Software rendering in 500 lines of bare C++

I have a whole chapter on that! https://gabrielgambetta.com/computer-graphics-from-scratch/1...

You only need to clip triangles is you're worried about attribute interpolation for very large triangles. There's two ways to handle this: (1) discard (fast but not a great user experience); or, (2) primitive synthesis. Just frustum clipping is enabled by point picking in the local tile. Primitive synthesis requires some FP kung fu; but, is easiest done in barycentric space against a reverse transformed clipping rectangle. This lets you carefully control clip rounding error using either doubles or (better) fixed point. Abrash likes to use integer fixed point, but that is historical — modern fixed point can be handled with careful control of the fp unit in the mantissa. The major issue is regenerating the Z and the 1/Z values for the new vertices of the synthesized primitives. Everything else should flow down the pipe naturally, assuming a deferred attribute synthesis rasterizer.

There are examples in the open source version of my rasterizer: OpenSWR.org.

My renderer attempts always got stuck on the "should implement clipping" phase too, until I finally bit the bullet and managed to write a working one without much effort, independently "rediscovering" the Sutherland–Hodgman algorithm [1] as I found out later (googling it beforehand would've been cheating, of course).

The algorithm itself is fairly straightforward and intuitive, I think the biggest mental block is the weirdness of the projective space and working with homogeneous coordinates (actually the only frustum plane that you have to clip against in P₃(ℝ) is the front plane, the rest could be clipped after the perspective division, but no reason not to do it all at the same time while you're at it). The plane equations in the clip space are super simple (assuming your projection matrix is correct of course), basically the six equations of the form ax + by + cz = w simplify to

  x = ±w 
  y = ±w 
  z = ±w.

Meaning, for example, that if the x coordinate of your vertex is greater than the w coordinate, that vertex is outside the right clipping plane. The Sutherland–Hodgman itself goes something like this:

  # Returns true if point is inside the half-space defined by plane
  def point_inside_plane(point, plane) -> bool:
    ...

  # Returns t such that the edge (p1, p2) intersects plane at lerp(t, v1, v2)
  def edge_intersect_plane(edge: (Point, Point), plane) -> float:
    ...

  def clip_against_plane(verts: [Vertex], plane):
    let result: [Vertex] = []
    let [(v_1, v_2), (v_2, v_3), ..., (v_n, v_1)] = verts.edges()
    for each (v_i, v_j) of the edges:
      let i_inside = point_inside_plane(v_i, plane)
      let j_inside = point_inside_plane(n_j, plane)

      if i_inside and j_inside:
        result.push(v_i)
      else if not i_inside and not j_inside:
        pass # Nothing to do!
      else:
        # One is inside, the other is not, we have to clip
        let t = edge_intersect_plane((v_i.pos, v_j.pos), plane)
        # Synthetize a new vertex straddling the plane
        let new_vert = Vertex(
          pos = lerp(t, v_i.pos, v_j.pos), 
          attribs = lerp(t, v_i.attribs, v_j.attribs)
        )
        if i_inside:
          result.push(v_i); result.push(new_vert) # discard v_j
        else:
          result.push(new_vert); result.push(v_j) # discard v_i
      
   return result

Then you just call this for all the planes so that the output of one call becomes the input for the next call! The end result of this process is a convex polygon (of at most nine vertices for a triangle against six planes), which can be trivially triangulated.

[1]: I. Sutherland and G. Hodgman. 1974. "Reentrant polygon clipping." Communications of the ACM, Volume 17, Issue. Available: https://dl.acm.org/doi/10.1145/360767.360802

What image was that? The first image I get is a headshot.

Personally I’d have gone with a teapot as my demo but I don’t see anything shocking about the model the author chose.

> I jumped when the first image loaded on the page.. didn't expect that.

mbappe'?