# Classical Viewing

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### Classical Viewing

• Viewing requires three basic elements - One or more objects

- A viewer with a projection surface

- Projectors that go from the object(s) to the projection surface

• Classical views are based on the relationship among these elements

- The viewer picks up the object and orients it how she would like to see it

• Each object is assumed to constructed from flat principal faces

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### • Projectors are lines that either

- converge at a center of projection - are parallel

### • Such projections preserve lines

- but not necessarily angles

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### Taxonomy of PlanarGeometric Projections

parallel perspective

axonometric multiview

orthographic oblique

isometric dimetric trimetric

2 point

1 point 3 point

planar geometric projections

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### Orthographic Projection

Projectors are orthogonal to projection surface

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### Multiview OrthographicProjection

• Projection plane parallel to principal face

• Usually form front, top, side views

isometric (not multiview

orthographic view) front

top side in CAD and architecture, we often display three

multiviews plus isometric

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### • Preserves both distances and angles

- Shapes preserved

- Can be used for measurements

Building plans

Manuals

### • Cannot see what object really looks like because many surfaces hidden from view

- Often we add the isometric

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### Axonometric Projections

Allow projection plane to move relative to object

classify by how many angles of a corner of a projected cube are the same

none: trimetric two: dimetric three: isometric

θ 1 θ 3 θ 2

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### Projections

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• Lines are scaled (foreshortened) but can find scaling factors

• Lines preserved but angles are not

- Projection of a circle in a plane not parallel to the projection plane is an ellipse

• Can see three principal faces of a box-like object

• Some optical illusions possible

- Parallel lines appear to diverge

• Does not look real because far objects are scaled the same as near objects

• Used in CAD applications

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### Oblique Projection

Arbitrary relationship between projectors and projection plane

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• Can pick the angles to emphasize a particular face

- Architecture: plan oblique, elevation oblique

• Angles in faces parallel to projection plane are preserved while we can still see “around” side

• In physical world, cannot create with simple

camera; possible with bellows camera or special lens (architectural)

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### Vanishing Points

• Parallel lines (not parallel to the projection plan) on the object converge at a single point in the projection (the vanishing point)

• Drawing simple perspectives by hand uses these vanishing point(s)

vanishing point

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### Three-Point Perspective

• No principal face parallel to projection plane

• Three vanishing points for cube

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### Two-Point Perspective

• On principal direction parallel to projection plane

• Two vanishing points for cube

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### One-Point Perspective

• One principal face parallel to projection plane

• One vanishing point for cube

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• Objects further from viewer are projected

smaller than the same sized objects closer to the viewer (diminution)

- Looks realistic

• Equal distances along a line are not projected into equal distances (nonuniform foreshortening)

• Angles preserved only in planes parallel to the projection plane

• More difficult to construct by hand than parallel projections (but not more difficult by computer)

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## References

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