Help!
I have drawn a parabolic shape using the formula y = X^2
The parabola is composed of spheres scaled into ellipses with the longside
in the y direction
I have been trying to rotate each ellipse so the the length is pointing in
the direction of the parabola
I need to calculate the gradient at each point. I'm no mathmatician so
Please help
From: Simon de Vet
Subject: Re: Help with parabola
Date: 5 Sep 1998 14:07:18
Message: <359FC109.B707411B@istar.ca>
mick wrote:
> Help!>> I have drawn a parabolic shape using the formula y = X^2>> The parabola is composed of spheres scaled into ellipses with the longside> in the y direction>> I have been trying to rotate each ellipse so the the length is pointing in> the direction of the parabola>> I need to calculate the gradient at each point. I'm no mathmatician so> Please help
Calculus. Now I've been out of calc for all summer, but I remember the basics.
The slope of a line is determined by it's first derivative. Therefore, if
y=x^2, then the slope at any given point = 2x.
ie: The slope a y=-10 is -20 (ie: down 20 units for every unit to the right)
at y=1 the slope is 2, and at y=0 the slope is 0 (ie: flat)
Am I wrong? I feel this is right...
It's been too long....
Simon
http://home.istar.ca/~sdevet
From: Nathan Kopp
Subject: Re: Help with parabola
Date: 5 Sep 1998 14:25:13
Message: <35F1731F.7B289DDF@ltu.edu>
The slope (i.e. derivative, gradient) of a parabola at any point is
dy
-- = 2x
dx
For example, the slope at x=1 is 2*1=2, while the slope at x=2 is 2*2=4.
To find the angle that you need to rotate, plug the slope into the inverse
tangent function (which is called "atan2" in POV-Ray).
-Nathan
mick wrote:
> > Help!> > I have drawn a parabolic shape using the formula y = X^2> > The parabola is composed of spheres scaled into ellipses with the longside> in the y direction> > I have been trying to rotate each ellipse so the the length is pointing in> the direction of the parabola> > I need to calculate the gradient at each point. I'm no mathmatician so> Please help
