Prisms | |
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| Arrays of Extruded Prisms: "Bricklaying" | |
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| Extrusions with a "Twist" | |
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| Building Segmented Extrusions: Tubes and Snakes | |
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| "Discretely" Swept Surfaces of Revolution | |
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| Mesh Approximations to Smooth Objects | |
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| Representations for Surfaces | |
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| The Normal Vector to a Surface | |
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| The Effect of an Affine Transformation | |
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| Three "Generic" Shapes: the Sphere, Cylinder, and Cone | |
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| Forming a Polygonal Mesh for a Curved Surface | |
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| Ruled Surfaces | |
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| Surfaces of Revolution | |
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| The Quadric Surfaces | |
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| The Superquadrics | |
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| Tubes Based on 3D Curves | |
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| Surfaces Based on Explicit Functions of Two Variables | |
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| Three-Dimensional Viewing | |
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| Introduction | |
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| The Camera Revisited | |
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| Setting the View Volume | |
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| Positioning and Pointing the Camera | |
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| Building a Camera in a Program | |
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| "Flying" the Camera | |
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| Perspective Projections of 3D Objects | |
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| Perspective Projection of a Point | |
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| Perspective Projection of a Line | |
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| Incorporating Perspective in the Graphics Pipeline | |
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| Producing Stereo Views | |
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| Taxonomy of Projections | |
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| One-, Two-, and Three-Point Perspective | |
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| Types of Parallel Projections | |
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| Rendering Faces for Visual Realism | |
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| Introduction | |
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| Introduction to Shading Models | |
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| Geometric Ingredients for Finding Reflected Light | |
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| Computing the Diffuse Component | |
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| Specular Reflection | |
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| The Role of Ambient Light | |
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| Combining Light Contributions | |
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| Adding Color | |
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| Shading and the Graphics Pipeline | |
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| Using Light Sources in OpenGL | |
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| Working with Material Properties in OpenGL | |
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| Shading of Scenes Specified by SDL | |
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| Flat Shading and Smooth Shading | |
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| Flat Shading | |
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| Smooth Shading | |
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| Removing Hidden Surfaces | |
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| The Depth Buffer Approach | |
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| Adding Texture to Faces | |
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| Pasting the Texture onto a Flat Surface | |
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| Rendering the Texture | |
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| What Does a Texture Modulate? | |
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| A Texture Example Using OpenGL | |
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| Wrapping Texture on Curved Surfaces | |
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| Reflection Mapping | |
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| Adding Shadows of Objects | |
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| Shadows as Texture | |
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| Creating Shadows with the Use of a Shadow Buffer | |
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| Approaches to Infinity | |
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| Introduction | |
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| Fractals and Self-Similarity | |
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| Successive Refinement of Curves | |
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| Drawing Koch Curves and Snowflakes | |
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| Fractional Dimension | |
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| String Production and Peano Curves | |
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| Producing Recursively and Drawing in a Program | |
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| Allowing Branching | |
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| Tiling the Plane | |
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| Monohedral Tilings | |
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| Dihedral Tilings | |
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| Drawing Tilings | |
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| Reptiles | |
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| Creating an Image by Means of Iterated Functions Systems | |
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| An Experimental Copier | |
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| Some Underlying theory of the Copying Process | |
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| Drawing the k-th Iterate | |
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| The Chaos Game | |
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| Finding the IFS, Fractal Image Compression | |
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| The Mandelbrot Set | |
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| Mandelbrot Sets and Iterated Functions Systems | |
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| Defining the Mandelbrot Set | |
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| Computing whether the point c is in the Mandelbrot Set | |
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| Drawing the Mandelbrot Set | |
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| Some Notes on the Mandelbrot Set | |
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| Julia Sets | |
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| The Filled-in Julia Set K[subscript c] | |
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| Drawing Filled-in Julia Sets | |
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| Some Notes on Fixed points and Basins of Attraction | |
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| The Julia Set J[subscript c] | |
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| Random Fractals | |
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| Fractalizing a Segment | |
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| Controlling the Spectral Density of the Fractal Curve | |
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| Tools for Raster Displays | |
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| Introduction | |
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| Manipulating Pixmaps | |
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| Operations of Interest for Pixmaps | |
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| Useful Data Types for Pixmaps | |
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| Scaling and Rotating Images | |
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| Combining Pixmaps | |
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| The Read-Modify-Write Cycle | |
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| The Alpha Channel and Image Blending | |
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| Logical Combinations of Pixmaps | |
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| The BitBlt operation | |
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| Do-It-Yourself Line Drawing: Bresenham's Algorithm | |
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| Bresenham's Line-Drawing Algorithm | |
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| Defining and Filling Regions of Pixels | |
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| Defining Regions | |
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| Pixel-Defined Regions | |
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| A Recursive Flood-Fill Algorithm | |
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| Filling Regions with Patterns | |
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| Using Coherence: Region Filling Based on Runs of Pixels | |
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| Manipulating Symbolically Defined Reigions | |
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| Rectangle-defined Regions | |
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| Path-defined Regions | |
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| Filling Polygon-Defined Regions | |
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| Which Pixels on an Edge Belong to a Polygon? | |
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| Improving the Algorithm's Performance | |
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| Aliasing; Antialiasing Techniques | |
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| Antialiasing Techniques | |
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| Antialiasing of Texture | |
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| Antialiasing Using OpenGL | |
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| Creating More Shades and Colors | |
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| Ordered Dither | |
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| Error Diffusion | |
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| Curve and Surface Design | |
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| Introduction | |
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| Parametric Curves as Trajectories | |
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| Smoothness of Motion | |
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| Describing Curves by Means of Polynomials | |
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| On Interactive Curve Design | |
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| Bezier Curves for Curve Design | |
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| The de Casteljau Algorithm | |
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| Properties of Bezier Curves | |
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| Finding Better Blending Functions | |
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| The Problem of Local Control | |
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| Wish List for a Set of Blending Functions | |
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| Piecewise Polynomial Curves and Splines | |
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| Building a set of Blending Functions Out of g(t) | |
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| Spline Curves and Basis Functions | |
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| The B-Spline Basis Functions | |
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| Definition of B-Spline Functions | |
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| Using Multiple Knots in the Knot Vector | |
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| Open B-Spline Curves: Standard Knot Vector | |
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| Useful Properties of B-Spline Curves for Design | |
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| Using Multiple Control Points | |
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| Rational Splines and NURBS Curves | |
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| A Glimpse at Interpolation | |
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| Interpolation Using Piecewise Cubic Polynomials | |
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| Hermite Interpolation | |
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| The Natural Cubic Spline | |
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| Computing the Slopes in Cubic Interpolation | |
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| Specifying the Tangent Vectors Interactively | |
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| Modeling Curved Surfaces | |
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| Ruled Surfaces Based on B-Splines | |
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| Surfaces of Revolution Based on B-Splines | |
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| Bezier Surface Patches | |
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| Patching Together Bezier Patches | |
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| B-Spline Patches | |
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| NURBS Surfaces | |
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| Color Theory | |
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| Introduction | |
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| Describing Colors | |
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| Dominant Wavelength | |
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| Color Matching | |
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| The International Commission on Illumination Standard | |
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| Constructing the CIE Chart | |
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| Using the CIE Chromaticity Diagram | |
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| Color Gamuts | |
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| Color Spaces | |
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| The RGB and CMY Color Spaces | |
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| Additive and Subtractive Color Systems | |
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| The HLS Color Model | |
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| Color Quantization | |
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| Uniform Quantization | |
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| The Popularity Algorithm | |
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| The Median-cut Algorithm | |
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| Octree Quantization | |
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| Hidden Surface Removal | |
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| Introduction | |
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| Object Precision versus Image Precision Approaches | |
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| Description of the Polygon Mesh Data | |
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| The Depth Buffer Algorithm Revisited | |
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| List Priority HSR Methods | |
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| The Heedless Painter's Algorithm | |
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| HSR Using Binary Space Partition Trees | |
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| The Depth Sort Algorithm | |
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| A Scan-Line HSR Method | |
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| Area Subdivision Approaches | |
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| Quadrant Subdivision | |
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| Other Definitions of a Simple Region | |
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| On Hidden Line Removal Methods | |
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| The Geometric Testing in edgeTest() | |
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| HSR Methods for Curved Surfaces | |
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| Ray Tracing | |
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| Introduction | |
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| Setting Up the Geometry of Ray Tracing | |
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| Overview of the Ray-Tracing Process | |
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| Intersection of a Ray with an Object | |
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| Intersection of a Ray with a Generic Plane | |
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| Intersection with a Generic Sphere | |
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| Intersection of the Ray with Transformed Objects | |
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| Organizing a Ray Tracer Application | |
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| A Routine to Compute Ray-Sphere Intersections | |
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| A Complete Ray Tracer for Emissive-Sphere Scenes | |
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| Intersecting Rays with Other Primitives | |
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| Intersecting with a Square | |
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| Intersecting with a Tapered Cylinder | |
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| Intersecting with a Cube (or any Convex Polyhedron) | |
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| Adding More Primitives | |
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| Drawing Shaded Pictures of Scenes | |
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| Finding the Normal at the Hit Spot | |
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| Coloring Objects According to their Surface Materials | |
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| Physically-based Shading Models: Cook-Torrance Shading | |
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| Adding Surface Texture | |
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| Solid Texture | |
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| Pasting Images onto Surfaces | |
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| Antialiasing Ray Tracings | |
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| Using Extents | |
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| Box and Sphere Extents | |
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| Using Projection Extents | |
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| Adding Shadows for Greater Realism | |
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| Reflections and Transparency | |
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| The Refraction of Light | |
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| Dealing with Refraction in shade() | |
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| Compound Objects: Boolean Operations on Objects | |
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| Ray Tracing CSG Objects | |
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| Data Structure for Boolean Objects | |
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| Intersecting Rays with Boolean Objects | |
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| Building and Using Extents for CSG Objects | |
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| Appendixes | |
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| Graphics Tools - Obtaining OpenGL | |
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| Obtaining and Installing OpenGL | |
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| Some Mathematics for Computer Graphics | |
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| Some Key Definitions for Matrices and their Operations | |
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| Some Properties of Vectors and their Operations | |
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| The Arithmetic of Complex Numbers | |
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| Spherical Coordinates and Direction Cosines | |
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| Some Useful Classes and Utility Routines | |
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| Classes for 2D Graphis | |
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| RGBPixmap Class | |
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| The Scene and Supporting Classes | |
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| Noise Class | |
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| Some Classes that are Useful for Ray Tracing | |
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| An Introduction to PostScript | |
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| About the PostScript Language | |
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| Graphics Operators in PostScript | |
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| Drawing Text in PostScript | |
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| Defining New Variables and Procedures | |
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| Decisions and Iterations | |
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| Printing Values | |
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| Drawing Gray-scale Image | |
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| An Introduction to SDL | |
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| Syntax of SDL | |
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| Macros in SDL | |
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| Extending SDL | |
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| References | |
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| Index | |