1. Unit 4 3D Viewing Pipeline Part - 2
Projections

2. 3D Viewing Pipeline Primitives Object space World space Camera space
Modeling Transformation
World space
Viewing Transformation
Camera space
Hidden Surface Removal
Lighting & Shading
3D-Clipping
Projection
Normalized view space
Scan conversion, Hiding
Image space, Device coordinates
Balwinder Kaur, Assistant Professor, LPU.
Image

3. Introduction Perspective Projections Parallel Projections
Contents
Introduction
Perspective Projections
Parallel Projections

4. Viewing and Projection
Camera Analogy:
1. Set up your tripod and point the camera at
the scene (viewing transformation).
2. Arrange the scene to be photographed into
the desired composition (modeling transformation).
3. Choose a camera lens or adjust the zoom
(projection transformation).
4. Determine how large you want the final
photograph to be - for example, you might
want it enlarged (viewport transformation).
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5. Balwinder Kaur, Assistant Professor, LPU.

6. Balwinder Kaur, Assistant Professor, LPU.
Projections
Our 3-D scenes are all specified in 3-D world coordinates
To display these we need to generate a 2-D image - project objects onto a picture plane
So how do we figure out these projections?
Picture Plane
Objects in
World Space
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7. Projections
Projection is just one part of the process of converting from 3-D world coordinates to a 2-D image
3-D world coordinate output primitives
Clip against view volume
Project onto projection plane
Transform to 2-D device coordinates
2-D device coordinates
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8. Projection Transformation
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9. Balwinder Kaur, Assistant Professor, LPU.

10. Balwinder Kaur, Assistant Professor, LPU.
Projections
There are two broad classes of projection:
Parallel: Typically used for architectural and engineering drawings
Perspective: Realistic looking and used in computer graphics
Perspective Projection
Parallel Projection
Balwinder Kaur, Assistant Professor, LPU.

11. Balwinder Kaur, Assistant Professor, LPU.
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
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12. Classical Projections
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13. Balwinder Kaur, Assistant Professor, LPU.
Projections
Balwinder Kaur, Assistant Professor, LPU.

14. Introduction Perspective Projections Parallel Projections
Contents
Introduction
Perspective Projections
Parallel Projections

15. Perspective Projections
Perspective projections are much more realistic than parallel projections and are used by artists.
Balwinder Kaur, Assistant Professor, LPU.

16. Perspective Projections
Perspective projections are described by
Centre of projection: Eye of artists or lens of camera
View Plane: Plane containing canvas or film strip or frame buffer
A ray called projector is drawn from COP to object point, its intersection with view plane determines the projected image point on view plane.
Projector
COP
View Plane
Y-axis
Z-axis
Object point
Projected point
X-axis
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17. Perspective Projection
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18. Balwinder Kaur, Assistant Professor, LPU.
Parallel Projections
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19. Perspective Projections
There are a number of different kinds of perspective views
The most common are one-point and two point perspectives
Balwinder Kaur, Assistant Professor, LPU.

20. Perspective Projections
Perspective drawings are characterised by
Perspective foreshortening
Vanishing points
View Confusion
Topological Distortion
These are also known as Perspective Anomalies.
These anomalies enhance realism in terms of depth cues, but distorts the actual size, shape and relationship between parts of object.
Balwinder Kaur, Assistant Professor, LPU.

21. Perspective Projections
1. Perspective foreshortening: an illusion that objects and lengths appear smaller as their distance form COP increases.
We can see three balls have different dimensions, since they placed at different distances they are projected to same length
Y-axis
Z-axis
COP(0,0,-d)
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22. Perspective Projections
Increasing the field of view angle increases the height of the view plane and so increases foreshortening
Balwinder Kaur, Assistant Professor, LPU.

23. Perspective Projections
The amount of foreshortening that is present can greatly affect the appearance of our scenes
Balwinder Kaur, Assistant Professor, LPU.

24. Perspective Projections
2. Vanishing points: An illusion that certain sets of parallel lines appear to meet at a point (called vanishing point).
These are those lines that are not parallel to view plane i.e. lines that are not  to view plane normal.
Principal vanishing points are formed by apparent intersection of lines parallel to one of the three principal axes.
The number of principal vanishing points is determined by the number of principal axis intersected by the view plane.
X-axis
Z-axis
Y-axis
COP
(0,0,-d) L1 L2
L’1
L’2 O
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25. Perspective Projections
(from Donald Hearn and Pauline Baker)
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26. Classes of Perspective Projection
One-Point Perspective
Two-Point Perspective
Three-Point Perspective
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27. One-Point Perspective
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28. Two-point perspective projection:
This is often used in architectural, engineering and industrial design drawings.
Balwinder Kaur, Assistant Professor, LPU.

29. Three-point perspective projection
Three-point perspective projection is used less frequently as it adds little extra realism to that offered by two-point perspective projection
Balwinder Kaur, Assistant Professor, LPU.

30. Perspective Projections
3. View Confusion: An object behind the COP is projected upside down and backward onto the view plane.
X-axis
Z-axis
Y-axis
COP(0,0,-d) L1 L2
L’1
L’2 O
Balwinder Kaur, Assistant Professor, LPU.

31. Perspective Projections
4. Topological Distortion: All points lying on the plane parallel to view plane and passing through the COP are projected to ∞ by the perspective transformation.
This may make a finite line segment
to appear as two infinite rays.
X-axis
Z-axis
Y-axis
COP(0,0,-d) O P1 P2
P’1
P’2 P3 ∞
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32. Perspective Projections
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33. Perspective Projections
Although a perspective projection is set up by specifying the position and size of the view plane and the position of the projection reference point called COP
However, this can be kind of awkward
Balwinder Kaur, Assistant Professor, LPU.

34. Perspective Projections
The field of view angle can be a more intuitive way to specify perspective projections
This is analogous to choosing a lense for a camera
Balwinder Kaur, Assistant Professor, LPU.
Field of view

35. Perspective Projections
We need one more thing to specify a perspective projections using the filed of view angle
The aspect ratio gives the ratio between the width sand height of the view plane
Balwinder Kaur, Assistant Professor, LPU.

36. Introduction Perspective Projections Parallel Projections
Contents
Introduction
Perspective Projections
Parallel Projections

37. Balwinder Kaur, Assistant Professor, LPU.
Parallel Projections
Parallel projections are used by drafter and engineers to create working drawings of an object as they preserve scale and shape
These are described by
Viewing Direction: which describe the direction of projection
View Plane: Plane containing canvas or film strip or frame buffer
A ray called projector is drawn || to Viewing direction and passing through object point, its intersection with view plane determines the projected image point on view plane.
Y-axis
Object
Viewing Direction
Object’
View Plane
X-axis
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Z-axis

38. Balwinder Kaur, Assistant Professor, LPU.
Parallel Projection
Center of projection is at infinity
Direction of projection (DOP) same for all points
View
Plane
DOP
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39. Balwinder Kaur, Assistant Professor, LPU.
Parallel Projections
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40. Orthographic Projections
DOP perpendicular to view plane
Front
Top
Side
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41. Balwinder Kaur, Assistant Professor, LPU.
Oblique Projections
DOP not perpendicular to view plane
Cavalier
(DOP  = 45o)
Cabinet
(DOP  = 63.4o)
Balwinder Kaur, Assistant Professor, LPU.

42. Balwinder Kaur, Assistant Professor, LPU.
Cavalier Projection- It is obtained when the angle between the oblique projectors and the plane of projection is 45 degree and the foreshortening factors for all three principal directions are equal.
In Cavalier projection , the resulting figure is too thick.
Balwinder Kaur, Assistant Professor, LPU.

43. Balwinder Kaur, Assistant Professor, LPU.
Cabinet Projection- It is used to correct the deficiency that is produced by Cavalier projection.
An oblique projection for which the foreshortening factor for the edge perpendicular to the plane of projection is one-half is called Cabinet projection.
For a cabinet projection, the angle between the projectors and the plane of projection is
Balwinder Kaur, Assistant Professor, LPU.

44. Balwinder Kaur, Assistant Professor, LPU.
Parallel Projections
Oblique Projection
Identify type parallel projections
Orthographic Projection
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Isometric Projection

45. Balwinder Kaur, Assistant Professor, LPU.
Parallel Projections
Isometric projections have been used in computer games from the very early days of the industry up to today
Q*Bert
Sim City
Virtual Magic Kingdom
Balwinder Kaur, Assistant Professor, LPU.

46. Balwinder Kaur, Assistant Professor, LPU.
Auxiliary View
An auxiliary view is an orthographic view taken in such a manner that the lines of sight are not parallel to the principal projection planes (frontal, horizontal, or profile). There are an infinite number of possible auxiliary views of any given object. Principal faces of the object are not parallel to PP planes.
Balwinder Kaur, Assistant Professor, LPU.

47. Balwinder Kaur, Assistant Professor, LPU.
Why Auxiliary View?
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48. Balwinder Kaur, Assistant Professor, LPU.
Why Auxiliary View?
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49. Balwinder Kaur, Assistant Professor, LPU.
Why Auxiliary View?
Inclined planes and oblique lines do not appear true length or true size in any of the principle planes of projection
To determine the true length of an oblique line or the true size of an inclined plane, an auxiliary view must be created.
The auxiliary view shows the true shape and size of circular shapes.
Balwinder Kaur, Assistant Professor, LPU.

50. Balwinder Kaur, Assistant Professor, LPU.
Orthogonal:
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
Orthogonal:
1. glOrtho(left, right, bottom, top, near, far);
2. gluOrtho2D(left, right, bottom, top);
Balwinder Kaur, Assistant Professor, LPU.

51. Balwinder Kaur, Assistant Professor, LPU.
Perspective:
Perspective:
1. gluPerspective(fovy, aspect, zNear, zFar );
2. (glFrustum)
Balwinder Kaur, Assistant Professor, LPU.

52. Balwinder Kaur, Assistant Professor, LPU.

53. Balwinder Kaur, Assistant Professor, LPU.