SPLINES

Ejercicio4.cpp

#include <iostream>
#include <cmath>
#include <list>

using namespace std;

string colors[13] = {"blueviolet", "cadetblue", "coral", "cyan", "darkorchid", "darkred",
                    "goldenrod", "hotpink", "lime", "orange", "tomato", "darkgreen", "red"};

void NaturalCubicSpline(double x[], double y[], int N, double b[], double c[], double d[])
{
    double h[N];
    double alpha[N];
    double l[N];
    double u[N];
    double z[N];

    // Paso 1
    for (int i = 0; i <= N-1; i++)
        h[i] = x[i+1] - x[i];

    // Paso 2
    for (int i = 1; i <= N-1; i++)
        alpha[i] = ((3e0/h[i])*(y[i+1] - y[i])) - ((3e0/h[i-1])*(y[i] - y[i-1]));

    // Paso 3
    l[0] = 1; 
    u[0] = 0; 
    z[0] = 0;

    // Paso 4
    for (int i = 1; i <= N-1; i++)
    {
        l[i] = (2e0*(x[i+1] - x[i-1])) - (h[i-1]*u[i-1]);
        u[i] = h[i]/l[i];
        z[i] = (alpha[i] - (h[i-1]*z[i-1]))/l[i];

    }

    // Paso 5
    l[N] = 1;
    z[N] = 0; 
    c[N] = 0;

    for (int i = N-2; i >= 0; i--)
    {
        c[i] = z[i] - (u[i]*c[i+1]);
        b[i] = ((y[i+1] - y[i])/h[i]) - (h[i]*(c[i+1]+(2e0*c[i])))/3e0;
        d[i] = (c[i+1] - c[i])/(3e0*h[i]);
    }
}

int DIST_MAX;

int main()
{
    int N;
    cin >> N;
	double n = N;
	double* x = new double[N];
    double* y = new double[N];
    double* t = new double[N];
    double* dt = new double[N];
	double* bx = new double[N];
	double* cx = new double[N];
	double* dx = new double[N];
	double* by = new double[N];
	double* cy = new double[N];
	double* dy = new double[N];
	
	double j = 0e0;
    for (int i = 0; i < N; i++, j++)
    {
        cin >> x[i];
        cin >> y[i];
    }

    DIST_MAX = 0;
    dt[0] = 0;
    for (int i = 1; i < N; i++)
    {
        dt[i] = sqrt( pow(x[i]-x[i-1],2) + pow(y[i]-y[i-1],2) );
        DIST_MAX = DIST_MAX + dt[i];
    }
	
	for (int i = 0; i < N; i++)
	{
		t[i] = 0;
		for (int j = 1; j <= i; j++)
		{
			t[i] = t[i] + dt[j];
		}
		t[i] = t[i] / DIST_MAX;
	}
	
	NaturalCubicSpline(t, x, N, bx, cx, dx);
	NaturalCubicSpline(t, y, N, by, cy, dy);
    
    /* =====================================================
	 * Imprimir los Spline listos para graficar con SageMath
	 * */
	 
	char letter = 'a';
	for (int i = 0; i < N-1; i++)
	{
		cout << "WX" << letter << "(t) = "
		<< x[i] << " + "
		<< "(" << bx[i] << ")*(t-(" << t[i] << ")) + " 
		<< "(" << cx[i] << ")*(t-(" << t[i] << "))^2 + " 
		<< "(" << dx[i] << ")*(t-(" << t[i] << "))^3" << endl;

        cout << "WY" << letter << "(t) = "
		<< y[i] << " + "
		<< "(" << by[i] << ")*(t-(" << t[i] << ")) + " 
		<< "(" << cy[i] << ")*(t-(" << t[i] << "))^2 + " 
		<< "(" << dy[i] << ")*(t-(" << t[i] << "))^3" << endl;
		letter++;
	}
	cout << endl;
	
	letter = 'a';
	for (int i = 0; i < N-1; i++)
	{		
		cout << "W" << letter << " = parametric_plot("
		<< "(WX" << letter << "(t), " 
		<< "WY" << letter << "(t)), "
		<< "(t," << t[i] << ", " << t[i+1] << "), "
		<< "color='" << colors[i%13] << "', "
		<< "thickness=2" 
		<< ")" << endl;
		letter++;
	}
	cout << endl;
	
	letter = 'a';
	for (int i = 0; i < N-1; i++, letter++)
		cout << "W" << letter << " + ";
	
	cout << endl;
	
    
    return 0;
}

Ejercicio4Spline1.in

15
29 56
14 34
4 44
19 64
45 52
57 55
61 65
51 63
40 36
23 4
51 32
70 56
62 33
46 4
108 64

Ejercicio4Spline2.in

10
91 14
120 26
102 36
80 16
101 3
140 29
169 63
142 48
135 63
115 44

Ejercicio4Spline3.in

9
126 23
154 34
165 36
191 47
192 62
156 19
156 4
167 8
172 15