Splines of Order 3 tested and implemented. Added .m file to compare with...

Splines of Order 3 tested and implemented. Added .m file to compare with matlab (not a knob condition).

include/ITABase/Spline.h

@@ -52,6 +52,8 @@ namespace ITABase
 
 		//! Evaluate the piecewise polynomial at a given x value.
 		float Value(const float xValue) const;
+		//! Evaluates the piecewise polynomial at all given x values.
+		std::vector<float> Value(const std::vector<float>& vdValues) const;
 		//! Finds the index of Interval at a given x value
 		int IntervalIndex(const float xValue) const;
 		//! Return a piecewise polynomial containing the derivations of the polynomials of this one

src/ITABase/Spline.cpp

@@ -40,6 +40,14 @@ float CPiecewisePolynomial::Value(const float xValue) const
 		ITA_EXCEPT_INVALID_PARAMETER("currently only splines of order 3");
 }
 
+std::vector<float> ITABase::CPiecewisePolynomial::Value(const std::vector<float>& vdValues) const
+{
+	std::vector<float> result(vdValues.size());
+	for (int i = 0; i < vdValues.size(); i++)
+		result[i] = Value(vdValues[i]);
+	return result;
+}
+
 int ITABase::CPiecewisePolynomial::IntervalIndex(const float xValue) const
 {
 	if (xValue < vdBreakPoints[0] || xValue > vdBreakPoints[NumIntervals()])
@@ -160,7 +168,7 @@ CPiecewisePolynomial ITABase::Spline(const std::vector<float>& vdSupportingPoint
 	int iCoefficients = (iPoints - 1) * (iPolynomialOrder + 1);
 	std::vector<float> vdCoefficients(iCoefficients);
 	int k = 0;
-	for (int k = 0; k < iPolynomialOrder + 1;k++) {
+	for (int k = 0; k < iPoints - 1;k++) {
 		vdCoefficients[4*k] = vdA[k];
 		vdCoefficients[4*k + 1] = vdB[k];
 		vdCoefficients[4*k + 2] = vdC[k];

tests/SplineTest.cpp

@@ -24,19 +24,49 @@
 #include <iostream>
 
 //using namespace std;
+bool MyCompare(std::vector<float> a, std::vector<float> b, float epsilon) { 
+	if (a.size() != b.size()) return false;
+	bool temp = true;
+	for (int i = 0; i < a.size(); i++) {
+		if (std::abs(a[i] - b[i]) > epsilon) {
+			std::cout << "Value of index " << i << " differs over the tolerance of +-"<<epsilon << std::endl;
+			temp = false;
+		}
+	}
+	return temp;
+}
 
 int main(int iNumInArgs, char* pcInArgs[])
 {
+	/*beispiel von TM interaktiv
 	std::vector<float> vdSupportingPoints{1,7,12,15,19};
 	std::vector<float> vdDataPoints = {8,10,7,8,7};
-	//std::vector<float> vdSolution{ -0.01045, 0, 0.7091, 8, 0.0304, -1.88185, -0.4194, 10, -0.05005, 0.268014, -0.02026, 7, 0.01520, -0.182432, 0.2365, 8 };
 	int iPolynomialOrder = 3;
-	IW_ITA_BASE_SPLINE::ITABase::CPiecewisePolynomial myPoly = IW_ITA_BASE_SPLINE::ITABase::Spline(vdSupportingPoints,vdDataPoints,iPolynomialOrder);
-	std::cout << "Quick and dirty test: "<< myPoly.Value(5)<<" -hier soll grob 10 rauskommen;)";
-
-	/*for (int i=0; it < vdDataPoints.size(); i++) {
-		std::cout << vdSolution[i] - myPoly.get_Coefficient(i);
-	}
+	IW_ITA_BASE_SPLINE::ITABase::CPiecewisePolynomial myPoly1 = IW_ITA_BASE_SPLINE::ITABase::Spline(vdSupportingPoints,vdDataPoints,iPolynomialOrder);
+	if MyCompare(std::cout << "Quick and dirty test: "<< myPoly1.Value(5)<<" -hier soll grob 10 rauskommen;)";
 	*/
+	float epsilon = 0.1;
+	//Matlab spline. DataPoints sind aus randi
+	std::vector<float> vdSupportingPoints{ -10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
+	std::vector<float> vdDataPoints = { 13,14,2,14,10,2,5,9,15,15,3,15,11,4,0,-1,-5,-15,-11,-3,2 };
+	std::vector<float> vdX = { -10,  float(1.5),  float(-7.898),3, float(3.3), float(9.9),-2 };
+	std::vector<float> vdResult = { float(13.0000),  float(17.4325),    float(2.4282),    float(8.0000),    float(9.4143),   float(11.4819),    float(15.0000) };
+	int iPolynomialOrder = 3;
+	/*IW_ITA_BASE_SPLINE::ITABase::CPiecewisePolynomial myPoly1 = IW_ITA_BASE_SPLINE::ITABase::Spline(vdSupportingPoints, vdDataPoints, iPolynomialOrder);
+	std::cout << "MATLAB SPLINE TEST 1" << std::endl;
+	if (MyCompare(vdResult, myPoly1.Value(vdX),epsilon))
+		std::cout << "Test 1 bestanden" << std::endl;
+	*/
+	//Test 2
+
+	std::vector<float> vdDataPoints2{ 77,    80,    19,    49,    45,    65,    71,    76,    28,    68,    66,    17,12,    50,    96,    35,    59,    23,    76,    26,    51 };
+	std::vector<float> vdResult2 = { float(77.0000),    float(7.9485),   float(18.7512),   float(50.0000),   float(70.7647),   float(36.3051),   float(28.0000) };
+	iPolynomialOrder = 3;
+	IW_ITA_BASE_SPLINE::ITABase::CPiecewisePolynomial myPoly2 = IW_ITA_BASE_SPLINE::ITABase::Spline(vdSupportingPoints, vdDataPoints2, iPolynomialOrder);
+	std::cout << "MATLAB SPLINE TEST 2" << std::endl;
+	if (MyCompare(vdResult2, myPoly2.Value(vdX),epsilon))
+		std::cout << "Test 2 bestanden" << std::endl;
+	
+	
 	return 0;
 }

tests/spline_compare.m

+%% Create Matlab and ITA::BASE splines
+X = [-10:1:10];
+Y = [77 80 19 49 45 65 71 76 28 68 66 17 12 50 96 35 59 23 76 26 51]; %randi(100,1,21)
+Coeffs = [-24.4868088000000 0 27.4868088000000 77;...%Copy & Paste from the resulting ITA::BASE Spline 
+    58.4340477000000 -73.4604263000000 -45.9736176000000 80;...
+    -54.2493782000000 101.841713000000 -17.5923386000000 19;...
+    33.5634651000000 -60.9064217000000 23.3429565000000 49;...
+    -22.0044861000000 39.7839775000000 2.22050858000000 45;...
+    16.4544754000000 -26.2294807000000 15.7750053000000 65;...
+    -30.7892181747901 23.0766833120257 12.6794720000000 71;...
+    54.7927242498993 -69.2909712123447 -33.5017530375546 76;...
+    -47.3816788248071 95.0872015373532 -7.70552271254611 28;...
+    4.73399104932904 -47.0578349370681 40.3238438877390 68;...
+    23.4457146274910 -32.8558617890810 -39.5898528384100 66;...
+    -7.51684955929288 37.4812820933919 -34.9644325340990 17;...
+    5.62168360968059 14.9307334155133 17.4475829748062 12;...
+    -49.9698848794294 31.7957842445550 64.1741006348744 50;...
+    79.2578559080372 -118.113870393733 -22.1439855143039 96;...
+    -75.0615387527194 119.659697330378 -20.5981585776589 35;...
+    77.5513382000000 -106.515846000000 -7.03549194000000 59;...
+    -85.7249985000000 126.138168000000 12.5868301000000 23;...
+    73.3486862000000 -131.036835000000 7.68815231000000 76;...
+    -29.6697369000000 89.0092087000000 -34.3394737000000 26];
+myPoly = mkpp(X,Coeffs);
+%% Plot
+plot(X,Y,'o',xx,spline(X,Y,xx));
+hold on
+grid on
+title 'Splines: Matlab vs. ITA'
+plot(xx,ppval(myPoly2,xx));
+plot(xx,spline(X,Y,xx)-ppval(myPoly2,xx));
+legend('Data','Matlab','ITA','Diff');