spirograph Namespace Reference

Functions
template<std::size_t N>
void	spirograph (std::array< std::pair< double, double >, N > *points, double l, double k, double rot)
void	test ()
	Test function to save resulting points to a CSV file. More...

Detailed Description

Functions related to spirograph.cpp

Function Documentation

spirograph()

template<std::size_t N>

void spirograph::spirograph	(	std::array< std::pair< double, double >, N > *	points,
		double	l,
		double	k,
		double	rot
	)

Generate spirograph curve into arrays x and y such that the i^th point in 2D is represented by (x[i],y[i]). The generating function is given by:

\begin{eqnarray*} x &=& R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right) \right]\\ y &=& R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\right) \right] \end{eqnarray*}

where

• \(R\) is the scaling parameter that we will consider \(=1\)
• \(l=\frac{\rho}{r}\) is the relative distance of marker from the centre of inner circle and \(0\le l\le1\)
• \(\rho\) is physical distance of marker from centre of inner circle
• \(r\) is the radius of inner circle
• \(k=\frac{r}{R}\) is the ratio of radius of inner circle to outer circle and \(0<k<1\)
• \(R\) is the radius of outer circle
• \(t\) is the angle of rotation of the point i.e., represents the time parameter

Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.

Template Parameters

N	number of points = size of array

Parameters

[out]	points	Array of 2D points represented as std::pair
	l	the relative distance of marker from the centre of inner circle and \(0\le l\le1\)
	k	the ratio of radius of inner circle to outer circle and \(0<k<1\)
	rot	the number of rotations to perform (can be fractional value)

                                      {
    double dt = rot * 2.f * M_PI / N;
    double R = 1.f;
    const double k1 = 1.f - k;
    int32_t step = 0;
 
#ifdef _OPENMP
#pragma omp for
#endif
    for (step = 0; step < N; step++) {
        double t = dt * step;
        double first = R * (k1 * std::cos(t) + l * k * std::cos(k1 * t / k));
        double second = R * (k1 * std::sin(t) - l * k * std::sin(k1 * t / k));
        points[0][step].first = first;
        points[0][step].second = second;
    }
}

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test()

void spirograph::test

(

)

Test function to save resulting points to a CSV file.

            {
    const size_t N = 500;
    double l = 0.3, k = 0.75, rot = 10.;
    std::stringstream fname;
    fname << std::setw(3) << "spirograph_" << l << "_" << k << "_" << rot
          << ".csv";
    std::ofstream fp(fname.str());
    if (!fp.is_open()) {
        perror(fname.str().c_str());
        exit(EXIT_FAILURE);
    }
 
    std::array<std::pair<double, double>, N> points;
 
    spirograph(&points, l, k, rot);
 
    for (size_t i = 0; i < N; i++) {
        fp << points[i].first << "," << points[i].first;
        if (i < N - 1) {
            fp << '\n';
        }
    }
 
    fp.close();
}

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