# Plane and line segment intersection

I have a plane represented by the equation ax + by + cz + d = 0, and I know its 4 vertices and have a line segment represented by its two endpoints

How to check if the line cross the plane by the given information ?

I found some solution but all with parametric vector and vectors generally, I don't want solutions with vectors, I want a geometric one

• By $4$ vertices do you know $a, b, c, d$? Jun 28, 2021 at 18:35
• I mean by "By 4 vertices" that I know its left-top vertex and right-top etc.. And yes I know a, b, c, d of the equation Jun 28, 2021 at 18:40
• Do you mean the infinite plane or the plane confined by your four vertices? Jun 28, 2021 at 18:50
• The plane confined by my vertices Jun 28, 2021 at 19:28
• When you calculate the value of the equation by inserting the end "points", you should get a result with same sign if there is no intersection and different signs if there is intersection. To check if it is in the rectangle created by the 4 vertices you use the lines equations. I am sure somewhere on th enet you can find a detailed solution.
– Moti
Jun 30, 2021 at 3:32