11-ray-intersection

11-ray-intersection - Lecture 12 Ray-Object Intersections...

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Lecture 12 Ray-Object Intersections
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Mathematics • The heart of any ray tracer, or ray casting for hidden surface removal, is the intersection routines. • Each kind of primitive has different properties, so we have different intersection equations. ( x 0 , y 0 ,z 0 ) T ( d x ,d y ,d z ) T
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Parametric Ray Equation •L e t – the COP be P 0 = ( x 0 , y 0 ,z 0 ) T and – the viewing direction be D = ( d x , d y z ) T • Any point P lying on the eye ray is given by: • Or writing each coordinate separately:
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Ray Parameterization • The parametric ray equation is given by: • Points along the line of sight is parametrized by t: t = 0 , at COP (eye/viewpoint) t < 0 , behind COP t > 0 , in front of COP ( d x ,d y ,d z ) T Non-negative t ( x 0 , y 0 ,z 0 ) T
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Mathematics • Given an implicit surface (i.e., spheres and other quadrics defined by an implicit equation) F ( x , y , z ) = 0 • In the followings, all surface equations are assumed to be in the object space coordinate system. Therefore, we need to transform the ray before testing for intersection.
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11-ray-intersection - Lecture 12 Ray-Object Intersections...

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