using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows;
using System.Windows.Media;

namespace Microsoft.Research.DynamicDataDisplay
{
	/// <summary>
	/// Base class for all data transforms.
	/// Defines methods to transform point from data coordinate system to viewport coordinates and vice versa.
	/// Derived class should be immutable; to perform any changes a new new instance with different parameters should be created.
	/// </summary>
	public abstract class DataTransform
	{
		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns>Transformed point in viewport coordinates.</returns>
		public abstract Point DataToViewport(Point pt);
		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns>Transformed point in data coordinates.</returns>
		public abstract Point ViewportToData(Point pt);

		private static readonly DataRect defaultDomain = DataRect.Empty;
		/// <summary>
		/// Gets the data domain of this dataTransform.
		/// </summary>
		/// <value>The data domain of this dataTransform.</value>
		public virtual DataRect DataDomain { get { return defaultDomain; } }
	}

	/// <summary>
	/// Represents identity data transform, which applies no transformation.
	/// is by default in CoordinateTransform.
	/// </summary>
	public sealed class IdentityTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="IdentityTransform"/> class.
		/// </summary>
		public IdentityTransform() { }

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			return pt;
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			return pt;
		}
	}

	/// <summary>
	/// Represents a logarithmic transform of y-values of points.
	/// </summary>
	public sealed class Log10YTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="Log10YTransform"/> class.
		/// </summary>
		public Log10YTransform() { }

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			double y = pt.Y;

			if (y < 0)
				y = Double.MinValue;
			else
				y = Math.Log10(y);

			return new Point(pt.X, y);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			return new Point(pt.X, Math.Pow(10, pt.Y));
		}

		/// <summary>
		/// Gets the data domain of this dataTransform.
		/// </summary>
		/// <value>The data domain of this dataTransform.</value>
		public override DataRect DataDomain
		{
			get { return DataDomains.YPositive; }
		}

	}

	/// <summary>
	/// Represents a logarithmic transform of x-values of points.
	/// </summary>
	public sealed class Log10XTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="Log10XTransform"/> class.
		/// </summary>
		public Log10XTransform() { }

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			double x = pt.X;

			if (x < 0)
				x = Double.MinValue;
			else
				x = Math.Log10(x);

			return new Point(x, pt.Y);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			return new Point(Math.Pow(10, pt.X), pt.Y);
		}

		/// <summary>
		/// Gets the data domain.
		/// </summary>
		/// <value>The data domain.</value>
		public override DataRect DataDomain
		{
			get { return DataDomains.XPositive; }
		}
	}

	/// <summary>
	/// Represents a mercator transform, used in maps.
	/// Transforms y coordinates.
	/// </summary>
	public sealed class MercatorTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="MercatorTransform"/> class.
		/// </summary>
		public MercatorTransform()
		{
			CalcScale(maxLatitude);
		}

		/// <summary>
		/// Initializes a new instance of the <see cref="MercatorTransform"/> class.
		/// </summary>
		/// <param name="maxLatitude">The maximal latitude.</param>
		public MercatorTransform(double maxLatitude)
		{
			this.maxLatitude = maxLatitude;
			CalcScale(maxLatitude);
		}

		private void CalcScale(double maxLatitude)
		{
			double maxLatDeg = maxLatitude;
			double maxLatRad = maxLatDeg * Math.PI / 180;
			scale = maxLatDeg / Math.Log(Math.Tan(maxLatRad / 2 + Math.PI / 4));
		}

		private double scale;
		/// <summary>
		/// Gets the scale.
		/// </summary>
		/// <value>The scale.</value>
		public double Scale
		{
			get { return scale; }
		}

		private double maxLatitude = 85;
		/// <summary>
		/// Gets the maximal latitude.
		/// </summary>
		/// <value>The max latitude.</value>
		public double MaxLatitude
		{
			get { return maxLatitude; }
		}

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public sealed override Point DataToViewport(Point pt)
		{
			double y = pt.Y;
			if (-maxLatitude <= y && y <= maxLatitude)
			{
				y = scale * Math.Log(Math.Tan(Math.PI * (pt.Y + 90) / 360));
			}

			return new Point(pt.X, y);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public sealed override Point ViewportToData(Point pt)
		{
			double y = pt.Y;
			if (-maxLatitude <= y && y <= maxLatitude)
			{
				double e = Math.Exp(y / scale);
				y = 360 * Math.Atan(e) / Math.PI - 90;
			}

			return new Point(pt.X, y);
		}
	}

	/// <summary>
	/// Represents transform from polar coordinate system to rectangular coordinate system.
	/// </summary>
	public sealed class PolarToRectTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="PolarToRectTransform"/> class.
		/// </summary>
		public PolarToRectTransform() { }

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			double r = pt.X;
			double phi = pt.Y;

			double x = r * Math.Cos(phi);
			double y = r * Math.Sin(phi);

			return new Point(x, y);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			double x = pt.X;
			double y = pt.Y;
			double r = Math.Sqrt(x * x + y * y);
			double phi = Math.Atan2(y, x);

			return new Point(r, phi);
		}
	}

	/// <summary>
	/// Represents a data transform which applies rotation around specified center at specified angle.
	/// </summary>
	public sealed class RotateDataTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="RotateDataTransform"/> class.
		/// </summary>
		/// <param name="angleInRadians">The angle in radians.</param>
		public RotateDataTransform(double angleInRadians)
		{
			this.center = new Point();
			this.angle = angleInRadians;
		}

		/// <summary>
		/// Initializes a new instance of the <see cref="RotateDataTransform"/> class.
		/// </summary>
		/// <param name="angleInRadians">The angle in radians.</param>
		/// <param name="center">The center of rotation.</param>
		public RotateDataTransform(double angleInRadians, Point center)
		{
			this.center = center;
			this.angle = angleInRadians;
		}

		private readonly Point center;
		/// <summary>
		/// Gets the center of rotation.
		/// </summary>
		/// <value>The center.</value>
		public Point Center
		{
			get { return center; }
		}

		private readonly double angle;
		/// <summary>
		/// Gets the rotation angle.
		/// </summary>
		/// <value>The angle.</value>
		public double Angle
		{
			get { return angle; }
		}

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			return Transform(pt, angle);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			return Transform(pt, -angle);
		}

		private Point Transform(Point pt, double angle)
		{
			Vector vec = pt - center;
			double currAngle = Math.Atan2(vec.Y, vec.X);
			currAngle += angle;

			Vector rotatedVec = new Vector(Math.Cos(currAngle), Math.Sin(currAngle)) * vec.Length;

			return center + rotatedVec;
		}
	}

	/// <summary>
	/// Represents data transform performed by multiplication on given matrix.
	/// </summary>
	public sealed class MatrixDataTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="MatrixDataTransform"/> class.
		/// </summary>
		/// <param name="matrix">The transform matrix.</param>
		public MatrixDataTransform(Matrix matrix)
		{
			this.matrix = matrix;
			this.invertedMatrix = matrix;
			invertedMatrix.Invert();
		}

		private readonly Matrix matrix;
		private readonly Matrix invertedMatrix;

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			return matrix.Transform(pt);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			return invertedMatrix.Transform(pt);
		}
	}

	/// <summary>
	/// Represents a chain of transforms which are being applied consequently.
	/// </summary>
	public sealed class CompositeDataTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="CompositeDataTransform"/> class.
		/// </summary>
		/// <param name="transforms">The transforms.</param>
		public CompositeDataTransform(params DataTransform[] transforms)
		{
			if (transforms == null)
				throw new ArgumentNullException("transforms");
			foreach (var transform in transforms)
			{
				if (transform == null)
					throw new ArgumentNullException("transforms", Strings.Exceptions.EachTransformShouldNotBeNull);
			}

			this.transforms = transforms;
		}

		/// <summary>
		/// Initializes a new instance of the <see cref="CompositeDataTransform"/> class.
		/// </summary>
		/// <param name="transforms">The transforms.</param>
		public CompositeDataTransform(IEnumerable<DataTransform> transforms)
		{
			if (transforms == null)
				throw new ArgumentNullException("transforms");

			this.transforms = transforms;
		}

		private readonly IEnumerable<DataTransform> transforms;
		/// <summary>
		/// Gets the transforms.
		/// </summary>
		/// <value>The transforms.</value>
		public IEnumerable<DataTransform> Transforms
		{
			get { return transforms; }
		}

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			foreach (var transform in transforms)
			{
				pt = transform.DataToViewport(pt);
			}

			return pt;
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			foreach (var transform in transforms.Reverse())
			{
				pt = transform.ViewportToData(pt);
			}

			return pt;
		}
	}

	/// <summary>
	/// Represents a data transform, performed by given lambda function.
	/// </summary>
	public sealed class LambdaDataTransform : DataTransform
	{
		/// <summary>
		/// Initializes a new instance of the <see cref="DelegateDataTransform"/> class.
		/// </summary>
		/// <param name="dataToViewport">The data to viewport transform delegate.</param>
		/// <param name="viewportToData">The viewport to data transform delegate.</param>
		public LambdaDataTransform(Func<Point, Point> dataToViewport, Func<Point, Point> viewportToData)
		{
			if (dataToViewport == null)
				throw new ArgumentNullException("dataToViewport");
			if (viewportToData == null)
				throw new ArgumentNullException("viewportToData");

			this.dataToViewport = dataToViewport;
			this.viewportToData = viewportToData;
		}

		private readonly Func<Point, Point> dataToViewport;
		/// <summary>
		/// Gets the data to viewport transform delegate.
		/// </summary>
		/// <value>The data to viewport func.</value>
		public Func<Point, Point> DataToViewportFunc
		{
			get { return dataToViewport; }
		}

		private readonly Func<Point, Point> viewportToData;
		/// <summary>
		/// Gets the viewport to data transform delegate.
		/// </summary>
		/// <value>The viewport to data func.</value>
		public Func<Point, Point> ViewportToDataFunc
		{
			get { return viewportToData; }
		}

		/// <summary>
		/// Transforms the point in data coordinates to viewport coordinates.
		/// </summary>
		/// <param name="pt">The point in data coordinates.</param>
		/// <returns></returns>
		public override Point DataToViewport(Point pt)
		{
			return dataToViewport(pt);
		}

		/// <summary>
		/// Transforms the point in viewport coordinates to data coordinates.
		/// </summary>
		/// <param name="pt">The point in viewport coordinates.</param>
		/// <returns></returns>
		public override Point ViewportToData(Point pt)
		{
			return viewportToData(pt);
		}
	}

	/// <summary>
	/// Contains default data transforms.
	/// </summary>
	public static class DataTransforms
	{
		private static readonly IdentityTransform identity = new IdentityTransform();
		/// <summary>
		/// Gets the default identity data transform.
		/// </summary>
		/// <value>The identity data transform.</value>
		public static IdentityTransform Identity
		{
			get
			{
				return identity;
			}
		}
	}
}