using System;

using MathNet.Spatial.Euclidean;

using MathNet.Spatial.Units;

using MathNet.Numerics.LinearAlgebra;

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// --- UTILITY FUNCTIONS --- (maybe mathnet also has these somewhere. I am not that experienced with it)

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// Creates a matrix which rotates the first axis of a coordinate system to v

Matrix<double> RotateTo(Vector2D v) => Matrix2D.Create(v.X, v.Y, -v.Y, v.X);

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// Creates a matrix which Non-uniformly scales a coordinate system (different scale for x and y axis) (it is just a diagonal matrix)

Matrix<double> Scale(double xScale, double yScale) => Matrix<double>.Build.DenseOfDiagonalArray(2, 2, new [] {xScale, yScale});

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// --- SOME TEST INPUT ---

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// We have a bearing

var bearing = Angle.FromDegrees(0);

Vector2D vBearing = Vector2D.FromPolar(1, bearing); // vBearing must be normalized for this to work. Not a problem we we create it from an angle. If we got the bearing as a velocity vector we would have to call Normalize

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// We have a wind vector

var windDir = Angle.FromDegrees(0);

var windSpeed = 20;

Vector2D wind = Vector2D.FromPolar(windSpeed, windDir);

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// --- CALCULATION STARTS HERE ---

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// We can check if the wind is head or tail wind

bool isTailWind = vBearing.DotProduct(wind) > 0; // dotproduct is proportional to cosine of angle between vectors. I am not using this value in this example, but I hope it is clear how the input to Scale below could be chosen based on the result here.

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var newWind = wind

    .TransformBy(RotateTo(vBearing)) // Transform the wind into a coordinate system relative to the bearing

    .TransformBy(Scale(1.05, 1))  // Scale the first axis (the one perpendicular to the bearing) by 1.05

    .TransformBy(RotateTo(vBearing).Inverse()); // Transform the wind back to the global coordinate system. (using a general Inverse function here is a bit of a waste, since we know what the inverse is by construction. But this code reads nicely and the matrix is very small anyway)

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Console.WriteLine(newWind);

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