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Lecture 12 - Spline surfaces (slides)

# May be multiple intersections between the ray and the

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Unformatted text preview: ationcostlybe costly ! Hence no closed form solution exists for a ray patch intersection Graphics Lecture 12: Slide 23! 23 / 35 Rendering a patch: Ray tracing " •  Numerical Ray-Patch algorithm ! ! 1.  Polygonise the patch at a low resolution (say 4 x 4) ! 2.  Calculate the ray intersection with the 32 triangles and ﬁnd the nearest intersection. ! 3.  Polygonise the immediate area of the intersection and calculate a better estimate of the intersection ! 4.  Continue until the best estimate is found ! Graphics Lecture 12: Slide 24! Rendering a patch: Ray tracing " •  Numerical Ray-Patch algorithm! –  May be multiple intersections between the ray and the surface ! –  Algorithm will ﬁnd an intersection, but not necessarily the nearest. !   If the object is relatively smooth it should work well in most cases. ! –  Note that it will be necessary to do a ray intersection with each patch of the object to ﬁnd the nearest intersection. ! Graphics Lecture 12: Slide 25! Example of Using a Coons Patch Example of Using a Coons Patch " •  Part of a terrain map deﬁned on a regular x-y grid is as follows: ! Part of a terrain map deﬁned on a regular xy grid is as follows: x, µ # 7 8 9 10 11 2 · · · · · y, ⌫ ! 3 4 5 · · · · 10 9 14 12 11 15 13 14 · 10 11 6 · · 10 10 · 7 · · · · · • the Coons patch patch on the centre four Find  Find the Coons on the centre four points points ! ! Graphics Lecture 12: Slide 26! Corners Corners Corners " •  The corners at µ, ν = 0, 1 are deﬁned directly in the The corners at µ, ,⌫⌫ = 00,11are deﬁned directly in the question: The question: ! corners at µ = , are deﬁned directly in the question: P(0, ,0) = (9, ,44,12) P(0 0) = (9 , 12) P(0, ,1) = (9, ,55,11) P(0 1) = (9 , 11) 77 88 x, ,µ x µ 99 ## 10 10 11 11 Graphics Lecture 12: Slide 27! 22 ·· ·· ·· ·· ·· P(1,,0) = (10,,44,13) P(1 0) = (10 , 13) P(1,,1) = (10,,55,14) P(1 1) = (10 , 14) yy ,⌫⌫ ! , ! 33 44 ·· ·· · · 10 10 14 12 14 12 15 13 15 13 · · 10 10 55 66 77 ·· ·· ··...
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