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: - \f{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] \f}
- where
-
- \f$R\f$ is the scaling parameter that we will consider \f$=1\f$
-
- \f$l=\frac{\rho}{r}\f$ is the relative distance of marker from the centre
- of inner circle and \f$0\le l\le1\f$
-
- \f$\rho\f$ is physical distance of marker from centre of inner circle
-
- \f$r\f$ is the radius of inner circle
-
- \f$k=\frac{r}{R}\f$ is the ratio of radius of inner circle to outer circle
- and \f$0<k<1\f$
-
- \f$R\f$ is the radius of outer circle
-
- \f$t\f$ is the angle of rotation of the point i.e., represents the time
- parameter
- Since we are considering ratios, the actual values of \f$r\f$ and
- \f$R\f$ are immaterial.
- @param [out] x output array containing absicca of points (must be
- pre-allocated)
- @param [out] y output array containing ordinates of points (must be
- pre-allocated)
- @param l the relative distance of marker from the centre of
- inner circle and \f$0\le l\le1\f$
- @param k the ratio of radius of inner circle to outer circle and
- \f$0<k<1\f$
- @param N number of sample points along the trajectory (higher = better
- resolution but consumes more time and memory)
- @param num_rot the number of rotations to perform (can be fractional value) */