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Lecture 11 Perspective Projection

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The document discusses different types of projections in 3D computer graphics, including orthographic, oblique, and perspective projections. It explains the geometry and matrices used to perform perspective projections, mapping 3D points onto a 2D view plane using similar triangles. The text also compares perspective versus parallel projections, noting that perspective projection preserves angles and looks more realistic while parallel projection preserves distances and angles.

TechnologyEntertainment & Humor
1 of 27
Projections Angel: Interactive Computer Graphics
Road in perspective
Taxonomy of Projections FVFHP Figure 6.10
Taxonomy of Projections
Parallel Projection ,[object Object],[object Object],Angel Figure 5.4 DOP View Plane
Orthographic Projections ,[object Object],Angel Figure 5.5 Top Side Front
Oblique Projections ,[object Object],H&B Cavalier (DOP  = 45 o ) tan(  ) = 1 Cabinet (DOP  = 63.4 o ) tan(  ) = 2
Orthographic Projection ,[object Object],[object Object],[object Object]
Perspective Transformation ,[object Object],[object Object],[object Object]
Perspective Projection ,[object Object],Angel Figure 5.10 3-Point Perspective 2-Point Perspective 1-Point Perspective
Perspective Projection ,[object Object],[object Object]
Perspective Projection ,[object Object],How tall should this bunny be?
Perspective Projection ,[object Object],[object Object],d P ( x, y, z ) X Z View plane (0,0,0) x’ = ?
Perspective Projection ,[object Object],[object Object]
A Perspective Projection Matrix ,[object Object]
A Perspective Projection Matrix ,[object Object],[object Object]
Projection Matrices ,[object Object],[object Object]
Perspective vs. Parallel ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Classical Projections Angel Figure 5.3
A 3D Scene ,[object Object],[object Object]
Q1 ,[object Object]
A1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Q2 ,[object Object]
Q3 ,[object Object]
A3 ,[object Object]
Q4 ,[object Object]
A4 ,[object Object],[object Object],[object Object],[object Object],[object Object]

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Lecture 11 Perspective Projection