Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf ·...
Transcript of Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf ·...
![Page 1: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/1.jpg)
Classical Viewing
Ed AngelProfessor of Computer Science,
Electrical and Computer Engineering, and Media Arts
University of New Mexico
![Page 2: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/2.jpg)
2Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Objectives
• Introduce the classical views•Compare and contrast image formation by computer with how images have been formed by architects, artists, and engineers
•Learn the benefits and drawbacks of each type of view
![Page 3: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/3.jpg)
3Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
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 - Buildings, polyhedra, manufactured objects
![Page 4: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/4.jpg)
4Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Planar 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 for applications such as map construction
![Page 5: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/5.jpg)
5Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Classical Projections
![Page 6: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/6.jpg)
6Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Perspective vs Parallel
•Computer graphics treats all projections the same and implements them with a single pipeline
•Classical viewing developed different techniques for drawing each type of projection
•Fundamental distinction is between parallel and perspective viewing even though mathematically parallel viewing is the limit of perspective viewing
![Page 7: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/7.jpg)
7Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Taxonomy of Planar Geometric Projections
parallel perspective
axonometricmultivieworthographic
oblique
isometric dimetric trimetric
2 point1 point 3 point
planar geometric projections
![Page 8: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/8.jpg)
8Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Perspective Projection
![Page 9: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/9.jpg)
9Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Parallel Projection
![Page 10: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/10.jpg)
10Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Orthographic Projection
Projectors are orthogonal to projection surface
![Page 11: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/11.jpg)
11Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Multiview Orthographic Projection
• Projection plane parallel to principal face• Usually form front, top, side views
isometric (not multivieworthographic view) front
sidetop
in CAD and architecture, we often display three multiviews plus isometric
![Page 12: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/12.jpg)
12Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Advantages and Disadvantages
•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
![Page 13: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/13.jpg)
13Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Axonometric Projections
Allow projection plane to move relative to object
classify by how many angles ofa corner of a projected cube are the same
none: trimetrictwo: dimetricthree: isometric
θ 1
θ 3θ 2
![Page 14: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/14.jpg)
14Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Types of Axonometric Projections
![Page 15: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/15.jpg)
15Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Advantages and Disadvantages
• 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
![Page 16: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/16.jpg)
16Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Oblique Projection
Arbitrary relationship between projectors and projection plane
![Page 17: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/17.jpg)
17Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Advantages and Disadvantages
• 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)
![Page 18: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/18.jpg)
18Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Perspective Projection
Projectors coverge at center of projection
![Page 19: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/19.jpg)
19Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
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
![Page 20: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/20.jpg)
20Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Three-Point Perspective
• No principal face parallel to projection plane• Three vanishing points for cube
![Page 21: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/21.jpg)
21Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Two-Point Perspective
• On principal direction parallel to projection plane• Two vanishing points for cube
![Page 22: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/22.jpg)
22Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
One-Point Perspective
• One principal face parallel to projection plane• One vanishing point for cube
![Page 23: Ed Angel Professor of Computer Science, Electrical and ...angel/CS433.S05/LECTURES/AngelCG16.pdf · Perspective vs Parallel •Computer graphics treats all projections the same and](https://reader030.fdocuments.net/reader030/viewer/2022041011/5ebba061213d646cde63e0d9/html5/thumbnails/23.jpg)
23Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002
Advantages and Disadvantages
• Objects further from viewer are projected smaller than the same sized objects closer to the viewer (diminuition)
- 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)