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3D Computer Graphics (3080/GV10) Week 5-6 Tutorial 3

Learn about OpenGL transformation pipeline, model-view matrix, camera space, projection matrix, and object space. Understand the process of perspective divide to convert from homogeneous clip space to normalized device coordinates in OpenGL.

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3D Computer Graphics (3080/GV10) Week 5-6 Tutorial 3

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  1. 3D Computer Graphics (3080/GV10)Week 5-6 Tutorial 3 Andrew Cox

  2. OpenGL Transformation Pipeline ModelView Matrix CameraSpace Projection Matrix Object Space HomogeneousClip Space Perspective Divide Normalized Device Coordinates Viewport Transform Viewport Coordinates Slide adapted from Eric Lengyel[1]

  3. OpenGL Perspective Projection Matrix • n, f = distances to near, far planes • e = focal length = 1 / tan(FOV / 2) • a = viewport height / width Picks up viewspace z and places negated in w: division by Z gives perspective Slide adapted from Eric Lengyel[1]

  4. Slide courtesy of Eric Lengyel[1]

  5. Matrix Multiplication and Concatenation

  6. Order of OpenGL Transformations • OpenGL calls define a matrix, then concatenate it with existing one • Transformations applied in reverse of lexical program order

  7. Matrix Modes • GL tracks two matrix stacks • Projection • ModelView • The matrix applied to vertices is • The matrix commands apply to the current mode: • glMatrixMode(GL_PROJECTION); • glMatrixMode(GL_MODELVIEW);

  8. glLoadIdentity() • Matrix commands are concatenated with matrix of current mode • Includes gluPerspective () etc. • Clear out current matrix with glLoadIdentity()

  9. References • Eric Lengyel, Projection Matrix Tricks, Game Developers Conference 2007, <http://www.terathon.com/lengyel/>.

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