Image Synthesis

1. Images.- 1.1. Images and communication.- 1.1.1. Speaking.- 1.1.2. Writing.- 1.1.3. Images.- 1.1.4. Discourse, image, and computer.- 1.2. Visual perception.- 1.2.1. Thought and vision.- 1.2.2. The mechanisms of photoreception.- 1.2.3. The optical paths.- 1.2.4. The treatment of visual information.- 1.2.5. Multiplexing of sensorial messages.- 1.3. Different aspects of images.- 1.3.1. Attempt to define the concept of an image.- 1.3.2. Physical images.- 1.3.3. Psychic images.- 1.3.4. The particular status of numerical images.- 2. Numerical images.- 2.1. Image and computer.- 2.1.1. Images as memory.- 2.1.1.1. Psychic images and memory.- 2.1.1.2. Encoding and decoding of images.- 2.1.2. Representations.- 2.1.2.1. Analogue representation.- 2.1.2.2. Numerical representation.- 2.1.3. Numerical (digital) images.- 2.1.3.1. Screen memory.- 2.1.3.2. Vector memory.- 2.2. The graphical peripherals.- 2.2.1. Central unit and peripherals.- 2.2.2. Graphical output peripherals.- 2.2.2.1. History.- 2.2.2.2. Printers, tape and card punchers.- 2.2.2.3. Plotters.- 2.2.2.4. Cathode ray tubes.- 2.2.2.5. COMs.- 2.2.2.6. Flat screens.- 2.2.2.7. Laser techniques.- 2.2.3. Peripherals of graphics processing.- 2.2.3.1. The optical pen.- 2.2.3.2. Data tablet.- 2.2.3.3. Mouse.- 2.2.3.4. Digitizers of images.- 2.2.3.5. Others.- 2.2.4. Interaction.- 2.3. Cathode ray tubes.- 2.3.1. History.- 2.3.2. Principles of functioning.- 2.3.3. Scanning modes.- 2.3.4. Graphics processor.- 2.3.5. Tubes with free scanning.- 2.3.6. Tubes with memory (or with image preservation).- 2.3.7. Tubes with recurrent scanning.- 2.3.8. Color screens.- 2.3.9. Linearization of the intensity levels.- 2.3.10. Look up tables.- 2.3.10.1. Principle.- 2.3.10.2. Applications.- 2.3.10.3. Digitizers of images.- 2.4. Flat screens.- 2.5. The programming of graphics processors.- 3. Modelling problems.- 3.1. Image and formalism.- 3.1.1. Image and model.- 3.1.2. The computer as a tool of creation.- 3.1.3. The different levels of description.- 3.2. The modelling of images.- 3.2.1. Processing of a numerical image.- 3.2.2. Synthesis.- 3.2.3. Abstract plane images.- 3.2.4. Figurative plane images.- 3.2.5. Three-dimensional images.- 3.2.6. Realistic images.- 3.3. Constructive geometry.- 3.3.1. Modular structures.- 3.3.2. Euler operators.- 3.3.3. Applications.- 3.4. Polyhedral models.- 3.4.1. Polyhedral approximation of a curved surface.- 3.4.1.1. Modelling by means of facets.- 3.4.1.2. Triangulation methods.- 3.4.2. Data structures associated with polyhedral descriptions.- 3.4.3. Domains of applications.- 3.5. Curves and surfaces.- 3.5.1. Graphical primitives.- 3.5.2. Generating plane curves.- 3.5.2.1. Polygonal approximations.- 3.5.2.2. Reduction of numerical plane curves.- 3.5.3. Parametic curves and surfaces.- 3.5.3.1. Cubics.- 3.5.3.2. Coons’ surfaces.- 3.5.3.3. Bezier curves and surfaces.- 3.5.3.4. B-spline curves and surfaces.- 3.5.3.5. Beta-splines.- 3.5.4. The visualization of curves and surfaces.- 3.6. Fractal objects.- 3.6.1. Fractal objects according to Benoit Mandelbrot.- 3.6.1.1. Continuity and reality.- 3.6.1.2. The concept of dimension.- 3.6.1.3. Measure.- 3.6.1.4. The concept of an internal homothety.- 3.6.1.5. Homothety dimension.- 3.6.1.6. Stochastic models.- 3.6.1.7. Terrain models.- 3.6.2. Algorithms for the generation of three-dimensional fractal objects.- 3.6.2.1. Numerical images and fractal dimension.- 3.6.2.2. Iteration of functions.- 3.6.2.3. Stochastic models.- 3.6.2.4. Stochastic primitives.- 3.6.2.5. Stochastic movement.- 3.7. Systems of particles.- 3.7.1. The modeling of unsharp objects.- 3.7.2. Systems of particles.- 3.7.3. Application to the modelling of fire and explosions.- 3.8. Modelling waves.- 3.8.1. Explanation of the problem.- 3.8.2. Peachey’s model.- 3.8.3. The model of Fournier and Reeves.- 3.9. The synthesis of fabrics.- 3.9.1. Explanation of the problem.- 3.9.2. Weil’s model.- 3.9.2.1. The conditions.- 3.9.2.2. Approximation of the surface.- 3.9.2.3. Iterative approximation.- 3.10. The modelling of shells and plants.- 3.10.1. Explanation of the problem.- 3.10.2. Kawaguchi and the sea.- 3.10.3. Plants and formal languages.- 3.10.4. Tree-like models of plants.- 3.10.5. AMAP.- 4. Problems of visualization.- 4.1. The visualization of numerical images.- 4.1.1. Numerical images.- 4.1.2. Coding numerical images.- 4.1.2.1. Run-length coding.- 4.1.2.2. Coding according to Freeman.- 4.1.2.3. Coding by means of quaternary trees.- 4.2. 2D-images.- 4.2.1. Graphical primitives.- 4.2.1.1. Points.- 4.2.1.2. Segments.- 4.2.1.3. Simple figures.- 4.2.2. 2D clipping.- 4.2.2.1. Explanation of the problem.- 4.2.2.2. Clipping of a segment by a rectangular window.- 4.2.2.3. Clipping by an arbitrary window.- 4.2.2.4. The clipping of polygons.- 4.2.2.5. Concave windows.- 4.2.3. Colouring surfaces.- 4.2.3.1. Explanation of the problem.- 4.2.3.2. Algorithms which work on the image memory.- 4.2.3.3. Algorithms which use associated data structures.- 4.2.4. The use of smoothing.- 4.2.4.1. Principles.- 4.2.4.2. Smoothings defined on the basis of poles.- 4.2.4.3. Methods of colour points.- 4.3. Perspective projections.- 4.3.1. 3D-Images.- 4.3.1.1. Object space and image space.- 4.3.1.2. The perception of space.- 4.3.1.3. Perspective projection.- 4.3.1.4. The problem of entering the data.- 4.3.2. Homogeneous coordinates.- 4.3.3. The matrix associated to a linear transformation.- 4.3.3.1. Matrix of a linear transformation.- 4.3.3.2. Product of linear transformations.- 4.3.3.3. Examples.- 4.3.4. Perspective transformations.- 4.3.5. Clipping.- 4.3.6. Coordinate system of the screen and perspective projection.- 4.4. Aliasing.- 4.4.1. Explanation of the problem.- 4.4.2. Filtering a numerical image.- 4.4.3. Increasing the resolution.- 4.4.4. Random sampling.- 4.4.5. The method of dividing pixels.- 4.5. Motifs, mappings.- 4.5.1. Explanation of the problem.- 4.5.2. Motifs.- 4.5.3. Maps.- 4.6. Textures.- 4.6.1. Definition of the concept of texture.- 4.6.2. Analysis and synthesis of textures.- 4.6.3. Blinn’s method.- 4.6.4. 3D-textures.- 5. The elimination of hidden parts.- 5.1. The problem of hidden parts.- 5.1.1. Explanation of the problem.- 5.1.2. Principles.- 5.2. Elements of geometry.- 5.2.1. Box tests.- 5.2.2. Belonging to the interior of a polygon.- 5.2.3. Equations of planes.- 5.2.4. Sorting problems.- 5.2.5. Coherence.- 5.3. Classification of algorithms.- 5.4. The algorithm with a mobile horizon.- 5.4.1. Principles.- 5.4.2. The algorithm.- 5.4.3. Implementation.- 5.5. Roberts’ algorithm.- 5.5.1. Principles.- 5.5.2. Elimination of back facets.- 5.5.3. Elimination of the remaining edges.- 5.6. Schumacker’s algorithm.- 5.7. The algorithm of Newell-Newell-Sancha.- 5.7.1. Principles.- 5.7.2. Newell’s algorithm.- 5.8. Warnock’s algorithm.- 5.8.1. Principles.- 5.8.2. Optimization.- 5.9. Scan-line algorithms.- 5.10. Application of automatic programming: Goad’salgorithm.- 5.11. Using coherence.- 5.12. The z-buffer algorithm.- 5.12.1. Principles.- 5.12.2. Implementation.- 5.12.3. Limitations of the method.- 5.12.4. Scan-line and z-buffer.- 5.13. The ray-tracing algorithm.- 5.13.1. Principles.- 5.13.2. Implementation.- 5.13.3. Calculating intersections.- 5.13.4. Arranging the objects in a hierarchy.- 6. Illumination models.- 6.1. Illumination of a scene.- 6.2. The models of Phong and of Blinn.- 6.2.1. Diffuse illumination (or ambient lighting).- 6.2.2. Lambert’s law.- 6.2.3. Specular reflection.- 6.2.4. Multiple sources.- 6.3. Cook’s model.- 6.3.1. The model.- 6.3.2. Bidirectional distribution of reflected light.- 6.3.3. Spectral distribution of reflected light.- 6.4. Transparency.- 6.5. Smoothing methods.- 6.5.1. The smoothing problem.- 6.5.2. Gouraud smoothing.- 6.5.3. Phong smoothing.- 6.5.4. Comparison of the two methods.- 6.6. Shadows.- 6.6.1. Explanation of the problem.- 6.6.2. Projection method.- 6.6.3. z-buffer method.- 6.6.4. Ray-tracing method.- 6.7. Radiosity.- 6.7.1. The illumination problem.- 6.7.2. The radiosity principle.- 6.7.3. Calculation of the form coefficients.- 6.7.4. Cohen’s hemi-cube.- 6.8. Ray-tracing.- 6.8.1. Principles.- 6.8.2. Whitted’s model.- 6.8.3. Calculating secondary rays.- 6.8.4. Anti-aliasing.- 6.8.5. Optimization.- 6.8.5.1. Box tests.- 6.8.5.2. Optimization according to the type of primitives.- 6.8.6. Bundle tracing.- 6.8.6.1. Ray and bundle.- 6.8.6.2. Representation of a ray in a bundle.- 6.8.6.3. Matrices associated to optical systems.- 6.8.6.4. Evaluation of the deviation.- 6.9. Simulation of clouds and fluffy surfaces.- 6.9.1. Dispersion models in a cloud.- 6.9.2. Phase functions.- 6.10. Simulation of atmospheric dispersion.- 6.10.1. Explanation of the problem.- 6.10.2. Nishita’s model.