Editing Projective Geometry (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Projective geometry is understood through '''Projection''' and '''Infinity'''.

'''1. The Artist's Eye''':
Imagine looking at a square tile on the floor from an angle.
* It doesn't look like a square (the far side is shorter).
* It doesn't look like a rectangle (the sides are not parallel).
* It looks like a '''Trapezoid'''.
Projective geometry asks: "What is still 'Square-like' about this trapezoid?"

'''2. Vanishing Points''':
In Euclidean geometry, parallel train tracks never touch. In Projective geometry:
* We add a "Special Point" to the world.
* We say the tracks *do* meet at that point (the Vanishing Point).
* This makes the math of cameras much simpler and more powerful.

'''3. Duality (The Mirror)''':
Projective geometry is perfectly symmetrical.
* For every two points, there is one line connecting them.
* For every two lines, there is one point where they cross.
In Euclidean math, this isn't true (parallel lines don't cross). By adding "Points at Infinity," the symmetry is restored.

'''Invariant''': The most important thing in projective geometry is finding what stays the same. While length and angle change when you tilt a camera, the "Order" of points and the "Cross-Ratio" do not.
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