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in reply to OT:Math problem: Grids and conical sections.
Are you assuming the four corner points are on the surface of the cone? If yes, then to determine the surface of the cone, you need four parameters: (x,y,z) of the tip, and the slop k. You are given four points, which would count as four conditions in generic position. But since you don't know the relative units of the xy and z, you have more variables, can you assume the xy are in the same unit and are proportional to the z? then you have only one additional variable, so another point should be enough. |
Re^2: OT:Math problem: Grids and conical sections.
by BrowserUk (Patriarch) on Nov 24, 2005 at 08:33 UTC
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Are you assuming the four corner points are on the surface of the cone?
Yes. They are point on the surface of the cone.
can you assume the xy are in the same unit and are proportional to the z?
I need the x and y in the same units as the grid. Whilst the z values I have are proportional to the units of the grid, the ratio is unknown. However, once the x & y have been determined in any units including the same units as the z components I have, the ratio between them and the grid will become known through pythagoras or other means, so conversion will be trivial.
The most promising stuff I've turned up is trilinear coordinates, but I'm unsure how to apply them, or even if they are applicable.
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Re^2: OT:Math problem: Grids and conical sections.
by QM (Parson) on Nov 24, 2005 at 18:42 UTC
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Are you assuming the four corner points are on the surface of the cone? If yes, then to determine the surface of the cone, you need four parameters: (x,y,z) of the tip, and the slop k
Thinking out loud here...
If you have a point on the surface (x1, y1, z1) and the peak (xp, yp, zp), doesn't that give you the slope k of the cone?
I don't think k and z are independent, though it may be easier to find one or the other.
-QM
--
Quantum Mechanics: The dreams stuff is made of
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