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

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?