the tangent plane is (x-x1)(x1-x0)+(y-y1)(y1-y0

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Posted on 2004-04-15

I have a arbitrary point on a sphere. The sphere has an arbitrary radius.

I want to find a tanget line to the point on the sphere, or perhaps more correctly put, I want to find the tangent plane and from the tanget plane obtain any arbitrary line within the plane that touches the point on the sphere.

I want to find a tanget line to the point on the sphere, or perhaps more correctly put, I want to find the tangent plane and from the tanget plane obtain any arbitrary line within the plane that touches the point on the sphere.

3 Comments

the tangent plane is (x-x1)(x1-x0)+(y-y1)(y1-y0

A generic vector with origin in (x1,y1,z1) has the following components:

(x-x1,y-y1,z-z1)

A vector corresponding to the radius of the sphere ending on (x1,y1,z1) has components:

(x1-x0,y1-y0,z1-z0)

Two vectors are perpendicular when their scalar product is zero. If you apply this to the two vectors just defined you get ozo's formula:

(x-x1)(x1-x0)+(y-y1)(y1-y0

You only need to remove the parentheses to get the equation of a plane in the usual form:

a*x + b*y + c*z + d = 0

This plane passes through (x1,y1,z1) and, being perpendicular to the radius ending in the same point, is tangent to the sphere.

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