# Geometry of Vision

- Institution: Azim Premji University
- Department: Mathematics
- Teacher: Prof. Vijay Ravikumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106156)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106156)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction - Geometry of Vision](https://invisiblenetwork.ai/learn/nptel/111106156/cabac66714b2) (Video)
2. [Chapter One: The Power of Vanishing Points](https://invisiblenetwork.ai/learn/nptel/111106156/62c9356f12d7) (Video)
3. [Video 1A: drawing parallel lines: a thought experiment](https://invisiblenetwork.ai/learn/nptel/111106156/994a40d22a5b) (Video)
4. [Video 1B: why do the images of lines terminate?](https://invisiblenetwork.ai/learn/nptel/111106156/916bd22305c8) (Video)
5. [Video 1C: why do some lines share a vanishing point?](https://invisiblenetwork.ai/learn/nptel/111106156/882724bcb869) (Video)
6. [Video 1D: why do some lines remain parallel?](https://invisiblenetwork.ai/learn/nptel/111106156/2d9112b65c5e) (Video)
7. [Video 1E: the vanishing point theorem](https://invisiblenetwork.ai/learn/nptel/111106156/c9fb036b703e) (Video)
8. [Video 1F: the horizon line theorem](https://invisiblenetwork.ai/learn/nptel/111106156/76671ebeab03) (Video)
9. [Video 2A: three views of a tiled floor](https://invisiblenetwork.ai/learn/nptel/111106156/4d52de8b963f) (Video)
10. [Video 2B: demo: drawing the third perspective view](https://invisiblenetwork.ai/learn/nptel/111106156/53ad3c23d22d) (Video)
11. [Video 2C: the second perspective view revisited](https://invisiblenetwork.ai/learn/nptel/111106156/cc480c2580be) (Video)
12. [Video 2D: demo: drawing railway tracks](https://invisiblenetwork.ai/learn/nptel/111106156/757106ee6522) (Video)
13. [Video 3A: three views of a box](https://invisiblenetwork.ai/learn/nptel/111106156/c376e167ec93) (Video)
14. [Video 3B: demo: drawing in one point and two point perspective](https://invisiblenetwork.ai/learn/nptel/111106156/87ecfc354941) (Video)
15. [Chapter Two: A Geometry of Coincidence](https://invisiblenetwork.ai/learn/nptel/111106156/8d64d2137cce) (Video)
16. [Video 4A: Incidence relations](https://invisiblenetwork.ai/learn/nptel/111106156/58da08f2fac4) (Video)
17. [Video 4B: Linear spaces](https://invisiblenetwork.ai/learn/nptel/111106156/cae202de27c7) (Video)
18. [Vidoe 4C: Extending the euclidean plane](https://invisiblenetwork.ai/learn/nptel/111106156/d158ca06c4d0) (Video)
19. [Video 4D: The shape of this exended plane](https://invisiblenetwork.ai/learn/nptel/111106156/9ae46cb3ccb7) (Video)
20. [Video 4E: Incidence relations in the extended plane](https://invisiblenetwork.ai/learn/nptel/111106156/6d49e3a7ee20) (Video)
21. [Video 5A: Coincidence #1 the harmonic conjugate theorem](https://invisiblenetwork.ai/learn/nptel/111106156/858833d8c42d) (Video)
22. [Video 5B: Proof of the harmonic conjugate theorem](https://invisiblenetwork.ai/learn/nptel/111106156/5981642b91d9) (Video)
23. [Video 5C: Coincidence #2 Pappus's theorem](https://invisiblenetwork.ai/learn/nptel/111106156/0f4becb2c10d) (Video)
24. [Video 5D: Coincidence #3 Desargues's theorem](https://invisiblenetwork.ai/learn/nptel/111106156/46444d1e3fc0) (Video)
25. [Video 6A: The exended euclidean space P3](https://invisiblenetwork.ai/learn/nptel/111106156/eb5011a4471f) (Video)
26. [Video 6B: Desargues's theorem in three dimensions](https://invisiblenetwork.ai/learn/nptel/111106156/e604c7156a82) (Video)
27. [Video 6C: A Shadow drawing challenge](https://invisiblenetwork.ai/learn/nptel/111106156/8a0a75933358) (Video)
28. [Video 6D: Solution to the Shadow drawing challenge](https://invisiblenetwork.ai/learn/nptel/111106156/9c1b747df8ea) (Video)
29. [Video 6E: Proving desargues's in three dimensions](https://invisiblenetwork.ai/learn/nptel/111106156/b1d0566495b2) (Video)
30. [Video 6F: Lifting Desargues's theorem from the plane](https://invisiblenetwork.ai/learn/nptel/111106156/8d5f8aaf08bb) (Video)
31. [Chapter Three: The Shadow of a Square](https://invisiblenetwork.ai/learn/nptel/111106156/790e06b75d3a) (Video)
32. [Video 7A: perspectivities the maps that shift perspective](https://invisiblenetwork.ai/learn/nptel/111106156/62cfbb2b45e6) (Video)
33. [Video 7B: Visualizing perspectivities](https://invisiblenetwork.ai/learn/nptel/111106156/1691280b82e4) (Video)
34. [Video 7C : Perspectivities are well defined](https://invisiblenetwork.ai/learn/nptel/111106156/1d38ac1b3140) (Video)
35. [Video 7D: the harmonic conjugate theorem revisited](https://invisiblenetwork.ai/learn/nptel/111106156/0b203c18606c) (Video)
36. [Video 8A: Projectivities sequences of perspectivities](https://invisiblenetwork.ai/learn/nptel/111106156/7b5b2f8ef26d) (Video)
37. [Video 8B: 1D projectivities a puzzle](https://invisiblenetwork.ai/learn/nptel/111106156/915cc5939d2c) (Video)
38. [Video 8C: 1D projectivities a harder puzzle](https://invisiblenetwork.ai/learn/nptel/111106156/e84fcc3fc8b0) (Video)
39. [Video 8D: projectivities as functions](https://invisiblenetwork.ai/learn/nptel/111106156/6355006d2960) (Video)
40. [Video 8E: the three fixed points theorem](https://invisiblenetwork.ai/learn/nptel/111106156/9eb74b4abd6d) (Video)
41. [Video 9A: 1D fundamental theorem of projective geometry](https://invisiblenetwork.ai/learn/nptel/111106156/b7dfcfb679be) (Video)
42. [Video 9B: the criss cross construction](https://invisiblenetwork.ai/learn/nptel/111106156/33616ee6dee5) (Video)
43. [Video 9C: Proving pappus’s theorem](https://invisiblenetwork.ai/learn/nptel/111106156/bca71f518ad6) (Video)
44. [Video 9D: 2D Fundamental theorem of projective geometry](https://invisiblenetwork.ai/learn/nptel/111106156/af428d4bdd60) (Video)
45. [Video 9E: The four fixed points lemma](https://invisiblenetwork.ai/learn/nptel/111106156/cf8ffe210b05) (Video)
46. [Chapter Four: The Analytic Framework](https://invisiblenetwork.ai/learn/nptel/111106156/5f73ec977654) (Video)
47. [Video 10A: introducing the cross ratio](https://invisiblenetwork.ai/learn/nptel/111106156/fbc73365fd1f) (Video)
48. [Video 10B: Evenly spaced points](https://invisiblenetwork.ai/learn/nptel/111106156/990e9dc661ab) (Video)
49. [Video 10C: how many cross ratios?](https://invisiblenetwork.ai/learn/nptel/111106156/48fa23a69215) (Video)
50. [Video 10D: invariance of the cross ratio](https://invisiblenetwork.ai/learn/nptel/111106156/50a2d6475cce) (Video)
51. [Video 10E: injectivity of the cross ratio](https://invisiblenetwork.ai/learn/nptel/111106156/4353370190be) (Video)
52. [Video 10F: proving the ‘3 fixed points’ theorem](https://invisiblenetwork.ai/learn/nptel/111106156/4adacf3f3e3d) (Video)
53. [Video 10G: bonus: the cross ratio as a function](https://invisiblenetwork.ai/learn/nptel/111106156/0d7c18cdcbc4) (Video)
54. [Video 11A: the real projective plane](https://invisiblenetwork.ai/learn/nptel/111106156/d9fdc5f470e1) (Video)
55. [Video 11B: homogeneous coordinates](https://invisiblenetwork.ai/learn/nptel/111106156/41ed69c22f24) (Video)
56. [Video 11C: homogenous proof that parallel lines converge](https://invisiblenetwork.ai/learn/nptel/111106156/fa94b297ac27) (Video)
57. [Video 11D: bonus: join and meet as cross product](https://invisiblenetwork.ai/learn/nptel/111106156/38d05fc03b5b) (Video)
58. [Video 12A: affine charts](https://invisiblenetwork.ai/learn/nptel/111106156/d99966abb58d) (Video)
59. [Video 12B: the matrix group of transformations of RP2](https://invisiblenetwork.ai/learn/nptel/111106156/ca8a3c25d86a) (Video)
60. [Video 12C: the fundamental theorem of PGL(3,R)](https://invisiblenetwork.ai/learn/nptel/111106156/9691af5373ed) (Video)
61. [Video 12D: visualizing the action of PGL(3,R)](https://invisiblenetwork.ai/learn/nptel/111106156/62125838c68e) (Video)
62. [Video 12E: proving the fundamental theorem of PGL(3,R)](https://invisiblenetwork.ai/learn/nptel/111106156/92887893cbec) (Video)
63. [Live Session 07-09-2023](https://invisiblenetwork.ai/learn/nptel/111106156/cabac66714b2-2) (Video)