[vox-tech] [OT] Math question: help me make a rainbow

[Bill Broadley]

Bill Kendrick wrote:
> On Tue, Mar 31, 2009 at 07:21:36PM -0700, Bill Broadley wrote:
>> Some.  Not sure what you are getting at though.  You want to draw 180 degrees
>> of a circle with the end points defined by p1 and p2?  What if you want to
>> make an upside down rainbow?  Or 1/2 of one?
> 
> I only want to draw all 180 degress if y1==y2.  Otherwise, it'd be
> less of the arc.  (See my ASCII diagrams)

Hrm, I don't think ascii is going to help, at least for me.  Ah, ok, I have an
idea of what you think you want to do.  I think you do need 3 points.  A
center, radius, range of angles.  Basically there are an infinite number of
180 degree curves that go through 2 points, and there's no way to know how
high the peak should be, nor which exact fraction of a circle to display.

So for your diagrams how do you decide that in case 1 you do 1/2 a circle and
the circle doesn't go above P2, but in case #3 you get 60% of a circle.