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CS 3220 Root finding applications Steve Marschner Spring 2010 - - PowerPoint PPT Presentation
CS 3220 Root finding applications Steve Marschner Spring 2010 - - PowerPoint PPT Presentation
CS 3220 Root finding applications Steve Marschner Spring 2010 [Visible Human Project, Natl Library of Medicine] [Fovia Inc.] [Fovia Inc.] [Fovia Inc.] [Fovia Inc.] [Fovia Inc.] [CS 417 slidessource unknown] view rect viewpoint
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[Visible Human Project, Nat’l Library of Medicine]
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[Fovia Inc.]
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[Fovia Inc.]
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[Fovia Inc.]
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[Fovia Inc.]
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[Fovia Inc.]
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[CS 417 slides—source unknown]
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viewing ray pixel position view rect viewpoint
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s e d = s – e p = e r(t) = p + td
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s e d = s – e p = e r(t) = p + td
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[Brian Wyvill]
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[sayinghai.com]
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[sayinghai.com]
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h
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i
- i
- t
- R (p = 0)
h
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i
- i
- t
- R (p = 0)
i
- t
- TT (p = 1)
h
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i
- i
- t
- R (p = 0)
i
- t
- TT (p = 1)
i
- t
t
- TRT (p = 2)
h
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h
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primary secondary
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primary secondary
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primary secondary
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glints
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glint transmission
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float InvSqrt(float x) { float xhalf = 0.5f*x; int i = *(int*)&x; i = 0x5f3759df - (i>>1); x = *(float*)&i; x = x*(1.5f-xhalf*x*x); return x; }
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float InvSqrt(float x) { float xhalf = 0.5f*x; int i = *(int*)&x; // get bits for floating value i = 0x5f3759df - (i>>1); // gives initial guess y0 x = *(float*)&i; // convert bits back to float x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy return x; }