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An in-depth exploration of 3d transformations, including translations, scalings, and rotations, using homogeneous coordinates and matrix-based transformations. Additionally, it covers the concept of projections, their history, geometrical constructions, and various types, such as perspective and parallel projections, in computer graphics.
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( x, y, z ) Translated Position ( x’, y’, z’ ) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004) Docsity.com
( x, y, z ) Scaled Position
( x’, y’, z’ ) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004) Docsity.com
Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)
y’ = x·^ x’ = x· sincosθθ +^ - y·y· cossinθθ z’ = z y’ = y· cos^ x’ = x θ - z· sinθ z’ = y· sinθ + z· cosθ
x’ = z· sin y’ = y θ + x· cosθ z’ = z· cosθ - x· Docsity.comsinθ
1^ z
yx
x axis
y axis
z axis
P
y
P( x, y, z ) =^ z x Docsity.com
Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004) Docsity.com
Picture Plane Objects inWorld Space
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Parallel Projection Perspective Projection Docsity.com
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QBert Sim City Virtual Magic Kingdom* Docsity.com
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Elements Of A Perspective Projection
Camera^ Virtual Docsity.com
Up vector (^) Look vector Position
Projection ofup vector
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