LinePlaneIntersection.h

#pragma once
 
#include <glm/geometric.hpp>
#include <glm/vec3.hpp>
 
namespace Cogs
{
  namespace Geometry
  {
    static bool intersect(const glm::vec3 normal, const float distance, const glm::vec3 & origin, const glm::vec3 & direction, glm::vec3 & intersection)
    {
      // Check if the line is parallel to the plane.
      if (glm::dot(direction, normal) == 0.0f) return false;
 
      // From the discussion on SbDPLine::getClosestPoint() we know that
      // any point on the line can be expressed as:
      //                    Q = P + t*D    (1)
      //
      // We can also easily see that a point must satisfy this equation to lie
      // in the plane:
      //                    N·(Q - d*N) = 0, where N is the normal vector,
      //                                     Q is the point and d the offset
      //                                     from the origin.
      //
      // Combining these two equations and simplifying we get:
      //
      //                          d*|N|² - N·P
      //                    t = ----------------, |N| == 1
      //                               N·D
      //
      // Substituting t back in (1), we've solved the problem.
      //                                                         19980816 mortene.
 
      float t = (distance - glm::dot(normal, origin)) / glm::dot(normal, direction);
 
      intersection = origin + t * direction;
 
      return true;
    }
  }
}