Prospective Projection

• I'm going to skip the derivation of the prospective projection.
  • There is a really nice presentation here if you wish.
  • The book discussion 18.1.2 is not the best.
• There is an alternative to glFrustum
• 
  • void gluPerspective(GLdouble fovy, GLdouble aspect, GLdouble zNear, GLdouble zFar);
  • fovy : specify a field of view angle in the y direction
  • aspect: Aspect ratio (1 is good)
  • znear,zfar as in glFrustum
• This is from the GL Utility Library (glu)
  • You need to link with -lGLU
• 
• These images are indirectly from an old copy of the "Red Book".
• There is one more useful transformation
  • void gluLookAt( GLdouble eyeX, GLdouble eyeY, GLdouble eyeZ, GLdouble centerX, GLdouble centerY, GLdouble centerZ, GLdouble upX, GLdouble upY, GLdouble upZ);
  • (eyex, eyey, eyez) are the location of the camera
  • (centerx, centery, centerz) is the center of projection.
  • (upx, upy, upz) specify the up direction for the camera.
  • This command will generate a matrix
    The eye position is at the origin.
    • LookAt: (eyex, eyey, eyez) to (centerx, centery, centerz) define an axis along which the shot will be performed (the Z axis)
    • Up: (eyex, eyey, eyez) to (upx, upy, upz) define the y axis or up direction for the camera.
    • LookAt and Up should be orthogonal.
    • To specify a complete system, a third vector is required (the x axis)
    • This achieved by the cross product: left = up × lookAt
    • Frequently, one does not trust up and lookAt to be orthogonal, so after the first cross product, a second is performed up = lookAt × left
  • These concepts, while not in use in OpenGL 3+, are still valid
    • The Red Book contains code, which includes:
    • mat.h
    • Look for
      • RotateX, ... Translate, Scale
      • Orhto
      • Frustum, Perspective, LookAt