Here, line segment ab is cast upward on arbitrary vector n where I do somethings to find the black point on the line segment cd. My question is, how do I find the point on ab that intersects with the inverted n vector coming down from the new point?

CodePudding user response：

Looks like it will have the same x-coordinate as the black point (call this x). The slope of ab is m = (b_y - a_y) / (b_x - a_x), so the y coordinate is mx a_y.

CodePudding user response：

If the projection is parallel, by the Thales theorem the ratios are preserved.

|ae| / |ab| = |cf| / |cd| = r

which is known.

The searched point is, vectorially

e = a   r.ab = a   |cf|/|cd|.ab