Lecture 37 of 63week-03
Video 8B: 1D projectivities a puzzle
Prof. Vijay Ravikumar · Azim Premji University
Credits and licence
- From
- Geometry of Vision, Azim Premji University (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Introduction - Geometry of Vision
- Chapter One: The Power of Vanishing Points
- Video 1A: drawing parallel lines: a thought experiment
- Video 1B: why do the images of lines terminate?
- Video 1C: why do some lines share a vanishing point?
- Video 1D: why do some lines remain parallel?
- Video 1E: the vanishing point theorem
- Video 1F: the horizon line theorem
- Video 2A: three views of a tiled floor
- Video 2B: demo: drawing the third perspective view
- Video 2C: the second perspective view revisited
- Video 2D: demo: drawing railway tracks
- Video 3A: three views of a box
- Video 3B: demo: drawing in one point and two point perspective
- Chapter Two: A Geometry of Coincidence
- Video 4A: Incidence relations
- Video 4B: Linear spaces
- Vidoe 4C: Extending the euclidean plane
- Video 4D: The shape of this exended plane
- Video 4E: Incidence relations in the extended plane
- Video 5A: Coincidence #1 the harmonic conjugate theorem
- Video 5B: Proof of the harmonic conjugate theorem
- Video 5C: Coincidence #2 Pappus's theorem
- Video 5D: Coincidence #3 Desargues's theorem
- Video 6A: The exended euclidean space P3
- Video 6B: Desargues's theorem in three dimensions
- Video 6C: A Shadow drawing challenge
- Video 6D: Solution to the Shadow drawing challenge
- Video 6E: Proving desargues's in three dimensions
- Video 6F: Lifting Desargues's theorem from the plane
- Chapter Three: The Shadow of a Square
- Video 7A: perspectivities the maps that shift perspective
- Video 7B: Visualizing perspectivities
- Video 7C : Perspectivities are well defined
- Video 7D: the harmonic conjugate theorem revisited
- Video 8A: Projectivities sequences of perspectivities
- Video 8B: 1D projectivities a puzzle
- Video 8C: 1D projectivities a harder puzzle
- Video 8D: projectivities as functions
- Video 8E: the three fixed points theorem
- Video 9A: 1D fundamental theorem of projective geometry
- Video 9B: the criss cross construction
- Video 9C: Proving pappus’s theorem
- Video 9D: 2D Fundamental theorem of projective geometry
- Video 9E: The four fixed points lemma
- Chapter Four: The Analytic Framework
- Video 10A: introducing the cross ratio
- Video 10B: Evenly spaced points
- Video 10C: how many cross ratios?
- Video 10D: invariance of the cross ratio
- Video 10E: injectivity of the cross ratio
- Video 10F: proving the ‘3 fixed points’ theorem
- Video 10G: bonus: the cross ratio as a function
- Video 11A: the real projective plane
- Video 11B: homogeneous coordinates
- Video 11C: homogenous proof that parallel lines converge
- Video 11D: bonus: join and meet as cross product
- Video 12A: affine charts
- Video 12B: the matrix group of transformations of RP2
- Video 12C: the fundamental theorem of PGL(3,R)
- Video 12D: visualizing the action of PGL(3,R)
- Video 12E: proving the fundamental theorem of PGL(3,R)
- Live Session 07-09-2023