1. Geometric transformations The Pipeline
Computer Graphics Ben-Gurion University of the Negev
Fall 2012
Some slides are based on Shay Shalom slides from TAU

2. How to … Establish your position in the scene
Position objects within the scene
Scale objects
Establish a perspective transformation
Moving around in OpenGL using a camera

3. Terminology Use Tnrasformation
Specifies the location of the viewer or camera
Viewing
Moves objects around the scene
Modeling
Describes the duality of viewing and modeling transformations
ModelView
Clips and sizes the viewing volume
Projection
Scales the final output to the window
Viewport

4. The Pipeline

5. Eye Coordinates Viewpoint of the observer
They are a virtual fixed coordinate system
Used as a common frame of reference

6. Viewing Transformations
Like placing and pointing the camera at the scene
To be specified before any other transformation
By default, the point of observation is at the origin, looking down the negative Z-axis.
What about objects drawn with positive Z values?
Subsequent transformations occur based on the newly modified coordinate system

7. Modeling Transformation
Manipulate the model and the particular objects within it
Move objects into place, rotate them, and scale them
These are the most common modeling transformations

8. Modeling Transformation - the ORDER matters
Final appearance of an object depends greatly on the order of transformations

9. ModelView Duality
In fact, viewing and modeling transformations are the same
Induce the same effects on the final appearance of the scene
The distinctions is made as a convenience for the programmer

10. Projection Transformations
Applied after the modelview transformation
Defines the viewing volume and the clipping planes
Specifies how a finished scene is projected to the screen

11. Orthographic Vs. Perspective
In an Orthographic projection:
objects are mapped directly on the 2D screen using parallel lines
No matter how far away something is
In Perspective projection:
Scenes are more realistic
Distant objects appear smaller than nearby objects of the same size
Parallel lines in 3D space do not always appear parallel
See Code Example 3

12. The Pipeline - Recall

13. Slow but steady .. Current Matrix is part of the OpenGL state
Options are:
GL_MODELVIEW – changes, rotate, translate the model
GL_PROJECTION – changes, translate, rotate the camera
To specify which one is the “Current Matrix” : glMatrixMode(…)
Subsequent matrix operations affect the specified matrix
One of this matrices could be change in a given time

14. Translation
void glTranslatef(GLfloat x, GLfloat y, GLfloat z ) This function takes as parameters the amount to translate along the x, y, and z directions

15. Translation – (cont’)
glTranslate(0.0f, 10.0f, 0.0f) glutWireCube(10.0f)
Construct a translation matrix for positive 10 Y
Multiply it by the modelview matrix

16. Rotation
void glRotatef(Glfloat angle,GLfloat x, GLfloat y, GLfloat z ) This function performs a rotation around the vector specified by the x, y, and z arguments. The angle of rotation is in the counterclockwise direction. A rotation around an arbitrary axis could be done.

17. Scaling void glScalef(GLfloat x, GLfloat y, GLfloat z )
Multiplies the x, y and z values by the scaling factors specified. Scaling does not have to be uniform.

18. The Identity Matrix Matrix operations are cumulative
Erroneous artifacts may occur to the scene
You reset the origin by loading the modelview matrix with the identity matrix
glTranslate(0.0f, 10.0f, 0.0f);
glutSolidSphere(1.0f);
glTranslatef(10.0f, 0.0f, 0.0f);
glutSolidSphere(1.0f)

19. The Identity Matrix – (cont’)
glMatrixMode(GL_MODELVIEW) glLoadIdentity(); glTranslate(0.0f, 10.0f, 0.0f); glutSolidSphere(1.0f); glTranslatef(10.0f, 0.0f, 0.0f); glutSolidSphere(1.0f)

20. Matrix stack
Resetting the modelview matrix to identity before placing the every object is not always desirable
To save the current transformation state
OpenGL maintains a matrix stack for both the modelview and projection matrices
glPushMatrix() – push the current state matrix to the stack
glPopMatrix() – pop the top matrix out of the stack, and replace the current state matrix with it

21. Matrix stack – (cont’)
See Code Example 4

22. glOrtho(left, right, bottom, top, near, far)
Viewing Volume
glOrtho(left, right, bottom, top, near, far)

23. Viewing Volume – (cont’)
glFrustum(left, right, bottom, top, near, far) gluPerspective(GLdouble fov ,GLdouble aspectRatio,GLdouble zNear,GLdouble zFar)

24. Camera Management
gluLookAt(GLdouble eyex, GLdouble eyey, Gldouble eyez, GLdouble centerx, GLdouble centery, GLdouble centerz, GLdouble upx, GLdouble upy, GLdouble upz)

25. Buffers Important aspect of the current state of OpenGL
Buffers dimensions are the same as the window’s dimension
Color Buffer – stores the current color for each pixel
Depth Buffer – stores the depth of each pixel of the scene (Z-Buffer)
Accumulation buffer, stencil buffer, etc’ ..
glEnable(GL_DEPTH_TEST) – enables the Z-Buffer in OpenGL. ….. Otherwise?