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• date: 27 March 2024
• posted by: voska89

Table of contents
Chapter 1. Getting started
Chapter 1. What is geometry for programmers?
Chapter 1. Why not let my tools take care of geometry?
Chapter 1. Applied geometry has been around forever; why learn it now?
Chapter 1. You don't have to know much to start
Chapter 1. SymPy will do your math for you
Chapter 1. Summary
Chapter 2. Terminology and jargon
Chapter 2. Vertices and triangles
Chapter 2. Lines, planes, and their equations
Chapter 2. Functions and geometric transformations
Chapter 2. The shortest possible introduction to matrix algebra
Chapter 2. Exercises
Chapter 2. Solutions to exercises
Chapter 2. Summary
Chapter 3. The geometry of linear equations
Chapter 3. Overspecified and underspecified systems
Chapter 3. A visual example of an interactive linear solver
Chapter 3. Direct solver
Chapter 3. Linear equations system as matrix multiplication
Chapter 3. Solving linear systems with Gaussian elimination and LU-decomposition
Chapter 3. Which solver fits my problem best?
Chapter 3. 3.8 Practical example: Does a ray hit a triangle?
Chapter 3. Exercises
Chapter 3. Solutions to exercises
Chapter 3. Summary
Chapter 4. Projective geometric transformations
Chapter 4. Generalizations
Chapter 4. Projective space and homogeneous coordinates
Chapter 4. Practical examples
Chapter 4. Exercises
Chapter 4. Solutions to exercises
Chapter 4. Summary
Chapter 5. The geometry of calculus
Chapter 5. Smooth piecewise parametric curves
Chapter 5. Practical example: Crafting a curve out of lines and circles
Chapter 5. Exercises
Chapter 5. Solutions to exercises
Chapter 5. Summary
Chapter 6. Polynomial approximation and interpolation
Chapter 6. Polynomial approximation
Chapter 6. Polynomial interpolation
Chapter 6. Practical example: Showing a trend with both approximation and interpolation
Chapter 6. Solutions to exercises Exercises
Chapter 6. Solutions to exercises
Chapter 6. Summary
Chapter 7. Splines
Chapter 7. Understanding polynomial splines and Bézier curves
Chapter 7. Understanding NURBS
Chapter 7. Exercises
Chapter 7. Solutions to exercises
Chapter 7. Summary
Chapter 8. Nonlinear transformations and surfaces
Chapter 8. 3D surface modeling
Chapter 8. Using nonpolynomial spatial interpolation in geometry
Chapter 8. Exercises
Chapter 8. Solutions to exercises
Chapter 8. Summary
Chapter 9. The geometry of vector algebra
Chapter 9. Dot product: Projection and angle
Chapter 9. Cross product: Normal vector and the parallelogram area
Chapter 9. Triple product: The parallelepiped volume
Chapter 9. Generalization for parallelotopes
Chapter 9. Exercises
Chapter 9. Solutions to exercises
Chapter 9. Summary
Chapter 10. Modeling shapes with signed distance functions and surrogates
Chapter 10. How to work with SDFs
Chapter 10. Some techniques of not-really-SDF implicit modeling
Chapter 10. Exercises
Chapter 10. Solutions to exercises
Chapter 10. Summary
Chapter 11. Modeling surfaces with boundary representations and triangle meshes
Chapter 11. Segments and triangles
Chapter 11. Practical example: Contouring with marching cubes and dual contouring algorithms
Chapter 11. Practical example: Smooth contouring
Chapter 11. Exercises
Chapter 11. Solutions to exercises
Chapter 11. Summary
Chapter 12. Modeling bodies with images and voxels
Chapter 12. Segmentation by a threshold
Chapter 12. Typical operations on 3D images: Dilation, erosion, cavity fill, and Boolean
Chapter 12. Practical example: Image vectorization
Chapter 12. How voxels, triangles, parametric surfaces, and SDFs work together
Chapter 12. Exercises
Chapter 12. Solutions to exercises
Chapter 12. Summary








   
   
   

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