Viewing in OpenGL

1
Viewing in OpenGL

• CS4451A

2
Camera Analogy

• Set up the tripod and point the camera (view
  transform)
• Arrange the objects in the scene (model
  transform)
• Choose a lens and adjust zoom (projection
  transform)
• Choose photo print size (viewport transform)

3
Camera Analogy

• Caveat! Beware!
• This is an analogy
• Analogies break

4
Camera Analogy

• This one is brittle when moving to stereoscopic
  displays
• You specify transforms in this order, but
  mathematical operations do not follow this order.

5
Vertex Transformation
6
Modelview Matrix

• Modelview matrix converts object coordinates into
  eye coordinates
• Model transformations move the object, view
  transformations move the eyepoint,
  interchangeable!

7
Projection Matrix

• Selecting the lens, telephoto or wide angle
• Mathematically, selecting the volume to be mapped
  to viewport (mapping, homology, projective
  transform)

8
Perspective Division

• The divide by w step x y z z/d
• xprojected dx/z x/(z/d)
• yprojected dy/z y/(z/d)

9
Vertex Transformation

• Mapping window on projection plane to viewport
• Use glViewport
• Done in reshape function so you know what size
  the viewport has become

10
Cube.c

• void reshape (int w, int h)
• glViewport (0, 0, (GLsizei) w, (GLsizei) h)
• glMatrixMode (GL_PROJECTION)
• glLoadIdentity ()
• glFrustum (-1.0, 1.0, -1.0, 1.0, 1.5, 20.0)
• glMatrixMode (GL_MODELVIEW)
• void display(void)
• glClear (GL_COLOR_BUFFER_BIT)
• glColor3f (1.0, 1.0, 1.0)
• glLoadIdentity () / clear the matrix /
• / viewing transformation /
• gluLookAt (0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0,
  1.0, 0.0)
• glScalef (1.0, 2.0, 1.0) / modeling
  transformation /
• glutWireCube (1.0)
• glFlush ()

• void init(void)
• glClearColor (0.0, 0.0, 0.0, 0.0)
• glShadeModel (GL_FLAT)
• int main(int argc, char argv)
• glutInit(argc, argv)
• glutInitDisplayMode (GLUT_SINGLE GLUT_RGB)
• glutInitWindowSize (500, 500)
• glutInitWindowPosition (100, 100)
• glutCreateWindow (argv0)
• init ()
• glutDisplayFunc(display)
• glutReshapeFunc(reshape)
• glutMainLoop()
• return 0

11
Cube.c

• void reshape (int w, int h)
• glViewport (0, 0, (GLsizei) w, (GLsizei) h)
• glMatrixMode (GL_PROJECTION)
• glLoadIdentity ()
• glFrustum (-1.0, 1.0, -1.0, 1.0, 1.5, 20.0)
• glMatrixMode (GL_MODELVIEW)

• void display(void)
• glClear (GL_COLOR_BUFFER_BIT)
• glColor3f (1.0, 1.0, 1.0)
• glLoadIdentity () / clear the matrix /
• / viewing transformation /
• gluLookAt (0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0,
  1.0, 0.0)
• glScalef (1.0, 2.0, 1.0) / modeling
  transformation /
• glutWireCube (1.0)
• glFlush ()

12
Viewing

• Use rotations and translations or
• void gluLookAt(
• GLdouble eyex, GLdouble eyey, GLdouble eyez,
• GLdouble centerx, GLdouble centery, GLdouble
  centerz,
• GLdouble upx, GLdouble upy, GLdouble upz)
• Eye point
• Center of field of view (aim point)
• Up vector
• Default
• gluLookat (0.0, 0.0, 0.0, 0.0, 0.0, -100.0, 0.0,
  1.0, 0.0)

13
Modeling

• void glTranslatefd(TYPE x, TYPE y, TYPE z)
• void glRotatefd(TYPE angle, TYPE x, TYPE y,
  TYPE z)
• void glScalefd(TYPE x, TYPE y, TYPE z)

14
Projection

• Parallel
• glOrtho
• gluOrtho2D
• Perspective
• glFrustum
• glPerspective

15
Orthogonal View Volumes

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

16
Orthogonal View Volumes

• void gluOrtho2D(
• GLdouble left, GLdouble right,
• GLdouble bottom, GLdouble top)
• Assumes z within 1.0,1.0

17
Perspective View Volumes

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

18
Perspective View Volumes

• void gluPerspective(GLdouble fovy, GLdouble
  aspect, GLdouble near, GLdouble far)
• Easier to use, but limited to symmetric, (not off
  axis)

19
Viewport

• void glViewport(GLint x, GLint y,
• GLsizei width, GLsizei height)
• You may need to preserve aspect ratio

20
Correcting distortion

• Left
• gluPerspective(fovy, 1.0, near, far)
• glViewport(0, 0, 400, 400)
• Right
• gluPerspective(fovy, 1.0, near, far)
• glViewport (0, 0, 400, 200)
• Corrected
• gluPerspective(fovy, 2.0, near, far)
• glViewport(0, 0, 400, 200)

21
Pushing and Popping Matrices

• Draw the car body.
• Remember where you are, and translate to the
  right front wheel.
• Draw the wheel and throw away the last
  translation so your current position is back at
  the origin of the car body.
• Remember where you are, and translate to the left
  front wheel....

22
Pushing and Popping Matrices
23
Pushing and Popping Matrices

• draw_wheel_and_bolts()
• long i
• draw_wheel()
• for(i0ilt5i)
• glPushMatrix()
• glRotatef(72.0i,0.0,0.0,1.0)
• glTranslatef(3.0,0.0,0.0)
• draw_bolt()
• glPopMatrix()

• draw_body_and_wheel_and_bolts()
• draw_car_body()
• glPushMatrix()
• glTranslatef(40,0,30) /move to first
  wheel position/
• draw_wheel_and_bolts()
• glPopMatrix()
• glPushMatrix()
• glTranslatef(40,0,-30) /move to 2nd
  wheel position/
• draw_wheel_and_bolts()
• glPopMatrix()
• ... /draw last two wheels
  similarly/

24
Unproject

• Reverses the projection process. Instead of
  mapping points in object space to the screen,
  maps screen points to object space.
• int gluUnProject(
• GLdouble winx, GLdouble winy, GLdouble winz,
• const GLdouble modelMatrix16,
• const GLdouble projMatrix16,
• const GLint viewport4,
• GLdouble objx, GLdouble objy, GLdouble objz)
• Maps from viewport space into object space
• winz0 gives near clipping plane point
• winz1 gives far clipping plane point