For those that give a hoot, here is the equation for only one of a million patterns that can come from a sine or cosine wave on a pattern bar.
x=t  rsin(atan(sin(t)))
y=cos(t) + rcos(atan(sin(t))), where t is the evaluation parameter.
This one's easy because there is a nice mathematical function that describes the pattern bar and the solution is analytical and not numeric. This equation is adaptable to other continuous functions as I think all that might need to change is the substituion of the first derivative (slope) for the "sin(t)" factor which is the slope of the cosine curve. Also those with better math skills and determination can carry on with other patterns that are not so nicely described and for ones on a rose engine. Have at it! I suspect Bill Ooms has some nice stuff in his program.
I'll go back to making chips, now.
Cheers,
Rich
x=t  rsin(atan(sin(t)))
y=cos(t) + rcos(atan(sin(t))), where t is the evaluation parameter.
This one's easy because there is a nice mathematical function that describes the pattern bar and the solution is analytical and not numeric. This equation is adaptable to other continuous functions as I think all that might need to change is the substituion of the first derivative (slope) for the "sin(t)" factor which is the slope of the cosine curve. Also those with better math skills and determination can carry on with other patterns that are not so nicely described and for ones on a rose engine. Have at it! I suspect Bill Ooms has some nice stuff in his program.
I'll go back to making chips, now.
Cheers,
Rich
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