View Full Version : Mathematical Question

02-15-2002, 07:34 AM
in 2 dimensions, it is possible to find point x,y using just one angle. Is there some way of doing this in 3d? i would guess you need 2 angles, one off the horizon, and one for z, but i'm not sure. anyone know?

02-15-2002, 07:50 AM
more info please.
with an angle in 2d all you have is an angle.
with an angle and a point you have a line.

02-15-2002, 07:17 PM
trying to find a point on a sphere a specific radius away. my 2d example: cos(angle)=x, sin(angle)=y, on a unit circle(circle with radius of 1). Is there something relevant to this in spheres? i assume, however, that you need 2 angles instead of one to find the x, y, and z. am i right?

02-15-2002, 09:51 PM
Yes, you can use two angles to define a point on a sphere. Elevation/azimuth, or longitude/latitude, whatever you want to call them.

If theta is the angle from the North pole (90-latitude) and phi is the longitude, then

x = sin(phi) * sin(theta)
y = cos(phi) * sin(theta)
z = cos(theta)

To fully define an orientation you'll need a third angle which is a rotation about this vector. Look up the term "Euler angles" in Google for more details.