Re: Finding line intercepts on plane in 3D space
- From: Ray Koopman <koopman@xxxxxx>
- Date: Wed, 3 Dec 2008 23:44:18 -0800 (PST)
On Dec 3, 4:41 pm, groups2...@xxxxxxxxxxxx wrote:
I have a triangle in 3D space where each corner coordinate (X,Y,Z) is
known. How do I determine the Z coordinate where an arbitrary line
intersects the plane given that the line's (X,Y) coordinates are known
and constant? (Line is parallel to Z axis and is guaranteed to
intercept the triangle's surface.)
Solve for right-triangles if easier.
Bonus question: I want to enlarge the plane by adding a duplicate
triangle. How do I find the fourth coordinate? (The resulting plane
must not have a seam.)
Your help is appreciated!
There's got to be some short-cut to solving these problems! Without a
solution I will need to resort to successive approximation!
Thank You!
[x1 x2 x3] [p1] [x]
[y1 y2 y3] * [p2] = [y]
[ 1 1 1] [p3] [1]
Solve the above equation for the pi. Then z1*p1 + z2*p2 + z3*p3
is the z-coordinate of the intersection of the line and the plane.
If all pi are positive then the intersection is inside the triangle.
If any pi is negative then the interesection is outside the triangle.
Otherwise the intersection is on the border of the triangle.
.
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- Finding line intercepts on plane in 3D space
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