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) {
			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      );
        }
	}
}