OT - math question.

[narf poit chez BOOM]

say you had a point at the bottom of a sphere and then moved it to the right a random distance along the surface of the sphere. how would you calculate the height from the bottom?

[ February 19, 2004, 06:11: Message edited by: narf poit chez BOOM ]

[Fyron]

Calculate the degrees away from the pure vertical radius that the new radial line connecting to the new point on both the x and y planes. Then use some arc length calculations.

[narf poit chez BOOM]

that's the problem. i know neither the y position nor the arc calculations.

[Fyron]

Umm... if you are moving it in a random direction, should you not be able to see where it is moving to?

Either way, measure the vector between the start point and the end point. You can get the angles from this vector with pythagorian theorm used a few times. If you have coordinates, no measurement is required, just calculations.

[Member 4148]

Originally posted by narf poit chez BOOM:
say you had a point at the bottom of a sphere and then moved it to the right a random distance along the surface of the sphere. how would you calculate the height from the bottom?

if it is traveling in a straight line, it might as well be on the edge of a circle, as you are starting from the ultimate "south" position (nowhere to go but north)

you need your distance traveled - call that d
you need the radius of the sphere - call that r

now, set your graphin calculater into radian mode
then tell it to do the following equation

height from bottom = (sin((d/r) - pi/2) * r) + r

there are lots o variation on this equation

drop the +r to get the height above (+) or below (-) th center

[Member 4148]

Originally posted by Imperator Fyron:
Umm... if you are moving it in a random direction, should you not be able to see where it is moving to?

Either way, measure the vector between the start point and the end point. You can get the angles from this vector with pythagorian theorm used a few times. If you have coordinates, no measurement is required, just calculations.

i think he is looking for y position - he has starting point, path traveled (along surface of sphere), distance traveled, wants ending point

[Fyron]

y position is not height. Not sure what I was thinking with arc length, but you definitely need the angles associated with the vector from the starting point to the ending point. The relative height is just the z component of that vector.

Treating the movement as along a circle only works if the only component that is changing is the z component. If x or y change (but not both), then it is no longer a circle, but an ellipse.

[narf poit chez BOOM]

yes, thank you, will try the calculation.

[Fyron]

Actually... if you have the arc length, that gives you the angles you need to calculate the height, as you can calculate the percent of the 360 degress of the circle that that arc takes up using the 2 * pi * radius calculation for circumference.

[narf poit chez BOOM]

no, that part wasn't stated well. i don't have the arc length, only the x distance moved.