/// <summary>
/// Projects a polygon onto an axis.
/// </summary>
/// <param name="polygon">The polygon to project.</param>
/// <param name="axis">The axis to project onto.</param>
/// <returns>The interval on the axis that the polygon projects onto.</returns>
public static Linel Project(Polygon2l polygon, Vector2l axis)
{
var min = long.MaxValue;
var max = long.MinValue;
for (int i = 0; i < polygon.Count; ++i)
{
var proj = Vector.Dot((Vector2l)polygon[i], axis);
min = Functions.Min(min, proj);
max = Functions.Max(max, proj);
}
return(new Linel(min, max));
}
public IEnumerable<Tuple<Point2l, Point2l>> Trace(Point2l start, Point2l end)
{
var x0 = start.X / GridSize.Width;
var y0 = start.Y / GridSize.Height;
var x1 = end.X / GridSize.Width;
var y1 = end.Y / GridSize.Height;
var dir = new Vector2l(end.X - start.X, end.Y - start.Y);
var dx = Math.Sign(dir.X);
var dy = Math.Sign(dir.Y);
var deltax = (double)GridSize.Width / Math.Abs(dir.X);
var deltay = (double)GridSize.Height / Math.Abs(dir.Y);
var minx = x0 * GridSize.Width;
var maxx = minx + GridSize.Width;
var miny = y0 * GridSize.Height;
var maxy = miny + GridSize.Height;
var distx = ((dx >= 0) ? (maxx - start.X) : (start.X - minx)) / (double)GridSize.Width;
var disty = ((dy >= 0) ? (maxy - start.Y) : (start.Y - miny)) / (double)GridSize.Height;
var tx = distx * deltax;
var ty = disty * deltay;
var prev = new Point2l(x0, y0);
var hit = start;
while (true)
{
var grid = new Point2l(x0, y0);
yield return Tuple.Create(grid, hit);
prev = grid;
if (tx <= ty)
{
if (x0 == x1) break;
hit = new Point2l(
start.X + (long)(dir.X * tx),
start.Y + (long)(dir.Y * tx));
tx += deltax;
x0 += dx;
}
else
{
if (y0 == y1) break;
hit = new Point2l(
start.X + (long)(dir.X * ty),
start.Y + (long)(dir.Y * ty));
ty += deltay;
y0 += dy;
}
}
}
/// <summary>
/// Projects a point onto a vector, returns the distance of the projection from the origin.
/// </summary>
/// <param name="vector">The vector to project onto.</param>
/// <param name="point">The point to project.</param>
/// <returns>The distance from the origin of the projection.</returns>
public static long Project(Point2l point, Vector2l vector)
{
return(vector.X * point.X + vector.Y * point.Y);
}
/// <summary>
/// Subtracts a vector from a point and returns the result.
/// </summary>
/// <param name="point">The point value to subtract from (the minuend).</param>
/// <param name="vector">The vector value to subtract (the subtrahend).</param>
/// <returns>The result of subtracting vector from point (the difference).</returns>
public static Point2l Subtract(Point2l point, Vector2l vector)
{
return(new Point2l(point.X - vector.X, point.Y - vector.Y));
}
/// <summary>
/// Adds a point and a vector and returns the result.
/// </summary>
/// <param name="point">The point value to add.</param>
/// <param name="vector">The vector value to add.</param>
/// <returns>The sum of left and right.</returns>
public static Point2l Add(Point2l point, Vector2l vector)
{
return(new Point2l(point.X + vector.X, point.Y + vector.Y));
}
