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smart

Help - i couldn't understand this !!!

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hi guys : i put my problem in the math & physics but no answer until now so i wrote it again to this forum, perhaps someone help me here : ok, i need explanations about this subject : (quaternion) SLERP i was reading the book : 3d math primier for graphics and game development and i didn't understand this formulas, first these are 3 pages about the subject. first page: http://putfile.com/pic.php?pic=11/30610594064.jpg&s=x11 second page: http://putfile.com/pic.php?pic=11/30611043569.jpg&s=x11 third page: http://putfile.com/pic.php?pic=11/30611061934.jpg&s=x11 go at the third page and you gonna see this formula: sin(w) =sint(tw)/k1 <--- here i didn't understand this why he used sin(w) because the angle (w) here its the angle between v0,v1, but with the above formula its the angle that pertaining to the triangle k1v1,sin(tw),(v0-(k0v0)). and after that he solved for k0, and also i dont know how. thanks smart.

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Guest Anonymous Poster
v0, v1 and vt all have length 1. I.e. |v0|=1, |v1|=1, |vt|=1

You have the angle w at two places in the figure:
* as angle between v0 and v1
* since k1v1 is parallell with v1 you also have w between v0 and k1v1

A definition of sinus is sin(angle)=(length of leg)/(length of hypotenuse)

In this case the hypotenuse is k1v1 with length k1.
The length of the leg is |v1|*sin(wt)=1*sin(wt)=sin(wt)
therefore: sin(w)=sin(tw)/k1

Fredrik

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Thanks Fredrik for your answer, but the other angle that's w its the same angle for the arc !!!

you can see the line from the v1 until the v0, its the angle w ( the same angle for arc)

thanks Fredrik

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