If you have a point in a 3D coordinate plane at the coordinate X:b Y:n and Z: t, and another point at the coordinates X:s Y:l and Z:m, how do you find where a line spanning from point 1 to point 2 intersects the surface of a sphere that surrounds point 1 with a radius of 1 unit?
If you have a point in a 3D coordinate plane at the coordinate X:b Y:n and Z: t, and another point at the coordinates X:s Y:l and Z:m, how do you find where a line spanning from point 1 to point 2 intersects the surface of a sphere that surrounds point 1 with a radius of 1 unit?
So you are a geometry whizz, so what.
“What we think, or what we know, or what we believe is, in the end, of little consequence. The only consequence is WHAT WE DO.” John Ruskin (1819 - 1900)
Only managed to finish half of it. I figured out that you can create a pyramid using two triangles that share 1 coordinate with point two, and that the angles these two triangles form off of point 1 are the key to solving it, but I don't know HOW.
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fresco
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Sun 11 May, 2014 01:36 am
@Arc,
What I would do (if I had the time) is look up how to write the equations of the line and the sphere and solve them as a simultaneous pair.
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fresco
1
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Sun 11 May, 2014 02:06 am
@Arc,
Come to think of it, using pythagoras,
(x-b)^2 +(y-n)^2+(z-t)^2 = 1
is the equation of the sphere.
and (x-b)/s=(y-n)/l =(z-t)/m
gives equations for the line.
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