using System;

using System.Collections.Generic;

namespace Assistance {

	public static class Geometry {

		public delegate Point TransformFunc(Point p);

		public static readonly double precision = 1e-8;

		public static readonly double sqrt2Pi = Math.Sqrt(2.0*Math.PI);

		public static double logNormalDistribuitionUnscaled(double x, double x0, double w) {

			return Math.Exp(-0.5*Math.Pow(Math.Log(x/x0)/w, 2.0))/x;

		}

		public static double logNormalDistribuition(double x, double x0, double w) {

			return logNormalDistribuition(x, x0, w)/(w*sqrt2Pi);

		}

		public static void truncateInfiniteLine(Rectangle bounds, ref Point p0, ref Point p1) {

			if (p0.isEqual(p1)) return;

			Point d = p0 - p1;

			if (Math.Abs(d.x)*bounds.height > bounds.width*Math.Abs(d.y)) {

				// horizontal

				double k = d.y/d.x;

				p1 = new Point(bounds.x1, p0.y + k*(bounds.x1 - p0.x));

				p0 = new Point(bounds.x0, p0.y + k*(bounds.x0 - p0.x));

			} else {

				// vertical

				double k = d.x/d.y;

				p1 = new Point(p0.x + k*(bounds.y1 - p0.y), bounds.y1);

				p0 = new Point(p0.x + k*(bounds.y0 - p0.y), bounds.y0);

			}

		}

		public static Point noTransform(Point point) {

			return point;

		}

		public static Point transform(List<transformfunc> funcs, Point point) {</transformfunc>

			Point p = point;

			foreach(TransformFunc func in funcs)

				p = func(p);

			return p;

		}

		public static double splinePoint(double p0, double p1, double t0, double t1, double l) {

			return p0*(( 2.0*l - 3.0)*l*l + 1.0)

			     + p1*((-2.0*l + 3.0)*l*l      )

			     + t0*((     l - 2.0)*l*l + l  )

			     + t1*((     l - 1.0)*l*l      );

        }

		public static Point splinePoint(Point p0, Point p1, Point t0, Point t1, double l) {

			return p0*(( 2.0*l - 3.0)*l*l + 1.0)

			     + p1*((-2.0*l + 3.0)*l*l      )

			     + t0*((     l - 2.0)*l*l + l  )

			     + t1*((     l - 1.0)*l*l      );

        }

	}

}