using System;
using System.Collections.Generic;
using System.Linq.Expressions;
namespace Assistance {
public static class Geometry {
public static readonly double precision = 1e-8;
public static readonly double precisionSqr = precision*precision;
public static readonly double sqrt2Pi = Math.Sqrt(2.0*Math.PI);
public static bool isEqual(double a, double b)
{ return Math.Abs(b - a) <= precision; }
public static bool isGreaterOrEqual(double a, double b)
{ return b - a <= precision; }
public static bool isLessOrEqual(double a, double b)
{ return isGreaterOrEqual(b, a); }
public static bool isLess(double a, double b)
{ return !isGreaterOrEqual(a, b); }
public static bool isGreater(double a, double b)
{ return !isGreaterOrEqual(b, a); }
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 class Interpolation<T> {
public delegate T HalfFunc(T a, double b);
public delegate T FullFunc(T a, T b);
public static FullFunc add;
public static FullFunc sub;
public static HalfFunc mul;
public static HalfFunc div;
static Interpolation() {
{ // add
ParameterExpression a = Expression.Parameter(typeof(T));
ParameterExpression b = Expression.Parameter(typeof(T));
add = Expression.Lambda<FullFunc>(Expression.Add(a, b), a, b).Compile();
}
{ // sub
ParameterExpression a = Expression.Parameter(typeof(T));
ParameterExpression b = Expression.Parameter(typeof(T));
sub = Expression.Lambda<FullFunc>(Expression.Subtract(a, b), a, b).Compile();
}
{ // mul
ParameterExpression a = Expression.Parameter(typeof(T));
ParameterExpression b = Expression.Parameter(typeof(double));
mul = Expression.Lambda<HalfFunc>(Expression.Multiply(a, b), a, b).Compile();
}
{ // div
ParameterExpression a = Expression.Parameter(typeof(T));
ParameterExpression b = Expression.Parameter(typeof(double));
div = Expression.Lambda<HalfFunc>(Expression.Divide(a, b), a, b).Compile();
}
}
public static T linear(T p0, T p1, double l)
{ return add(mul(sub(p1, p0), l), p0); }
public static T spline(T p0, T p1, T t0, T t1, double l) {
double ll = l*l;
double lll = ll*l;
return add( add( mul(p0, ( 2.0*lll - 3.0*ll + 1.0)),
mul(p1, (-2.0*lll + 3.0*ll )) ),
add( mul(t0, ( lll - 2.0*ll + l )),
mul(t1, ( lll - 1.0*ll )) ));
}
public static T splineTangent(T p0, T p1, T t0, T t1, double l) {
double ll = l*l;
return add( mul(sub(p0, p1), 6.0*(ll - l)),
add( mul(t0, ( 3.0*ll - 4.0*l + 1.0)),
mul(t1, ( 3.0*ll - 2.0*l )) ));
}
}
public static double interpolationLinear(double p0, double p1, double l)
{ return (p1 - p0)*l + p0; }
public static double interpolationSpline(double p0, double p1, double t0, double t1, double l) {
double ll = l*l;
double lll = ll*l;
return p0*( 2.0*lll - 3.0*ll + 1.0)
+ p1*(-2.0*lll + 3.0*ll )
+ t0*( lll - 2.0*ll + l )
+ t1*( lll - 1.0*ll );
}
public static double interpolationSplineTangent(double p0, double p1, double t0, double t1, double l) {
double ll = l*l;
return (p0 - p1)*6.0*(ll - l)
+ t0*( 3.0*ll - 4.0*l + 1.0)
+ t1*( 3.0*ll - 2.0*l );
}
}
}