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Viewing - PowerPoint PPT Presentation

Viewing. The Camera and Projection. Gail Carmichael (gail_c@scs.carleton.ca). 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

The Camera and Projection

Gail Carmichael (gail_c@scs.carleton.ca)

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: MW

Orthographic Projection

Orthographic

Perspective

Orthographic View to Canonical View

Move to

Origin

Scale

World to Canonical Coordinates

Orthographic View to Canonical View

World to Canonical Coordinates

Drawing Lines in Orthographic View

Mo=Mw MscaleMmove_to_origin

= Mo

Arbitrary View Positions

Top of cameragoes this way

Camera is looking this way

Camera is centered here

Arbitrary View Positions

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

u = (t × w) / || t × w ||

v = w × u

Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv

Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv

Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv

?

?

=

Coordinate Transformations

p = (xp,yp) ≡ o + xpx + ypy

p = (up,vp) ≡ e + upu + vpv

=

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