Question

I have three points, for example:

Start 194 171
Right 216 131
Left  216 203

I want to get all the points within that triangle. How would I do that efficiently?

Answer 1

see z3nth10n’s answer for better input validation

Introduction:

The general idea was to get the triangle’s edges (y-Wise) for every x in it’s range, and then you have all the y’s that exist within the triangle for every single x, which with simple conversion turns into all points within the triangle.

You can look at it as if you cut the triangle into stripes, each being of width 1.
So for X=0, on the line between A and B, the Y is 6, and on the line between A and C, the Y is -2, so you can see that the stripe of X=0 is between -2 and 6. Therefore, you can tell that (0, -2) (0, -1) (0, 0) … (0, 5) (0, 6) are all in the triangle. Doing that for X’s between the smallest and the largest within the triangle, and you have all the points in the triangle!

Speed:

For the triangle (0, 0) (1, 8) (4, 6) – found 16 points.

Done 1,000,000 times in 3.68 seconds.

Implementation:

public IEnumerable<Point> PointsInTriangle(Point pt1, Point pt2, Point pt3)
{
    if (pt1.Y == pt2.Y && pt1.Y == pt3.Y)
    {
        throw new ArgumentException("The given points must form a triangle.");
    }

    Point tmp;

    if (pt2.X < pt1.X)
    {
        tmp = pt1;
        pt1 = pt2;
        pt2 = tmp;
    }

    if (pt3.X < pt2.X)
    {
        tmp = pt2;
        pt2 = pt3;
        pt3 = tmp;

        if (pt2.X < pt1.X)
        {
            tmp = pt1;
            pt1 = pt2;
            pt2 = tmp;
        }
    }

    var baseFunc = CreateFunc(pt1, pt3);
    var line1Func = pt1.X == pt2.X ? (x => pt2.Y) : CreateFunc(pt1, pt2);

    for (var x = pt1.X; x < pt2.X; x++)
    {
        int maxY;
        int minY = GetRange(line1Func(x), baseFunc(x), out maxY);

        for (var y = minY; y <= maxY; y++)
        {
            yield return new Point(x, y);
        }
    }

    var line2Func = pt2.X == pt3.X ? (x => pt2.Y) : CreateFunc(pt2, pt3);

    for (var x = pt2.X; x <= pt3.X; x++)
    {
        int maxY;
        int minY = GetRange(line2Func(x), baseFunc(x), out maxY);

        for (var y = minY; y <= maxY; y++)
        {
            yield return new Point(x, y);
        }
    }
}

private int GetRange(double y1, double y2, out int maxY)
{
    if (y1 < y2)
    {
        maxY = (int)Math.Floor(y2);
        return (int)Math.Ceiling(y1);
    }

    maxY = (int)Math.Floor(y1);
    return (int)Math.Ceiling(y2);
}

private Func<int, double> CreateFunc(Point pt1, Point pt2)
{
    var y0 = pt1.Y;

    if (y0 == pt2.Y)
    {
        return x => y0;
    }

    var m = (double)(pt2.Y - y0) / (pt2.X - pt1.X);

    return x => m * (x - pt1.X) + y0;
}