How to solve the lack of symmetry in this line rasterization algorithm?

Questions
1

Hello,

I am working on an algorithm to snap 3D lines to a 3D tessellated space.

Here is a 2D example of the algorithm that works for positive and negative slopes between -1 and 1 inclusive.

Using the slope to calculate the value of y at each x results in slow and error-prone floating calculations. The solution is to simulate the division with a remainder variable.

When dx >= dy, start with an initial remainder variable ry = 0. Then, for each x increment, add dy to ry variable. When it surpasses dx, increment y, then set ry equal to ry - dx.

function line(x1, y1, x2, y2) {
  let points = []
  let dx = Math.abs(x2 - x1);
  let dy = Math.abs(y2 - y1);
  // The remainder variable for y axes. 
  // No rx is created because we are assuming dx >= dy.
  let ry = 0;
  // Current value of y for a given point
  let y = 0;

  // The slope could be positive or negative, so increments coordinates as they go down or up.
  let pointIncrement;
  if (x2 > x1) {
    pointIncrement = 1;
  } else if (x2 < x1) {
    pointIncrement = -1;
    y = y1
  }
  for (let x = x1; pointIncrement < 0 ? x >= x2 : x <= x2; x += pointIncrement) {
    if (ry >= dx) {
      ry -= dx;
      y += pointIncrement;
    }
    // Add dy to ry until it surpasses dx. This simulates the division of dy/dx for slope.
    ry += dy;
    points.push([x, y])
  }
  return points
}

Now, if you call the function with a slope of 1/4th:

line(0,0,20,5)

You get the following results:

[[0,0],[1,0],[2,0],[3,0],[4,1],[5,1],[6,1],[7,1],[8,2],[9,2],[10,2],[11,2],[12,3],[13,3],[14,3],[15,3],[16,4],[17,4],[18,4],[19,4],[20,5]]

Now, if you call it again but in the negative direction, then reverse the coordinate order:

line(20,5,0,0).reverse()

You get the following results:

[[0,0],[1,1],[2,1],[3,1],[4,1],[5,2],[6,2],[7,2],[8,2],[9,3],[10,3],[11,3],[12,3],[13,4],[14,4],[15,4],[16,4],[17,5],[18,5],[19,5],[20,5]]

Why is this occurring?

Is anyone aware of a solution to this problem to make the negative slope symmetric to the positive slope?