c++ triangle rasterization using edge detection

Question

I am trying to implement triangle rasterization using this article as reference

https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/rasterization-stage

as such I have implemented an edge function with an input of 3 points. 2 defining a line and one as the point to be tested, annotated as p

bool SoftwareRendererImp::edgeFunction(float xa, float ya,
                                       float xb, float yb,
                                       float xp, float yp)
{
return ((xp - xa) * (yb - ya) - (yp - ya) * (xb - xa) >= 0);
}

in my rasterization function I am iterating over a set of integers ranging from the lowest to highest x and y values. This is to try and iterate over a box of best fit containing the triangle and test each point to see if it is contained in the triangle.

    void SoftwareRendererImp::rasterize_triangle(float x0, float y0,
                                               float x1, float y1,
                                               float x2, float y2,
                                               Color color)
  {
    // Task 3:
    // Implement triangle rasterization
    cout << "triangle----------------------------------------------------------------------------------------------------------------------- \n";

    float minX = std::min(x0, x1);
    minX = std::min(minX, x2);

    float minY = std::min(y0, y1);
    minY = std::min(minY, y2);

    float maxX = std::max(x0, x1);
    maxX = std::max(maxX, x2);

    float maxY = std::max(y0, y1);
    maxY = std::max(maxY, y2);

    bool inside;

    float px, py;

    for (int x = minX; x < maxX; x++)
    {
      for (int y = minY; y < maxY; y++)
      {
        inside = true;
        px = x + 0.5f;
        py = y + 0.5f;
        inside &= SoftwareRendererImp::edgeFunction(x0, y0, x1, y1, px, py);
        inside &= SoftwareRendererImp::edgeFunction(x1, y1, x2, y2, px, py);
        inside &= SoftwareRendererImp::edgeFunction(x2, y2, x0, y0, px, py);
        if (inside)
        {
          SoftwareRendererImp::rasterize_point(x, y, color);
          cout << "inside: " << x << ", " << y << "\n";
        }
        else
        {
          // cout << "outside: " << x << ", " << y << "\n";
        }
      }
    }
  }

From my understanding of the linked article this should work however it is not. Can anyone spot what it is that I am screwing up?

Answer 1

this expression was backwards

(xp - xa) * (yb - ya) - (yp - ya) * (xb - xa)

it should have been

(yp - ya) * (xb - xa) - (xp - xa) * (yb - ya)