Editing Projective Geometry (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Projective Matrix' (How a 3D point becomes a 2D Pixel):'''
<syntaxhighlight lang="python">
import numpy as np

def project_point(point_3d, focal_length):
    """
    Simplified Pin-hole camera projection.
    [x, y, z] -> [f*x/z, f*y/z]
    """
    x, y, z = point_3d
    
    # Avoid division by zero
    if z == 0: return (0, 0)
    
    # Projection math
    screen_x = (focal_length * x) / z
    screen_y = (focal_length * y) / z
    
    return (round(screen_x, 2), round(screen_y, 2))

# A point 10 units away
print(f"Point at distance 10: {project_point([2, 2, 10], 5)}")
# A point 20 units away (appears smaller/closer to center)
print(f"Point at distance 20: {project_point([2, 2, 20], 5)}")
</syntaxhighlight>

; Projective Landmarks
: '''The Renaissance''' → Brunelleschi and Alberti's discovery of linear perspective, which changed art from "flat" to "deep."
: '''Desargues's Theorem''' → A fundamental proof about triangles that is only "visible" if you look at them from a 3D perspective.
: '''Photogrammetry''' → The science of using 2D photos to reconstruct a 3D model of a building or a person.
: '''Computer Vision''' → How a self-driving car "knows" how far away a stop sign is just by looking at a 2D image.
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