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Viewing. The Camera and Projection. Gail Carmichael ([email protected]). The Goal. Understand the process of getting from 3D line segments to images of these lines on the screen. Canonical View Volume. Windowing transform brings points to pixels: M W. Canonical View Volume. =. M w.

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Presentation Transcript
Viewing

Viewing

The Camera and Projection

Gail Carmichael ([email protected])


The goal
The Goal

Understand the process of getting from 3D line segments to images of these lines on the screen.


Canonical view volume
Canonical View Volume

Windowing transform brings points to pixels: MW



Orthographic projection
Orthographic Projection

Orthographic

Perspective



Orthographic view to canonical view
Orthographic View to Canonical View

Move to

Origin

Scale

World to Canonical Coordinates


Orthographic view to canonical view1
Orthographic View to Canonical View

World to Canonical Coordinates


Drawing lines in orthographic view
Drawing Lines in Orthographic View

Mo=Mw MscaleMmove_to_origin

= Mo


Arbitrary view positions
Arbitrary View Positions

Top of cameragoes this way

Camera is looking this way

Camera is centered here


Arbitrary view positions1
Arbitrary View Positions

w = - (g / ||g||)

u = (t × w) / || t × w ||

v = w × u






Coordinate transformations3
Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv


Coordinate transformations4
Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv


Coordinate transformations5
Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv

?

?

=


Coordinate transformations6
Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv

=













Caution
CAUTION!!

Everything up until now used the more common right-hand coordinate system.

Direct3D uses the left-hand coordinate system.

See:http://msdn.microsoft.com/en-us/library/windows/desktop/bb204853%28v=vs.85%29.aspx


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