Rays and Positions

Rays and Positions

A ray is a line with an origin and a direction:

ray = origin + direction * t

The parameter t moves you along the ray: t = 0 is the origin, t = 1 is one step in the direction, negative t is behind the origin.

The Ray Class

class Ray {
public:
    double ox, oy, oz;  // origin
    double dx, dy, dz;  // direction
    Ray(double ox, double oy, double oz,
        double dx, double dy, double dz)
        : ox(ox), oy(oy), oz(oz), dx(dx), dy(dy), dz(dz) {}
};

Computing Position

// Position along ray at parameter t
double posX(Ray r, double t) { return r.ox + r.dx * t; }
double posY(Ray r, double t) { return r.oy + r.dy * t; }
double posZ(Ray r, double t) { return r.oz + r.dz * t; }

Or add position methods directly to the class:

double posX(double t) const { return this->ox + this->dx * t; }

Example

ray(origin=point(2,3,4), direction=vector(1,0,0)):
  position(0)   = point(2, 3, 4)   (origin)
  position(1)   = point(3, 3, 4)   (one step right)
  position(-1)  = point(1, 3, 4)   (one step left)
  position(2.5) = point(4.5, 3, 4)

Your Task

Add posX, posY, posZ methods to the Ray class.

Expected output:

4.5 3 4