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chern introduction computer graphics 2021

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Textbook in PDF format Introduction. What is computer graphics? A brief history. Topics in computer graphics. 3D computer graphics: Rasterization v.s. ray casting. Rasterization. Ray casting or ray tracing. Overview of this course. Rasterization-based Graphics with OpenGL. OpenGL Setup. Where is OpenGL? How to load the library? Overview. Windows Platform. Linux Platform. MacOS Platform. Summary. Hello Window. GLM and FreeImage. OpenGL: a Graphics Factory. A tour of the graphics factory. The GPU in the factory. The objects we will work with. The geometry spreadsheet studio. The shader studio. The framebuffers. Finishing the tour. Rasterization as a projection. Hello Square. Setup the square geometry. Shader setup. The draw command. Rasterization as an interpolator. Drawing a circle by the shader. Adding uniform variables. Modularizing OpenGL Code. Geometry. Geometry class. Square class. Shader. Implementation of the Shader class. Subclass of the Shader class. Screenshot (optional). Mandelbrot fractal shader. Linear Algebra and Projective Geometry. LinearAlgebra. Matrix algebra. Matrix transposition. Matrix inversion and linear system. Geometric and algebraic aspects of vectors. Vector space. Basis. Bridging the geometric and algebraic versions of vectors. Linear transformations. Transformations in graphics. Inner product. Lengths and angles. Algebraic representation. Orthonormal basis. Special transformations. Rotations and reflections. Stretching and shearing. 3D Rotations. Cross product. “Vector cross” as a linear transformation. Rodrigues’ axis-angle formula. Euler–Rodrigues matrix. Euler angles. Unpredictable interpolation. Gimbal lock. Euler angles for cameras. Geometric algebra. Insisting on associativity. Geometric interpretation. 3D rotation. Quaternions. Exercise. Affine Geometry. Positions and displacements. An extra component as an indicator. Other kinds of vectors. Affine space. Coordinate system. Affine transformation. Coordinate-free definition. Matrix representation of an affine transformation. Affine transformations in computer graphics. “Look-at” camera/view matrix. Transformation of normal vectors. Exercise: a Camera class for a model viewer. Camera class. Model viewer (main.cpp). A simple normal shader. Geometry class. Cube: a derived class from the Geometry class. Projective Geometry. Projections in graphics. Orthographic projection. Perspective projection. From Renaissant arts to projective geometry. Perspective drawing. Elements at infinity. Taylor’s Principles of Linear Perspective. Homogeneous coordinates. Homography. Projective transformation into the normalized device coordinate. Corners of the frustum. Sending the apex to infinity. Translating and scaling into the viewing box. Final formula. Hierarchical Modeling. Scene description. Memory-efficient modeling. Reading a scene graph. Data structure. Formal properties of a scene graph. Directed graphs. Stack. Traversing over a rooted directed acyclic graph. Draw the scene. Matrix stack. Lighting and Textures. Lighting. Direct lighting in rasterization-based graphics. Gouraud shading and Phong shading. Color vector. High dynamic range. Reflection model. Ambient reflection. Diffuse reflection. Blinn–Phong specular reflection. Multiple light sources. Light at infinity. Interpolations. Barycentric coordinates. Archimedes’ law of lever. Barycenter. Affine combinations. Barycentric coordinates. Linear interpolation in a simplex. Linear interpolation between two points. Linear interpolation of a triangle in a plane. Appendix. Compilation and Linking. From source code to executable. Multiple source code files. Library. Static and dynamic library linking. Mac’s framework directory. Makefile and Integrated Development Environment (IDE). Makefile. Using an IDE. Index

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Chern A. Introduction to Computer Graphics 2021.pdf 14.9 MB

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chern introduction computer graphics 2021

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