Viewing Transformation

1
Viewing Transformation

• Position and aim the camera
• gluLookAt(eyex, eyey, eyez, centerx, centery,
  centerz, upx, upy, upz)
• Default location at origin looking down the
  negative z-axis

2
Viewing Transformation (Cont)
gluLookAt(4.0, 2.0, 1.0, 2.0, 4.0, -3.0, 2.0,
2.0, -1.0)
Default location
3
Projection Transformation

• Define a viewing volume
• Orthographic projection
• Perspective projection

4
Projection Transformation (Orthographic)

• glOrtho(left, right, bottom, top, near, far)

5
Projection Transformation (Orthographic) Cont

• gluOrtho2D(left, right, bottom, top)
• A special case of glOrtho() withnear -1 and
  far 1
• Vertices with z-coordinate smaller than 1 or
  larger than 1 will be clipped away

6
Projection Transformation (Perspective)

• glFrustum(left, right, bottom, top, near, far)

7
Projection Transformation (Perspective) Cont

• gluPerspective(fovy, aspect, near, far), a
  special case of glFrustum() with symmetric
  perspective view

8
Projection Transformation

• Orthographic projections
• w component is always 1
• Perspective projections,
• w component may not be 1
• Perspective division has to be performed by
  dividing all coordinates values by w to get back
  the normalized device coordinates

9
Viewing Volume Clipping

• Six clipping planes
• Clip away the polygons outside the viewing volume

10
Viewport Transformation

• Map the OpenGL image to the window system
• glViewport(x, y, width, height)
• Generally, the aspet ratio of viewport should
  equal the aspect ratio of the image on the
  projection plane to avoid distortion

11
Accumulating Rotations

• Computer graphics application requires user to
  spin a model with mouse
• Incremental rotations must be accumulated for
  accurate orientation
• Two naive ways and quaternion way

12
Accumulating Rotations (Cont)

• Naïve 1 Perform glRotate() calls for each
  incremental rotation
• floating-point errors produce non-orthogonal
  matrices
• model may shrink or grow
• Requires saving and restoring multiple modelview
  matrices

X
X
X
13
Accumulating Rotations (Cont)

• Naïve 2 Represent each model orientation as
  three angles, each representing rotation around
  the x, y, z axis
• incorrect result because rotations are not
  commutative

X
14
Accumulating Rotations (Cont)

• Quaternion Way quaternion represents rotation as
  four floating-point values

15
Trackball Interface

• trackball.c implements quaternion math
• contains routines for
• converting a rotation matrices to a quaternion
• accumulating quaternions
• converting a quaternion representation to a
  rotation matrix

16
Trackball Interface (Cont)

• Converting rotations to quaternions
• Call trackball() with the beginning and ending
  window coordinates which are normalized to
  between 1 and 1.
• Example rotation around x-axis
• float deltaQuat4
• trackball(deltaQuat,
• 0.0, -0.1, / starting x, y /
• 0.0, 0.3) / ending x, y /

17
Trackball Interface (Cont)

• Accumulating quarternions
• Call add_quarts() to accumulate one quaternion
  with another
• Example accumulate the first two quaternions and
  store in the third one
• float currentQuat4
• add_quats(deltaQuat, currentQuat, currentQuat)

18
Trackball Interface (Cont)

• Converting a quarternion to a rotation matrix
• Call build_rotmatrix() to convert an accumulated
  quaternion to a rotation matrix for modelview
  matrix multiplication
• Example
• GLfloat rotationMatrix44
• build_rotmatrix(rotationMatrix, currentQuat)
• glPushMatrix()
• glMultMatrix(rotationMatrix00)
• ...
• glPopMatrix()

19
Trackball UI

• ui.c implements the trackball rotation, panning,
  zooming effected by mouse buttons movements
• The modelview stack is updated in the following
  order TRM
• Translation (panX, panY, zoom)x Rotation about
  center of scenex Original Viewing Transformation

20
Trackball UI (Cont)

• The original viewing transformation is first
  applied
• Rotation, panning and zooming are applied with
  respect to the eye coordinate frame
• First store the original viewing transformation
  matrix
• GLfloat originalViewMatrix44
• glGetFloatv (GL_MODELVIEW_MATRIX,
  originalViewMatrix00)

21
Trackball UI (Cont)

• Current modelview matrix is updated as follow
• glPushMatrix ()
• glLoadIdentity()glTranslatef (panX, panY,
  Zoom)
• glTranslatef (0.0, 0.0, -lengthOfView)
• build_rotmatrix (rotationMatrix, quat)
• glMultMatrixf (rotationMatrix00)
• glTranslatef (0.0, 0.0, lengthOfView)
• glMultMatrixf (originalViewMatrix00)
• drawScene()
• glPopMatrix ()