find the point of intersection of two lines

namespace fviz {

/**

 * Check if two lines intersect and if they do, return the intersection

 * point

 */

bool intersect_line_line(

    vec2 o0,

    vec2 p0,

    vec2 v0,

    vec2 o1,

    vec2 p1,

    vec2 v1,

    vec2* x /* = nullptr */) {

    vec2* p /* = nullptr */) {

  // ensure the direction vectors are normalized

  v0 = vec2_normalize(v0);

  v1 = vec2_normalize(v1);

    return false;

  }

  // if the lines are not parallel, but the user is not interested in the

  // intersection point, return

  if (!p) {

    return true;

  }

  // the next step is to compute the point of intersection. we start with the

  // implicit expressions that define the global y coordinates of all points on

  // the input lines in terms of the global x coordinate written in the standard

  // form:

  //

  //     aN * x + bN * y = cN

  //

  // we already have the direction vector (a and b) as an input argument, so

  // we can find a valid c that satisfies the equation simply by evaluating the

  // left part of the equation with the known point on the line that we also

  // have.

  auto a0 = -v0.y;

  auto a1 = -v1.y;

  auto b0 = v0.x;

  auto b1 = v1.x;

  auto c0 = a0 * p0.x + b0 * p0.y;

  auto c1 = a1 * p1.x + b1 * p1.y;

  // the x coordinate of the point of intersection can now be determined

  // by solving the following system of linear equations. the two equations are

  // the standard-form line equations derived above.

  //

  //    a0 * x + b0 * y = c0

  //    a1 * x + b1 * y = c1

  //

  // or written in matrix coefficient form:

  //

  //    | a0  b0 |     | x |     | c0 |

  //    |        |  +  |   |  =  |    |

  //    | a1  b1 |     | y |     | c1 |

  //

  // this system can be solved using cramer's rule (there must be a solution

  // since the lines are already determined not to be parallel). to do so, we

  // first calculate the three "denominator", "x numerator" and "y numerator"

  // determinants of the (substituted) coefficient matrix and then compute the

  // result by dividing the determinants as defined by cramer's rule:

  auto dd = (a0 * b1 - b0 * a1); // standard determinant

  auto dx = (b1 * c0 - b0 * c1); // replace x coefficients (a0/a1) with solution

  auto dy = (a0 * c1 - a1 * c0); // replace y coefficients (b0/b1) with solution

  p->x = dx / dd;

  p->y = dy / dd;

  return true;

}

namespace fviz {

/**

 * Given two (infinite) lines defined by a point on each of the the lines o0, o1

 * (their 'origins') and their normal direction vectors v0, v1, compute the point

 * of intersection. Returns false if the two lines are parallel.

 * Given two (infinite) lines defined by a point on each of the the lines p0, p1

 * and their normal direction vectors v0, v1, compute the point of intersection.

 * Returns false if the two lines are parallel.

 */

bool intersect_line_line(

    vec2 o0,

    vec2 p0,

    vec2 v0,

    vec2 o1,

    vec2 p1,

    vec2 v1,

    vec2* x = nullptr);

    vec2* p = nullptr);

} // namespace fviz

      true);

}

void test_intersect_point() {

  Point p;

  EXPECT_EQ(

      intersect_line_line(

          {0, 0},

          {1, 2},

          {0, 2},

          {1, 1},

          &p),

      true);

  EXPECT_EQ(p.x, 2);

  EXPECT_EQ(p.y, 4);

}

int main(int argc, char** argv) {

  test_intersect_parallel();

  test_intersect_point();

}