Tuesday, April 9, 2013

Sector/Segment Area

 There are two main "slices" of a circle:
     The "pizza" slice is called a Sector*white selection below*

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                   And the slice made by a chord is called a Segment. *white selection below*

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Lets take a look at this in Softimage....

* Watch in highest quility possible*

To work out the area of the segment and sector you will use the formulas:

Area of Sector = ½ × (θ × π/180) × r2   (when θ is in degrees)

Area of Segment = ½ × ( (θ × π/180) - sin θ) × r2   (when θ is in degrees)

*So basically what we need is the angle of the "center" corner, and the radius of the circle the sector belongs too*

Area of a Sector in Softimage
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What these formulas will look like in ICE - once you have the angle and raduis - :

Segment area:

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Sector area:

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So you will need to work out the lengths of the three sides of the triangle that fits inside the sector "pizza slice".
I did this by simple creating cluster centers on the last point of the three curves then getting the length between them....

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Here are the tree's for that...

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 they are all basically the same...

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....then you can work out the angle of the center corner in the circle your sector is part of.
I used the standard law of cosines node for this one but here is the math formula:
cos A = (b2 + c2 - a2)/2bc

I used this law because I already had all three side lengths worked out, but never fear here is a link to other ways of working out you triangles if you have say one angle and two sides... 

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law of cosines in Softimage
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You can also work out the "arc length" - the blue line in the image below - of your sector, by using the formula:

L = (θ × π/180) × r  

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Here's that ICE tree...

arc Length formula
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And there you have it. If you ever need to work out how big a pizza slice is ..... now you can do it :)


Monday, April 8, 2013

Lindy Hop

The animation project I'm buzy with at the moment involves some really cool dancing reference.

So started animating out this awesome dance routine for a learning challenge.
*the characters are made by AnimSchool - you can download them here: http://www.animschool.com/DownloadOffer.aspx *

This is the Blocking for the first 210 frames ...... he he loving it so far.

For now the only issue has been gimble lock.... but with them turning around so much and stuff, its to be expected.