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Viewing

Sheelagh Carpendale

Viewing• 3D object, flat display• Viewing pipeline• projection• View plane or projection

plane

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Analogous to Photography

• Position the camera

• Decide on the camera orientation

• Use a suitable lens

Entertainment Industry• More than real photography• Change the camera positions• Move position in any 3D path• Great impact on movie and game industry

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Modeling and Rendering Impossible scenes

Modeling and Rendering Impossible scenes

Guillermo Savransky, Dan Dimerman, Craig Gotsman: Modeling and Rendering Escher-Like Impossible Scenes

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Modeling and Rendering Impossible Scenes

Modeling and Rendering Impossible scenes

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Modeling and Rendering Impossible scenes

Parallel projection

• Simple projection

• Focus the lens of camera on infinity

• Example

• Transformation matrix

• Affine but non-invertible

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Generalization

• how about other viewplanes

• moving viewplane along the z axis

• Transformation matrix

Orthographic projection

B’s view C’s view

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Orthographic projection

front

top

• Front, side and top views

• Commonly are employed in engineering and architectural drawing

• Length and angles can be measured

side

Orthographic Projections

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What is the shape?

Oblique projection

• Generalizing the angle of the viewplane

• Vp is a given projector

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Oblique projection

• Generalizing the angle of the viewplane

• Vp is a given projector

Matrix form of Oblique Transformation

• The projector can be specified by 2 angles

• a, b ?• Affine transformation?

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Special Oblique Projections

Oblique Projections

xx

yy

zz

φ

cavaliercavalier

dd

dd

xx

yy

zz

φ

cabinetcabinet

dd

d/2d/2

• both have true front view• cavalier: distance true• cabinet: distance half

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Projection Taxonomy

planarplanarprojectionsprojections

perspective:perspective:1,2,31,2,3--pointpoint

parallelparallel

obliqueoblique orthographicorthographic

cabinetcabinet cavaliercavalier toptop frontfront sideside

Perspective projection

• The focus of the camera lens on a near point

• Distant lines are displayed smaller

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Ames Room