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1Dv438 Teori Contents 1dv438 Teori Contents 1 Math 1 1.1 Basis (linear algebra) ......................................... 1 1.1.1 Definition ........................................... 1 1.1.2 Expression of a basis ..................................... 2 1.1.3 Properties .......................................... 2 1.1.4 Examples ........................................... 3 1.1.5 Extending to a basis ..................................... 3 1.1.6 Example of alternative proofs ................................ 3 1.1.7 Ordered bases and coordinates ................................ 4 1.1.8 Related notions ........................................ 4 1.1.9 Proof that every vector space has a basis ........................... 5 1.1.10 See also ............................................ 6 1.1.11 Notes ............................................. 6 1.1.12 References .......................................... 6 1.1.13 External links ......................................... 6 1.2 Multiplication of vectors ........................................ 6 1.2.1 See also ............................................ 7 1.3 Identity matrix ............................................. 7 1.3.1 See also ............................................ 7 1.3.2 Notes ............................................. 7 1.3.3 External links ......................................... 7 1.4 Translation (geometry) ........................................ 8 1.4.1 Matrix representation ..................................... 8 1.4.2 Translations in physics .................................... 9 1.4.3 See also ............................................ 9 1.4.4 External links ......................................... 9 1.4.5 References .......................................... 9 1.5 Normal (geometry) .......................................... 9 1.5.1 Normal to surfaces in 3D space ................................ 10 1.5.2 Hypersurfaces in n-dimensional space ............................ 11 1.5.3 Varieties defined by implicit equations in n-dimensional space ................ 11 1.5.4 Uses .............................................. 12 i ii CONTENTS 1.5.5 Normal in geometric optics .................................. 12 1.5.6 See also ............................................ 12 1.5.7 References .......................................... 12 1.5.8 External links ......................................... 12 2 Materials 13 2.1 Cube mapping ............................................. 13 2.1.1 History ............................................ 13 2.1.2 Advantages .......................................... 13 2.1.3 Disadvantages ......................................... 14 2.1.4 Applications .......................................... 14 2.1.5 Related ............................................ 15 2.1.6 References .......................................... 15 2.1.7 See also ............................................ 15 2.2 Texture mapping ............................................ 15 2.2.1 Perspective correctness .................................... 16 2.2.2 Development ......................................... 17 2.2.3 See also ............................................ 17 2.2.4 References .......................................... 18 2.2.5 External links ......................................... 18 2.3 Reflection mapping .......................................... 18 2.3.1 Types ............................................. 19 2.3.2 History ............................................ 20 2.3.3 See also ............................................ 20 2.3.4 References .......................................... 20 2.3.5 External links ......................................... 20 2.4 Normal mapping ............................................ 20 2.4.1 History ............................................ 21 2.4.2 How it works ......................................... 21 2.4.3 Calculating tangent space ................................... 21 2.4.4 Normal mapping in video games ............................... 21 2.4.5 See also ............................................ 22 2.4.6 References .......................................... 22 2.4.7 External links ......................................... 22 2.5 Displacement mapping ........................................ 22 2.5.1 Meaning of the term in different contexts ........................... 23 2.5.2 See also ............................................ 23 2.5.3 Further reading ........................................ 23 2.6 Sphere mapping ............................................ 24 2.6.1 Usage example ........................................ 24 2.6.2 See also ............................................ 24 2.7 UV mapping .............................................. 24 CONTENTS iii 2.7.1 UV mapping ......................................... 24 2.7.2 Finding UV on a sphere .................................... 25 2.7.3 See also ............................................ 25 2.7.4 Notes ............................................. 25 2.7.5 References .......................................... 25 2.7.6 External links ......................................... 25 2.8 Mipmap ................................................ 26 2.8.1 Basic use ........................................... 26 2.8.2 Origin ............................................. 26 2.8.3 How it works ......................................... 26 2.8.4 Anisotropic filtering ..................................... 27 2.8.5 Summed-area tables ..................................... 27 2.8.6 References .......................................... 27 2.8.7 See also ............................................ 27 2.9 Skybox (video games) ......................................... 27 2.9.1 Advanced skyboxes ...................................... 28 2.9.2 See also ............................................ 29 2.9.3 External links ......................................... 29 2.10 Materials system ............................................ 29 2.10.1 References .......................................... 29 2.11 Shader ................................................. 29 2.11.1 History ............................................ 30 2.11.2 Design ............................................ 30 2.11.3 Types ............................................. 30 2.11.4 Parallel processing ...................................... 31 2.11.5 Programming ......................................... 31 2.11.6 See also ............................................ 31 2.11.7 References .......................................... 31 2.11.8 Further reading ........................................ 32 2.11.9 External links ......................................... 32 2.12 Shading ................................................ 32 2.12.1 Drawing ............................................ 32 2.12.2 Computer graphics ...................................... 32 2.12.3 Flat shading .......................................... 34 2.12.4 Smooth shading ........................................ 34 2.12.5 Flat vs. smooth shading .................................... 35 2.12.6 See also ............................................ 35 2.12.7 References .......................................... 35 2.13 Shading language ........................................... 35 2.13.1 Offline rendering ....................................... 35 2.13.2 Real-time rendering ..................................... 36 iv CONTENTS 2.13.3 References .......................................... 37 2.13.4 Notes ............................................. 37 2.14 OpenGL Shading Language ...................................... 37 2.14.1 Background .......................................... 37 2.14.2 Versions ............................................ 38 2.14.3 Operators ........................................... 38 2.14.4 Functions and control structures ............................... 38 2.14.5 Compilation and execution .................................. 38 2.14.6 Examples ........................................... 38 2.14.7 See also ............................................ 39 2.14.8 References .......................................... 39 2.14.9 Books ............................................. 40 2.14.10 External links ......................................... 40 2.15 Phong shading ............................................. 40 2.15.1 History ............................................ 40 2.15.2 Phong interpolation ...................................... 40 2.15.3 Phong reflection model .................................... 40 2.15.4 See also ............................................ 41 2.15.5 References .......................................... 41 2.16 Gouraud shading ............................................ 41 2.16.1 Description .......................................... 41 2.16.2 Comparison with other shading techniques .......................... 41 2.16.3 See also ............................................ 42 2.16.4 References .......................................... 42 3 Other 43 3.1 WebGL ................................................ 43 3.1.1 Design ............................................ 43 3.1.2 History ............................................ 43 3.1.3 Support ............................................ 43 3.1.4 Content creation and ecosystem ............................... 44 3.1.5 Security ............................................ 44 3.1.6 Similar technologies for 3D in a browser ........................... 44 3.1.7 References .......................................... 45 3.1.8 External links ........................................
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