Step by Step solution about How to resolve the algorithm Find the intersection of a line with a plane step by step in the Ruby programming language

The provided Ruby code defines a method intersectPoint for finding the intersection point of a ray with a plane. Here's a breakdown of the code:

1. Libraries:

   • require "matrix": This line imports the Ruby Matrix library, which provides classes and methods for representing and manipulating matrices and vectors.

2. intersectPoint Method:

   • This method takes four arguments:
     • rayVector (rv): A vector representing the direction of the ray.
     • rayPoint (rp): A vector representing the origin point of the ray.
     • planeNormal (pn): A vector perpendicular to the plane.
     • planePoint (pp): A vector representing a point on the plane.

3. Intersection Calculation:

   • The code calculates the intersection point of the ray with the plane using the following steps:
     • It computes the difference between the ray's origin point and the plane point (diff).
     • It calculates the dot product between the plane normal and the difference vector (prod1).
     • It calculates the dot product between the ray's direction vector and the plane normal (prod2).
     • It divides prod1 by prod2 to get a scalar value prod3.
     • It subtracts the result of rayVector * prod3 from the ray's origin point to get the intersection point (ip).

4. main Method:

   • This method sets up example values for the ray's direction vector, origin point, plane's normal vector, and a point on the plane.
   • It calls the intersectPoint method to find the intersection point.
   • It prints the coordinates of the intersection point.

5. Execution:

   • The main method is called at the end to execute the code and display the intersection point.

require "matrix"

def intersectPoint(rayVector, rayPoint, planeNormal, planePoint)
    diff = rayPoint - planePoint
    prod1 = diff.dot planeNormal
    prod2 = rayVector.dot planeNormal
    prod3 = prod1 / prod2
    return rayPoint - rayVector * prod3
end

def main
    rv = Vector[0.0, -1.0, -1.0]
    rp = Vector[0.0, 0.0, 10.0]
    pn = Vector[0.0, 0.0, 1.0]
    pp = Vector[0.0, 0.0, 5.0]
    ip = intersectPoint(rv, rp, pn, pp)
    puts "The ray intersects the plane at %s" % [ip]
end

main()