/// <summary>
/// Construct a linear spline using a set of input points.
/// <example>For example:
/// <code>
/// SortedList<double, double> splinePoints = new SortedList<double, double>();
/// splinePoints.Add(0.0f, 1.1f);
/// splinePoints.Add(0.3f, 0.4f);
/// splinePoints.Add(1.0f, 2.0f);
/// LinearSpline1D spline = new LinearSpline1D(splinePoints);
/// </code>
/// creates a linear spline that passes through three points: (0.0, 1.1), (0.3, 0.4) and (1.0, 2.0).
/// </example>
/// </summary>
/// <param name="points">A list of points that is sorted by the x-coordinate. This collection is copied.</param>
/// <exception cref="ArgumentException">
/// A linear spline must have at least two points to be properly defined. If <c>points</c> contains less than
/// two points, the spline is undefined, so an <c>ArgumentException</c> is thrown.
/// </exception>
public LinearSpline1D(SortedList <double, double> points)
{
if (points.Count < 2)
{
if (points.Count == 1)
{
throw new ArgumentException("List contains only a single point. A spline must have at least two points.", nameof(points));
}
else
{
throw new ArgumentException("List is empty. A spline must have at least two points.", nameof(points));
}
}
Points = new SortedPointsList <double>(points);
DebugUtil.AssertAllFinite(Points, nameof(Points));
// Calculate the coefficients for each segment of the spline:
_parameters = new double[points.Count];
// Recursively find the _parameters:
for (int i = 1; i < points.Count; i++)
{
double dx = Points.Key[i] - Points.Key[i - 1];
double dy = Points.Value[i] - Points.Value[i - 1];
_parameters[i] = dy / dx;
}
DebugUtil.AssertAllFinite(_parameters, nameof(_parameters));
}
/// <summary>
/// Construct a linear spline using a set of input points.
/// <example>For example:
/// <code>
/// SortedList{double, double} splinePoints = new SortedList{double, double}();
/// splinePoints.Add(0.0f, 1.1f);
/// splinePoints.Add(0.3f, 0.4f);
/// splinePoints.Add(1.0f, 2.0f);
/// LinearSpline1D spline = new LinearSpline1D(splinePoints);
/// </code>
/// creates a linear spline that passes through three points: (0.0, 1.1), (0.3, 0.4) and (1.0, 2.0).
/// </example>
/// </summary>
/// <param name="points">A list of points that is sorted by the x-coordinate. This collection is copied.</param>
/// <exception cref="ArgumentException">
/// A linear spline must have at least two points to be properly defined. If <c>points</c> contains less than
/// two points, the spline is undefined, so an <c>ArgumentException</c> is thrown.
/// </exception>
public LinearSpline1D(SortedList <double, double> points)
{
if (points.Count < 2)
{
if (points.Count == 1)
{
throw new ArgumentException("List contains only a single point. A spline must have at least two points.", nameof(points));
}
else
{
throw new ArgumentException("List is empty. A spline must have at least two points.", nameof(points));
}
}
Points = new SortedPointsList <double>(points);
DebugUtil.AssertAllFinite(Points, nameof(Points));
}
/// <summary>
/// Construct a quadratic spline using a set of input points.
/// <example>For example:
/// <code>
/// SortedList<double, double> splinePoints = new SortedList<double, double>();
/// splinePoints.Add(0.0f, 1.1f);
/// splinePoints.Add(0.3f, 0.4f);
/// splinePoints.Add(1.0f, 2.0f);
/// QuadraticSpline1D spline = new QuadraticSpline1D(splinePoints);
/// </code>
/// creates a quadratic spline that passes through three points: (0.0, 1.1), (0.3, 0.4) and (1.0, 2.0).
/// </example>
/// </summary>
/// <param name="points">A list of points that is sorted by the x-coordinate. This collection is copied.</param>
/// <exception cref="ArgumentException">
/// A spline must have at least two points to be properly defined. If <c>points</c> contains less than two
/// points, the spline is undefined, so an <c>ArgumentException</c> is thrown.
/// </exception>
public QuadraticSpline1D(SortedList <double, double> points)
{
if (points.Count < 2)
{
if (points.Count == 1)
{
throw new ArgumentException("List contains only a single point. A spline must have at least two points.", nameof(points));
}
else
{
throw new ArgumentException("List is empty. A spline must have at least two points.", nameof(points));
}
}
Points = new SortedPointsList <double>(points);
// Calculate the coefficients of the spline:
_parameters = new double[points.Count];
// Find the first segment parameter, which will be a straight line:
{
double dx = Points.Key[1] - Points.Key[0];
double dy = Points.Value[1] - Points.Value[0];
_parameters[0] = dy / dx;
}
// Recursively find the other _parameters:
for (int i = 1; i < points.Count; i++)
{
double dx = Points.Key[i] - Points.Key[i - 1];
double dy = Points.Value[i] - Points.Value[i - 1];
_parameters[i] = -_parameters[i - 1] + 2.0f * dy / dx;
}
}
/// <summary>
/// Construct a cubic spline using a set of input points.
/// <example>For example:
/// <code>
/// SortedList<float, float> splinePoints = new SortedList<float, float>();
/// splinePoints.Add(0.0f, 1.1f);
/// splinePoints.Add(0.3f, 0.4f);
/// splinePoints.Add(1.0f, 2.0f);
/// CubicSpline1D spline = new CubicSpline1D(splinePoints);
/// </code>
/// creates a cubic spline that passes through three points: (0.0, 1.1), (0.3, 0.4) and (1.0, 2.0).
/// </example>
/// </summary>
/// <param name="points">A list of points that is sorted by the x-coordinate. This collection is copied.</param>
/// <exception cref="ArgumentException">
/// A cubic spline must have at least two points to be properly defined. If <c>points</c> contains less than
/// two points, the spline is undefined, so an <c>ArgumentException</c> is thrown.
/// </exception>
public CubicSpline1D(SortedList<float, float> points)
{
if (points.Count < 2)
{
if (points.Count == 1)
{
throw new ArgumentException("List contains only a single point. A spline must have at least two points.", "points");
}
else
{
throw new ArgumentException("List is empty. A spline must have at least two points.", "points");
}
}
Points = new SortedPointsList<float>(points);
// Calculate the coefficients of the spline:
float[] a = new float[points.Count];
float[] b = new float[points.Count];
float[] c = new float[points.Count];
float[] d = new float[points.Count];
// Set up the boundary condition for a natural spline:
{
float x2 = 1.0f/(Points.Key[1] - Points.Key[0]);
float y2 = Points.Value[1] - Points.Value[0];
a[0] = 0.0f;
b[0] = 2.0f*x2;
c[0] = x2;
d[0] = 3.0f*(y2*x2*x2);
}
// Set up the tridiagonal matrix linear system:
for (int i = 1; i < points.Count-1; i++)
{
float x1 = 1.0f/(Points.Key[i] - Points.Key[i-1]);
float x2 = 1.0f/(Points.Key[i+1] - Points.Key[i]);
float y1 = Points.Value[i] - Points.Value[i-1];
float y2 = Points.Value[i+1] - Points.Value[i];
a[i] = x1;
b[i] = 2.0f*(x1 + x2);
c[i] = x2;
d[i] = 3.0f*(y1*x1*x1 + y2*x2*x2);
}
// Set up the boundary condition for a natural spline:
{
float x1 = 1.0f/(Points.Key[points.Count-1] - Points.Key[points.Count-2]);
float y1 = (Points.Value[points.Count-1] - Points.Value[points.Count-2]);
a[points.Count-1] = x1;
b[points.Count-1] = 2.0f*x1;
c[points.Count-1] = 0.0f;
d[points.Count-1] = 3.0f*(y1*x1*x1);
}
// Solve the linear system using the Thomas algorithm:
this.parameters = ThomasAlgorithm(a, b, c, d);
}