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1Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Classical ViewingEd AngelProfessor of Computer Science,Electrical and ComputerEngineering, and Media ArtsUniversity of New Mexico2Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Objectives• Introduce the classical views• Compare and contrast image formationby computer with how images have beenformed by architects, artists, andengineers• Learn the benefits and drawbacks ofeach type of view3Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Classical 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 projectionsurface• Classical views are based on the relationship amongthese elements- The viewer picks up the object and orients it how shewould like to see it• Each object is assumed to constructed from flatprincipal faces- Buildings, polyhedra, manufactured objects4Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Planar Geometric Projections• Standard projections project onto a plane• Projectors are lines that either- converge at a center of projection- are parallel• Such projections preserve lines- but not necessarily angles• Nonplanar projections are needed forapplications such as map construction5Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Classical Projections6Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Perspective vs Parallel• Computer graphics treats all projectionsthe same and implements them with asingle pipeline• Classical viewing developed differenttechniques for drawing each type ofprojection• Fundamental distinction is betweenparallel and perspective viewing eventhough mathematically parallel viewing isthe limit of perspective viewing7Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Taxonomy of PlanarGeometric Projectionsparallel perspectiveaxonometric multivieworthographicobliqueisometric dimetric trimetric2 point1 point 3 pointplanar geometric projections8Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Perspective Projection9Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Parallel Projection10Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Orthographic ProjectionProjectors are orthogonal to projection surface11Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Multiview OrthographicProjection• Projection plane parallel to principal face• Usually form front, top, side viewsisometric (not multivieworthographic view)frontsidetopin CAD and architecture, we often display three multiviews plus isometric12Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Advantages andDisadvantages• Preserves both distances and angles- Shapes preserved- Can be used for measurements• Building plans• Manuals• Cannot see what object really looks likebecause many surfaces hidden from view- Often we add the isometric13Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Axonometric ProjectionsAllow projection plane to move relative to objectclassify by how many angles ofa corner of a projected cube are the samenone: trimetrictwo: dimetricthree: isometricθ 1θ 3θ 214Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Types of AxonometricProjections15Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Advantages andDisadvantages• Lines are scaled (foreshortened) but can findscaling factors• Lines preserved but angles are not- Projection of a circle in a plane not parallel to theprojection 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 arescaled the same as near objects• Used in CAD applications16Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Oblique ProjectionArbitrary relationship between projectors andprojection plane17Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Advantages andDisadvantages• Can pick the angles to emphasize a particularface- Architecture: plan oblique, elevation oblique• Angles in faces parallel to projection plane arepreserved while we can still see “around” side• In physical world, cannot create with simplecamera; possible with bellows camera or speciallens (architectural)18Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Perspective ProjectionProjectors coverge at center of projection19Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Vanishing Points• Parallel lines (not parallel to the projection plan)on the object converge at a single point in theprojection (the vanishing point)• Drawing simple perspectives by hand usesthese vanishing point(s)vanishing point20Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Three-Point Perspective• No principal face parallel to projection plane• Three vanishing points for cube21Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Two-Point Perspective• On principal direction parallel to projection plane• Two vanishing points for cube22Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005One-Point Perspective• One principal face parallel to projection plane• One vanishing point for cube23Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005Advantages andDisadvantages• Objects further from viewer are projectedsmaller than the same sized objects closer tothe viewer (diminution)- Looks realistic• Equal distances along a line are not projectedinto equal distances (nonuniform foreshortening)• Angles preserved only in planes parallel to theprojection plane• More difficult to construct by hand than parallelprojections (but not more difficult by


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UNM CS 433 - CS 433 Classical Viewing

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