RE: [Algorithms] elliptical arc parameterization

[Arcot P. <pre...@at...>]

If clockwise corresponds to decreasing theta (the case when +x axis is to
the right and +y axis is up), 
then do the following.
 
if (theta_P < theta_Q)
    theta_P += 2*pi.
 
This should make sure theta_P is always greater than theta_Q.
Hence as t increases, theta decreases => clockwise direction.

Preetham
 
 

-----Original Message-----
From: Federico Pernici [mailto:pe...@io...]
Sent: Saturday, August 18, 2001 10:13 AM
To: gda...@li...
Subject: Re: [Algorithms] elliptical arc parameterization


  

Arcot Preetham wrote: 


  

Without loss of generality, lets assume the simplest ellipse equation. 
x = a * cos(theta), y = b * sin(theta). 


You can find theta by 
theta = atan2(y/b, x/a) 


You can therefore calculate theta_P and theta_Q for points P and Q. 
Now, theta_t = (1-t)*theta_P + t*theta_Q, t = [0,1]

Thank you very much!! It works! 
But now another pb arise.... 
How to select (always) the clockwise arc from P to Q ? 

FEd