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Analytic Two-Bone IK in 2D - Math review Print E-mail
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Written by Ryan Juckett   
Monday, 29 December 2008 07:46
Article Index
Analytic Two-Bone IK in 2D
Defining the problem
The solvable domain
Math review
Describing the problem with math
Solving for angle 2
Solving for angle 1
Writing the code
All Pages
Page 4 of 8

 

Math review

Before we hop into the derivation, I want to review a few trigonometric identities that we will be using. For more information on the identities, Wikipedia has an extensive list and also has a page on the derivations.

 

Right triange ratios

\sin \theta = \frac {\mathrm{opposite}}{\mathrm{hypotenuse}} \cos \theta = \frac {\mathrm{adjacent}}{\mathrm{hypotenuse}} \tan \theta = \frac {\mathrm{opposite}}{\mathrm{adjacent}}

 

Pythagorean trigonometric identity

\sin^2 x + \cos^2 x = 1

 

Angle sum and difference identities

\sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta

\cos(\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta

\tan(\alpha \pm \beta) = \frac{\tan \alpha \pm \tan \beta }{1 \mp \tan \alpha \tan \beta }
Last Updated ( Sunday, 02 May 2010 06:32 )
 
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