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

  • $\begingroup$ By $4$ vertices do you know $a, b, c, d$? $\endgroup$ Jun 28, 2021 at 18:35
  • $\begingroup$ 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 $\endgroup$ Jun 28, 2021 at 18:40
  • $\begingroup$ Do you mean the infinite plane or the plane confined by your four vertices? $\endgroup$ Jun 28, 2021 at 18:50
  • $\begingroup$ The plane confined by my vertices $\endgroup$ Jun 28, 2021 at 19:28
  • $\begingroup$ 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. $\endgroup$
    – Moti
    Jun 30, 2021 at 3:32


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