1. CS 352: Computer Graphics
Chapter 5:
Viewing

2. Overview Specifying the viewpoint Specifying the projection
Interactive Computer Graphics
Overview
Specifying the viewpoint
Specifying the projection
Types of projections
Viewing APIs
Walking through a scene
Projections and shadows

3. How do cameras work? Interactive Computer Graphics
Camera Obscura – what does it mean in Latin? (Dark room)

4. Synthentic camera model
Interactive Computer Graphics
Synthentic camera model
1. Camera is placed at a location, pointed in a direction (modeling matrix)
2. 3D points are flattened onto the viewing plane (projection matrix)
What do we need to know about the camera (real or synthetic)?

5. Synthetic camera parameters
Interactive Computer Graphics
Synthetic camera parameters
Position of camera
Direction it is pointed [look vector]
Angle of film to look vector [view plane normal]
Rotation around viewing direction [up vector]
Height angle (zoom setting) [fovy]
Aspect ratio of "film" (width/height)
Front and back clipping planes
Focal length
Field of view
Shutter speed

6. Interactive Computer Graphics
Depth of ffield
Focal length

7. Perspective distortion
Interactive Computer Graphics
Perspective distortion
How would you film dizziness?
Vertigo effect [2]
You can also make someone look like an ogre…

8. Projections Basic Elements: Basic Types Objects, viewer
Interactive Computer Graphics
Projections
Basic Elements:
Objects, viewer
Projection plane
Projectors
Center of projection
Direction of projection (DOP)
Basic Types
Perspective
Parallel (COP at infinity)

9. Classical viewing Interactive Computer Graphics
The point of classical viewing is to show a specific relationship among object, viewer and projection plane. These are all special cases of the more general “perspective” and “parallel” views of computer graphics.

10. Orthographic projection
Interactive Computer Graphics
Orthographic projection
Orthographic: parallel projection with projectors perpendicular to the projection plane.
Often used as front, side, top views for 3D design
Importance: preservation of distance and angle
Often used for top, front, and size views, e.g. in a modeling program or working drawing

11. Perspective projection
Interactive Computer Graphics
Perspective projection
Perspective projections: projectors converge at COP
Classical perspective views: 1, 2, and 3-point (1, 2, or 3 vanishing points)
Difference: how many of the principle axes of the object are parallel to projection plane (I.e., depends on relationship of object to viewing frame)

12. Interactive Computer Graphics
1. Position the camera
By default, camera is at origin, looking in –z dir
To “move the camera”, set up a modelview matrix that moves objects that are drawn
Ignore Z-coordinate when drawing
E.g. dimetric view?
Dimetric: 45 degree angle from x,z axes
Think of affecting object: rotate while it’s at the origin, then translate
modelview = identity
translate(0,0,-d)
rotate(-45,<0,1,0>);

13. Exercise: look from +x axis
Interactive Computer Graphics
Exercise: look from +x axis
How would you change the camera to generate a view down the +x axis to origin?
Do this before displaying objects:
modelview = identity;
translate(0, 0, -d);
rotate(-90, [0, 1, 0]);

14. Exercise: front/top view
Interactive Computer Graphics
Exercise: front/top view
How would you change the camera to generate a view from (0, 10, 10) to origin?
Do this before displaying objects:
modelview = identity;
translate(0,0,-14.14);
rotate(45, [1, 0, 0]);

15. Helper function: lookAt
Interactive Computer Graphics
Helper function: lookAt
Most 3D toolkits let you position the camera by setting eyepoint, lookpoint, and up direction
lookAt(Xeye, Yeye, Zeye, Xat, Yat, Zat, Xup, Yup, Zup):
Effect: set the modelview matrix

16. Rolling your own lookAt
Interactive Computer Graphics
Rolling your own lookAt
How could you write your own lookAt function?
lookAt(Xeye, Yeye, Zeye, Xat, Yat, Zat, Xup, Yup, Zup):

17. Defining a lookAt function
Interactive Computer Graphics
Defining a lookAt function
lookAt(Xeye, Yeye, Zeye, Xat, Yat, Zat, Xup, Yup, Zup):
translate <Xat, Yat, Zat> to origin
rotate so that <Xeye, Yeye, Zeye> points in the Z direction
normalize <Xeye, Yeye, Zeye>
trackball-like rotation to <0,0,1>
rotate so <Xup, Yup, Zup> is <0,1,0>
trackball-like rotation

18. Camera API 2: uvn frame Camera parameters:
Interactive Computer Graphics
Camera API 2: uvn frame
Camera parameters:
VRP: view reference point, a point on the image plane
VPN: view plane normal (n)
VUP: vector in up direction
(also need viewing direction, if not VPN)
Result: viewing coordinate system, u-v-n.
v = projection of VUP onto image plane
u = v x n
u, v axes: coordinates in the image plane
n axis: normal to image plane

19. Camera API 3: roll, pitch, yaw
Interactive Computer Graphics
Camera API 3: roll, pitch, yaw
Specify location + orientation: roll, pitch, yaw

20. Interactive Computer Graphics
2. Specify projection
Once we have located and pointed the camera along the –z axis, we still need to specify the lens (projection).

21. Parallel projection We’re already looking along the –z axis
Interactive Computer Graphics
Parallel projection
We’re already looking along the –z axis
Set z=0 for all points (or ignore z coordinate when rendering)

22. Interactive Computer Graphics
Parallel projection
View volume is generally specified with clipping planes: e.g.
glOrtho(xmin, xmax, ymin, ymax, near, far)
Z clipping planes at –near and –far

23. Perspective projection
Interactive Computer Graphics
Perspective projection
Need to build appropriate perspective projection matrix into vertex shader
What kind of transformation would this be?

24. Perspective projections
Interactive Computer Graphics
Perspective projections
COP at origin
Looking in –z direction
Projection plane in front of origin at z=d

25. Interactive Computer Graphics
Foreshortening
By similar triangles in previous image, we see that and similarly for y.
Using the perspective matrix we get p’ =
Adding divide-by-w to the graphics pipeline gives the correct result.
Note that using “distance-from” as Z gives positive values; using a right-handed XYZ coord system gives negative Z values in default view.

26. Perspective Frustum Perspective viewing region is a “frustum”:
Interactive Computer Graphics
Perspective Frustum
Perspective viewing region is a “frustum”:
Viewplane normally coincides with front clip plane

27. Interactive Computer Graphics
Camera APIs
In raw OpenGL ES, you “position the camera” by programming a vertex shader to apply a modelview matrix
Frameworks provide functions to build a viewing matrix for you, using a “camera API”
Example:
perspectiveCamera(FOV, aspect, near, far)

28. Perspective projection
Interactive Computer Graphics
Perspective projection
3D graphics toolkits provide tools for specifying a perspective projection, e.g.

29. Interactive Computer Graphics
Shadows
How can one generate shadows in a scene using interactive graphics techniques?
In general it's hard, not supported in standard graphics pipeline—you need to know where everything is globally to render a point locally
Special techniques let you “fake it”. How to use a projection?

30. Projections and shadows
Interactive Computer Graphics
Projections and shadows
Projections can be used to generate simple shadow polygons
Light (xl, yl, zl)
Translate light to origin
Project down y axis [M]
Translate back

31. Simple Shadow in OpenGL
Interactive Computer Graphics
Simple Shadow in OpenGL
GLfloat m[16]; //projection matrix
for (int i=0; i<16; i++) m[i]=0;
m[0]=m[5]=m[10]=1;
m[7] = -1/yl;
glBegin(); [draw polygon normally]; glEnd();
glMatrixMode(GL_MODELVIEW);
glPushMatrix; //save state
glTranslatef(xl, yl, zl);
glMultMatrix(m);
glTranslatef(-xl, -yl, -zl);
glColor3fv(shadow_color);
[draw polygon]
glEnd();
glPopMatrix();

32. Walking through a scene
Interactive Computer Graphics
Walking through a scene
How to animate viewer motion through a scene? [Demo]
Assume viewer’s height is fixed; looking direction is in y=6 plane
Store viewer’s location (x,6,z) and orientation (θ). Update appropriately with user commands
LookAt( x, y, z, x + cos(θ), y, z + sin(θ), 0, 1, 0);
Or adjust LookAt according to mouse position

33. Credits Interactive Computer Graphics Demos Musical solar system
1. (Pinhole camera): Wikipedia.
5. Synthetic camera parameters: Liz Marai, Pitt
Demos
Musical solar system

34. Interactive Computer Graphics
Khronos.org

35. Interactive Computer Graphics