CODEWITHSUNDEEP
math3d
David
David

Reputation:

Determine position in front of 3D plane (cartesian math)

I have a planar element in 3D space that I've rotated on the x, y and z axis. I'm positioning a 3D camera in front of the planar but I need to find a way to calculate the x, y, z of the camera.

I'm trying to figure out how to place the camera at x distance from the planes face. There's obviously a bit of trig involved but for the life of me can't figure it out. Gah.

Dave

Upvotes: 3

Views: 2080

Answers (2)

John
John

Reputation: 16007

The relation between distance of a point to a plane is

distance = (Aa + Bb + Cc + D) / sqrt(A^2+B^2+C^2)

for distance to plane Ax + By + Cz + D = 0 from point (a,b,c)

Might need to multiply by -1 to get distance positive.

The equations for the line through point (a,b,c) perpendicular to the same plane is

x = a + At; y = b + Bt; z = c + Ct

So if you have a point in the plane, you can find the equation of the line perpendicular to that plane. Then you can use the distance constraint to solve for two points a distance along that line - one above the plane, and one below.

Upvotes: 2

shoosh
shoosh

Reputation: 79003

If you have a plane then you also have its normal vector N and some point on it P.
If you calculate P'=P+x*N you'll get the point P' which is x units infront of point P in the direction of the normal.

Upvotes: 2

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