Transformations

1
Transformations

• Modeling Transformation
• Viewing Transformation
• Projection Transformation
• Viewport Transformation

2
How to Draw 3-D object on Screen?
3
Drawing a Scene

• Apply modeling and viewing transformations
• Apply projection transformation
• Clip if it lies outside the viewing volume
• Apply viewport transformation to display on the
  screen

4
Stages of Vertex Transformations

• Object Local Coordinates

• ModelView
• Matrix

• Projection
• Matrix

• Eye Coordinates

• Vertex

• Clip Coordinates

• Normalized Device Coordinates

• Viewport
• Transformation

• Perspective
• Division

• Windows Coordinates

5
Matrix Stacks

• OpenGL maintains 3 matrix stacks
• Projection, Modelview, Texture
• Use glMatrixMode() to specify which matrix stack
  is active
• glMatrixMode(GLenum mode)
• Modes GL_PROJECTION, GL_MODELVIEW, GL_TEXTURE

6
Matrix Stacks (Cont)

• The topmost matrix on a stack is called its
  current matrix
• When vertices of geometric primitive are drawn,
  OpenGL multiplies the current matrices of the
  stacks by the vertices

7
Matrix Stacks (Cont)

• There are several routines for manipulating
  matrix stacks
• glPushMatrix()
• glPopMatrix()
• glLoadMatrix()
• glMultMatrix()
• glLoadIdentity()

8
Modeling Transformation

• Positions and orients the objects
• Rotation glRotatefd(angle, x, y, z)
• Translation glTranslatefd(x, y, z)
• Scaling glScalefd(x, y, z)

9
Modeling Transformation (Cont)
10
Modelview Matrix

• Pulling the camera back from the object (viewing
  transformation) ? moving the object away from the
  camera (modeling transformation)
• Thus, both viewing and modeling transformations
  are stored in the modelview matrix stack

11
Post-multiplication
glTranslate()
glPushMatrix()
glRotate()
12
Order of Transformations

• Specify the transformations in the reverse order
  of the way you conceptualize them

Specify
M1M2v
Conceptualize
13
Order of Transformations (Cont)

• Example 1 TRv

glTranslatef(2.0,0.0,0.0) glRotatef(45.0,0.0,0.0,1
.0)
14
Order of Transformations (Cont)

• Example 2 RTv

glRotatef(45.0,0.0,0.0,1.0) glTranslatef(2.0,0.0,0
.0)