How to plot a contour in the plane defined by a vector cross-product

Question

I have some contours of a structure in 3D that I would like to plot in 2D, but how do I get from 3D to 2D? In other words, I would like to plot the contour in the plane defined by the cross-product of three points from the contour. For instance it could be the contours of a ship.

Answer 1

Setting $z=0$ for every point would project every point onto the $xy$-plane. You could also choose $x=0$ to project onto the $yz$-plane, or $y=0$ to project onto the $xz$-plane, or set any other fixed linear combination of the coordinates to zero to project onto another plane, whose orientation depends on the choice of the coefficients of that linear combination.