vector_plane_inters​ect

A function to fine the point where a line intersects a plane.

Given 1) a line parameterized by a point in 3D space along with a 3x1 vector indicating the line's direction, and 2) the coefficients (a b c) of a plane (z = a*x + b*y + c), vector_plane_intersect calculates the point on the plane at which the line will intersect it.

Inf is returned when the line is parallel to the plane.

From the code...

%%
% A line in 3 D space is parameterized by
%
% x = xo + n*t;
% y = yo + n*t;
% z = zo + n*t;
%
% A plane in 3D space is parameterized by
%
% z = C(1)*x+C(2)*y+C(3)
%
% To find the point where the line intersects the plane we substitute the
% equations for x, y and z into the plane equation above and solve for t.
% Then evaluate the x, y and z equations at that point.