public static void CentripetalMethod_createSplineByInterpolation(
int degree, Vector[] interpolationPoints, ref BCurve result)
{
// NOTE: result is equal to null(ArgumentNullException)
// Calculate interpolation parameters:
double[] interpolationParameters = null;
CentripetalMethod_calculateInterpolationParameters(interpolationPoints, ref interpolationParameters);
// Calculate knots:
double[] knots = null;
CentripetalMethod_calculateKnots(degree, interpolationParameters, ref knots);
// Create basis function:
var basis = new BasisFunction(knots);
// Number of control points:
var nControlPoints = interpolationPoints.Length;
// Create set of linearly independent equations:
var matrixElements = new double[nControlPoints][];
for (var i = 0; i < nControlPoints; i++)
{
matrixElements[i] = new double[nControlPoints];
for (var j = 0; j < nControlPoints; j++)
matrixElements[i][j] = basis.Evaluate(j, degree, interpolationParameters[i]);
}
// Create matrix:
var matrix = new BGeomMatrix(matrixElements);
var dimension = interpolationPoints[0].VectorDimension();
// Solve using Gaussian Elimination:
var rhs = new Vector(nControlPoints);
var controlPoints = new Vector[nControlPoints];
for (var i = 0; i < dimension; i++)
{
// Fill the elements of the rhs:
for (var j = 0; j < nControlPoints; j++)
rhs.Elements[j] = interpolationPoints[j].Elements[i];
double[] gaussResult = null;
LinearAlgebra.GaussianElimination(matrix, rhs, ref gaussResult);
// Fill the control points
for (var k = 0; k < nControlPoints; k++)
{
if ( i == 0)
controlPoints[k] = new Vector(dimension);
controlPoints[k].Elements[i] = gaussResult[k];
}
}
// Create spline:
result = new BCurve(degree, controlPoints, basis);
}
private void button1_Click(object sender, EventArgs e)
{
var knots = new List<double>
{
0.0,
0.0,
0.0,
1.0,
2.0,
3.0,
4.0,
4.0,
5.0,
5.0,
5.0
};
var controlPoints = new List<Vector>
{
new Vector(new[] {0.0, 0.0}),
new Vector(new[] {1.0, 1.0}),
new Vector(new[] {2.0, 0.0}),
new Vector(new[] {3.0, -1.0}),
new Vector(new[] {4.0, 0.0}),
new Vector(new[] {5.0, 1.0}),
new Vector(new[] {6.0, 0.0}),
new Vector(new[] {7.0, -1.0})
};
var basis = new BasisFunction(knots);
var curve = new BCurve(2, controlPoints, basis);
_sessionCurve = curve;
curve.Evaluate(2.5);
// Testing gaussian elimination:
var matrixElements = new List<List<double>>
{
new List<double>
{
1,
-3,
1
},
new List<double>
{
2,
-8,
8
},
new List<double>
{
-6,
3,
-15
}
};
var rhs = new Vector(new double[] { 4, -2, 9 });
var matrix = new BGeomMatrix(matrixElements);
double[] results = null;
LinearAlgebra.GaussianElimination(matrix, rhs, ref results);
// make straight line with points:
var straightLine0 = new List<Vector>();
for (var i = 0; i < 5; i++)
straightLine0.Add(new Vector(new[] { i, i % 2.0 }));
// Interpolate straight line
var straightLine1 = new BCurve();
GeomUtils.CentripetalMethod_createSplineByInterpolation(3, straightLine0.ToArray(), ref straightLine1);
_sessionCurve = straightLine1;
}
