[ODE] tanget vector

[Martin C. Martin]

Suppose they touch the earth at (X, Y, Z) where X^2 + Y^2 + Z^2 = R^2.

The the equation of the tangent plane is

x*X + y*Y + z*Z = R^2

- Martin

jnilson_99@yahoo.com wrote:
> 
> Hi,
> 
> I've been using ode to build a demo that zooms in on
> the surface on the earth from around 10 miles in space
> down to ground level.
> 
> Ode works great, no problems there. However since my
> problem is calculus related I thought someone might
> know a quick solution.
> 
>  I have a problem finding the tanget plane to the
> point on the surface of the earth where the user
> "touches down".
> 
> Is there a simple way of calculating this plane given
> the point (in cartesian or polar coordinates).
> 
> My first guess is to find the first derivative of the
> sphere equation: X^2 + Y^2 + Z^2 - r = 0. Then plug in
> my point to get the plane.
> 
> Is this the righ approach?
> 
> thanks,
> 
> john
> 
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