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From: ronny abraham <ronny@jl...>  20020825 23:01:22

Hi, I've only browsed through the Evas code, and that was a while ago, so I don't know if you have this in the new code. In any case, I think people will get a kick out of this. I found the code in "mathematical elements for computer graphics" by rogers & adams. pg 21516 Anyway, I'm going to go through the math of it, so just bear with me. I'll try to paraphrase as much as I can, but their style is very concise, so there isn't much I can do to improve on it. given a circle of radious r x = rcos(theta) y = rsin(theta) 0 <= theta <= pi assume a fixed number of points equally spaced apart are used to represent the circle delta_theta = 2 * pi/num_points the intial points are: x_0 = rcos(0) y_0 = rsin(0) from that you can do this: x_i+1 = rcos( theta_i + delta_theta ) y_i+1 = rsin( theta_i + delta_theta ) where theta_i is the angle we used for the last points ( x_i and y_i )we got. x_i+1 and y_i+1 are the current points we're trying to find. sum of angles formula gives us: x_i+1 = r( cos(theta_i) cos(delta_theta)  sin(theta_i) sin(delta_theta) ) y_i+1 = r( cos(theta_i) sin(delta_theta)  cose(delta_theta) sin(theta_i) ) if we take the original equations, with theta as theta_i x_i = rcos(theta_i) y_i = rsin(theta_i) we then get: x_i+1 = x_i * cos( delta_theta )  y_i * sin(delta_theta) y_i+1 = y_i * sin( delta_theta )  y_i * cos(delta_theta) the nifty thing about all this, is that you only need to compute: delta_theta cos(delta_theta) sin(delta_theta) ONCE. Which allows us to kick out the timeintensive trig stuff. I think that this makes having a circle function in evas very possible since it's fast. Of course, if it already exists, then at least this email was (hopefully) entertaining. :D 