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 RayPatch 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 RayPatch 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 xy grid is as
follows: ! Part of a terrain map deﬁned on a regular xy grid is as follows: x, µ
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· • 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
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x, ,µ
x µ 99
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Graphics Lecture 12: Slide 27! 22
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·· P(1,,0) = (10,,44,13)
P(1 0) = (10 , 13)
P(1,,1) = (10,,55,14)
P(1 1) = (10 , 14)
yy ,⌫⌫ !
,
!
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10 55 66 77
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 Spring '14
 Surface, Parametric equation, Parametric surface

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