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How do I calculate intersection of two circles in polar coordinates?
I'm starting to do art based on the mathematical way that plants grow based of the value of Phi.
Could you please help me with this math problem?
I'm drawing a blank at where to start because I haven't used trig or polar coordinates in such a long time.
I need to create a set of formulas.
My variables are
r1 = the radius of circle1 to be drawn
d1 = the distance of the center of the circle1 from the origin
o1 = the angle in degrees (or radians, don't care) where the center of circle 1 is located in polar coordinates.
r2 = the radius of circle2 to be drawn with a center at the the origin, and actually r2 will always = d1
I know how to convert between Cartesian and polar coordinates so that I can draw the shapes easily, but I'm struggling with where the intersects are which are going to determine where I draw the next circle.
The formulas I need:
f1 = angle of the first intersection point where the circles cross
f2 = the distance from the origin where the circles cross
From those two formulas, I can get the other values I need like the other intersection point and the length of the arc between the intersection points.
Any help is much appreciated.
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