Lecture 1 - Introduction - Geometry of Vision Lecture 2 - Chapter One: The Power of Vanishing Points Lecture 3 - Drawing parallel lines: a thought experiment Lecture 4 - Why do the images of lines terminate ? Lecture 5 - Why do some lines share a vanishing point ? Lecture 6 - Why do some lines remain parallel ? Lecture 7 - The vanishing point theorem Lecture 8 - The horizon line theorem Lecture 9 - Three views of a tiled floor Lecture 10 - Demo: drawing the third perspective view Lecture 11 - The second perspective view revisited Lecture 12 - Demo: drawing railway tracks Lecture 13 - Three views of a box Lecture 14 - Demo: drawing in one point and two point perspective Lecture 15 - What does a perspective drawing reveal about the viewer ? Lecture 16 - Chapter Two: A Geometry of Coincidence Lecture 17 - Incidence relations Lecture 18 - Linear spaces Lecture 19 - Extending the euclidean plane Lecture 20 - The shape of this exended plane Lecture 21 - Incidence relations in the extended plane Lecture 22 - Coincidence #1 the harmonic conjugate theorem Lecture 23 - Proof of the harmonic conjugate theorem Lecture 24 - Coincidence #2 Pappus's theorem Lecture 25 - Coincidence #3 Desargues's theorem Lecture 26 - The exended euclidean space P3 Lecture 27 - Desargues's theorem in three dimensions Lecture 28 - A Shadow drawing challenge Lecture 29 - Solution to the Shadow drawing challenge Lecture 30 - Proving Desargues's in three dimensions Lecture 31 - Lifting Desargues's theorem from the plane Lecture 32 - How to prove the converse Lecture 33 - Chapter Three: The Shadow of a Square Lecture 34 - Perspectivities the maps that shift perspective Lecture 35 - Visualizing perspectivities Lecture 36 - Perspectivities are well defined Lecture 37 - The harmonic conjugate theorem revisited Lecture 38 - Projectivities sequences of perspectivities Lecture 39 - 1D projectivities a puzzle Lecture 40 - 1D projectivities a harder puzzle Lecture 41 - Projectivities as functions Lecture 42 - The three fixed points theorem Lecture 43 - 1D fundamental theorem of projective geometry Lecture 44 - The criss cross construction Lecture 45 - Proving pappus’s theorem Lecture 46 - 2D Fundamental theorem of projective geometry Lecture 47 - The four fixed points lemma Lecture 48 - The shadow of a square Lecture 49 - Chapter Four: The Analytic Framework Lecture 50 - Introducing the cross ratio Lecture 51 - Evenly spaced points Lecture 52 - How many cross ratios ? Lecture 53 - Invariance of the cross ratio Lecture 54 - Injectivity of the cross ratio Lecture 55 - Proving the 3 fixed points theorem Lecture 56 - Bonus: the cross ratio as a function Lecture 57 - The real projective plane Lecture 58 - Homogeneous coordinates Lecture 59 - Homogenous proof that parallel lines converge Lecture 60 - Bonus: join and meet as cross product Lecture 61 - Affine charts Lecture 62 - The matrix group of transformations of RP2 Lecture 63 - The fundamental theorem of PGL(3,R) Lecture 64 - Visualizing the action of PGL(3,R) Lecture 65 - Proving the fundamental theorem of PGL(3,R) Lecture 66 - Conclusion to Geometry of Vision

Lecture 1 - Introduction - Geometry of Vision Lecture 2 - Chapter One: The Power of Vanishing Points Lecture 3 - Drawing parallel lines: a thought experiment Lecture 4 - Why do the images of lines terminate ? Lecture 5 - Why do some lines share a vanishing point ? Lecture 6 - Why do some lines remain parallel ? Lecture 7 - The vanishing point theorem Lecture 8 - The horizon line theorem Lecture 9 - Three views of a tiled floor Lecture 10 - Demo: drawing the third perspective view Lecture 11 - The second perspective view revisited Lecture 12 - Demo: drawing railway tracks Lecture 13 - Three views of a box Lecture 14 - Demo: drawing in one point and two point perspective Lecture 15 - What does a perspective drawing reveal about the viewer ? Lecture 16 - Chapter Two: A Geometry of Coincidence Lecture 17 - Incidence relations Lecture 18 - Linear spaces Lecture 19 - Extending the euclidean plane Lecture 20 - The shape of this exended plane Lecture 21 - Incidence relations in the extended plane Lecture 22 - Coincidence #1 the harmonic conjugate theorem Lecture 23 - Proof of the harmonic conjugate theorem Lecture 24 - Coincidence #2 Pappus's theorem Lecture 25 - Coincidence #3 Desargues's theorem Lecture 26 - The exended euclidean space P3 Lecture 27 - Desargues's theorem in three dimensions Lecture 28 - A Shadow drawing challenge Lecture 29 - Solution to the Shadow drawing challenge Lecture 30 - Proving Desargues's in three dimensions Lecture 31 - Lifting Desargues's theorem from the plane Lecture 32 - How to prove the converse Lecture 33 - Chapter Three: The Shadow of a Square Lecture 34 - Perspectivities the maps that shift perspective Lecture 35 - Visualizing perspectivities Lecture 36 - Perspectivities are well defined Lecture 37 - The harmonic conjugate theorem revisited Lecture 38 - Projectivities sequences of perspectivities Lecture 39 - 1D projectivities a puzzle Lecture 40 - 1D projectivities a harder puzzle Lecture 41 - Projectivities as functions Lecture 42 - The three fixed points theorem Lecture 43 - 1D fundamental theorem of projective geometry Lecture 44 - The criss cross construction Lecture 45 - Proving pappus’s theorem Lecture 46 - 2D Fundamental theorem of projective geometry Lecture 47 - The four fixed points lemma Lecture 48 - The shadow of a square Lecture 49 - Chapter Four: The Analytic Framework Lecture 50 - Introducing the cross ratio Lecture 51 - Evenly spaced points Lecture 52 - How many cross ratios ? Lecture 53 - Invariance of the cross ratio Lecture 54 - Injectivity of the cross ratio Lecture 55 - Proving the 3 fixed points theorem Lecture 56 - Bonus: the cross ratio as a function Lecture 57 - The real projective plane Lecture 58 - Homogeneous coordinates Lecture 59 - Homogenous proof that parallel lines converge Lecture 60 - Bonus: join and meet as cross product Lecture 61 - Affine charts Lecture 62 - The matrix group of transformations of RP2 Lecture 63 - The fundamental theorem of PGL(3,R) Lecture 64 - Visualizing the action of PGL(3,R) Lecture 65 - Proving the fundamental theorem of PGL(3,R) Lecture 66 - Conclusion to Geometry of Vision