C++ Triangle-Plane intersection to line

Question

Here's a simplified version of my triangle object and related objects:

class line{
   public:
    double x1;
    double y1;
    double x2;
    double y2;
}
class vertex{
  public:
    double x;
    double y;
    double z;
}; 
class triangle{
    vertex a;
    vertex b;
    vertex c;
  public:
    line *intersection(double z_axis){
        line *l = new line;

        //intersection code here

        return l;
    }
};

What I need to happen is for the intersection function to return the line where the triangle and the plane parallel to the x and y axis at the given z axis. All the sample code I've looked at either assumes having a force normal or returns doesn't return quite what I need. I'd really appreciate some insight on how to go about doing this in an optimal way. I'm having trouble making sense of the Plane-Plane intersection formal math solutions.

Thanks in advance,

Max

Answer 1

you should handle different situations:

1) there is no intersection. (for each vertex: z_axis > vertex.z) or (for each vertex: z_axis < vertex.z)

2) the triangle lies in the z=z_axis plane (for each vertex: z_axis = vertex.x). This is awkward for doubles but 0 or some powers of two or some nice binary fractions are represented precisely.

3) one vertex (let's call it P) is below and two vertices (Q, R) are above the z=z_axis plane (or vice versa)

here you'll be able to find the intersections. Your problem will be broken down to find intersection of line PQ and PR with the plane z=z_axis.

4) one or two vertices lie on the z=z_axis plane.

The intersections here are trivial, but they may still be computed the same way as in point 3.

Is it clear? You may start implementing...