Geometry of Vision 6PWFN82HEJ

URI	`m2://res/6PWFN82HEJ`
Kind	course
Creators	Vijay Ravikumar (instructor)
Date	2022-09-26
Scope	in

Expressions

e1: edition

Language	en
Date	2022-09-26

m1: page, Azim Premji University (record). nptel 111106156
m2: page, 2022-09-26 (record). nptel 111106156

Contents

part 1: week-01
session 1: Introduction - Geometry of Vision
session 2: Chapter One: The Power of Vanishing Points
session 3: Video 1A: drawing parallel lines: a thought experiment
session 4: Video 1B: why do the images of lines terminate?
session 5: Video 1C: why do some lines share a vanishing point?
session 6: Video 1D: why do some lines remain parallel?
session 7: Video 1E: the vanishing point theorem
session 8: Video 1F: the horizon line theorem
session 9: Video 2A: three views of a tiled floor
session 10: Video 2B: demo: drawing the third perspective view
session 11: Video 2C: the second perspective view revisited
session 12: Video 2D: demo: drawing railway tracks
session 13: Video 3A: three views of a box
session 14: Video 3B: demo: drawing in one point and two point perspective
part 2: week-02
session 15: Chapter Two: A Geometry of Coincidence
session 16: Video 4A: Incidence relations
session 17: Video 4B: Linear spaces
session 18: Vidoe 4C: Extending the euclidean plane
session 19: Video 4D: The shape of this exended plane
session 20: Video 4E: Incidence relations in the extended plane
session 21: Video 5A: Coincidence #1 the harmonic conjugate theorem
session 22: Video 5B: Proof of the harmonic conjugate theorem
session 23: Video 5C: Coincidence #2 Pappus's theorem
session 24: Video 5D: Coincidence #3 Desargues's theorem
session 25: Video 6A: The exended euclidean space P3
session 26: Video 6B: Desargues's theorem in three dimensions
session 27: Video 6C: A Shadow drawing challenge
session 28: Video 6D: Solution to the Shadow drawing challenge
session 29: Video 6E: Proving desargues's in three dimensions
session 30: Video 6F: Lifting Desargues's theorem from the plane
part 3: week-03
session 31: Chapter Three: The Shadow of a Square
session 32: Video 7A: perspectivities the maps that shift perspective
session 33: Video 7B: Visualizing perspectivities
session 34: Video 7C : Perspectivities are well defined
session 35: Video 7D: the harmonic conjugate theorem revisited
session 36: Video 8A: Projectivities sequences of perspectivities
session 37: Video 8B: 1D projectivities a puzzle
session 38: Video 8C: 1D projectivities a harder puzzle
session 39: Video 8D: projectivities as functions
session 40: Video 8E: the three fixed points theorem
session 41: Video 9A: 1D fundamental theorem of projective geometry
session 42: Video 9B: the criss cross construction
session 43: Video 9C: Proving pappus’s theorem
session 44: Video 9D: 2D Fundamental theorem of projective geometry
session 45: Video 9E: The four fixed points lemma
part 4: week-04
session 46: Chapter Four: The Analytic Framework
session 47: Video 10A: introducing the cross ratio
session 48: Video 10B: Evenly spaced points
session 49: Video 10C: how many cross ratios?
session 50: Video 10D: invariance of the cross ratio
session 51: Video 10E: injectivity of the cross ratio
session 52: Video 10F: proving the â€˜3 fixed pointsâ€™ theorem
session 53: Video 10G: bonus: the cross ratio as a function
session 54: Video 11A: the real projective plane
session 55: Video 11B: homogeneous coordinates
session 56: Video 11C: homogenous proof that parallel lines converge
session 57: Video 11D: bonus: join and meet as cross product
session 58: Video 12A: affine charts
session 59: Video 12B: the matrix group of transformations of RP2
session 60: Video 12C: the fundamental theorem of PGL(3,R)
session 61: Video 12D: visualizing the action of PGL(3,R)
session 62: Video 12E: proving the fundamental theorem of PGL(3,R)
part 5: Live Session
session 63: Live Session 07-09-2023

Catalogue records

nptel: 111106156 (manifestation)
nptel_video: 111106156 (manifestation)