Viewing CS418 Computer Graphics John C. Hart Graphics Pipeline - - PowerPoint PPT Presentation

Viewing

CS418 Computer Graphics John C. Hart

Graphics Pipeline

Homogeneous Divide Model Coords Model Xform World Coords Viewing Xform Still Clip Coords. Clipping Window Coordinates Window to Viewport Viewport Coordinates Clip Coords. Viewing Coords Perspective Distortion

Graphics Pipeline

Homogeneous Divide Model Coords Model Xform World Coords Viewing Xform Still Clip Coords. Clipping Window Coordinates Window to Viewport Viewport Coordinates Clip Coords. Viewing Coords Perspective Distortion

W2V Persp View Model 1 1

s m s m m

x x y y z                                                                         

Graphics Pipeline

Homogeneous Divide Model Coords Model Xform World Coords Viewing Xform Still Clip Coords. Clipping Window Coordinates Window to Viewport Viewport Coordinates Clip Coords. Viewing Coords Perspective Distortion

1

s s

x y                    1

m m m

x y z                  

M

Transformation Order

1

s s

x y                    1

m m m

x y z                  

M

x y z glutSolidTeapot(1); glRotate3f(-90, 0,0,1); glTranslate3f(0,1,0); glutSolidTeapot(1); glTranslate3f(0,1,0); glRotate3f(-90, 0,0,1); glutSolidTeapot(1);

1

s s

x y                    1

m m m

x y z                                          

M R T

1

s s

x y                    1

m m m

x y z                                          

M T R

Viewing Transformation

Homogeneous Divide Model Coords Model Xform World Coords Viewing Xform Still Clip Coords. Clipping Window Coordinates Window to Viewport Viewport Coordinates Clip Coords. Viewing Coords Perspective Distortion

W2V Persp View Model 1 1

s m s m m

x x y y z                                                                         

Viewing Transformation

W2V           Model           View           Persp          

Model Coords World Coords Viewing Coords Clip Coords Screen Coords x y z x y lookat point eye point

x y z

World Coordinates Viewing Coordinates

x y z

eye point lookat point eye point (at origin) lookat point (along –z axis)

x y z

World Coordinates Viewing Coordinates

x y

eye point lookat point lookat point (along –z axis)

x y z

World Coordinates Viewing Coordinates

x y

eye point lookat point

y' x' Why not these axes?

x y z

World Coordinates Viewing Coordinates

y z

eye point lookat point up vector up vector up

• 1. Specify up direction in

world coordinates

• 2. Transform up vector into

viewing coordinates

• 3. Rotate about z-axis until

up vector in x-y plane.

x

Lookat Transformation

x y z lookat point eye point up vector

Lookat Transformation

• 1. Translate the eye point

to the origin

x y z

1 1 1 1 x y z               

Lookat Transformation

• 1. Translate the eye point

to the origin

• 2. Rotate the view vector

into the negative z-axis

x y z

1 1 1 1 x y R z                           

x y z

Easier Way

• Orthogonalize lookat vector system

x y z up v

Easier Way

• Orthogonalize lookat vector system

– Let r = v  up/||vup|| x y z up r v

Easier Way

• Orthogonalize lookat vector system

– Let r = v  up/||vup|| – Let u = r  v x y z up u v r

Easier Way

• Orthogonalize lookat vector system

– Let r = v  up/||vup|| – Let u = r  v – Create rotation matrix from <r,u,-v> to <x.y,z> R r = x, R u = y, R v = -z x y z up u v r

Construct Lookat

• Translate eye point to origin
• Rotate view into -z axis

– Let v = (lookat - eye)/||lookat - eye|| – Let r = v  up/||vup|| – Let u = r  v x y z

x y z

lookat point eye point up vector

Viewing Transformation

W2V           Model           View           Persp          

Model Coords World Coords Viewing Coords Clip Coords Screen Coords x y z x y z lookat point eye point