For \(k = 1, 2, 3, ..., 9830\), the coordinates and radius of the \(k\)-th point are: \begin{split} X(k)=~& (\sin(\frac{\pi k}{20000}))^{12} * ( \frac12 (\cos(\frac{31 \pi k}{10000}))^{16} \sin(\frac{6 \pi k}{10000}) + \frac16 (\sin(\frac{31 \pi k}{10000}))^{20} ) \\ & + \frac{3 k}{20000} + (\cos(\frac{31 \pi k}{10000}))^6 \sin(\frac\pi2 (\frac{k - 10000}{10000})^7 - \frac\pi5) \\ Y(k)=~& \frac{-9}4 (\cos(\frac{31 \pi k}{10000}))^6 \cos(\frac\pi2 (\frac{k - 10000}{10000})^7 - \frac\pi5) (\frac23 + (sin(\frac{\pi k}{20000}) sin(\frac{3 \pi k}{20000}))^6) \\ & + \frac34 (\cos(3 \pi \frac{k - 10000}{100000}))^{10} (\cos(9 \pi \frac{k - 10000}{100000}))^{10} (cos(36 \pi \frac{k - 10000}{100000}))^{14} \\ & + \frac7{10} (\frac{k - 10000}{10000})^2 \\ R(k) =~& (\sin(\frac{\pi k}{20000}))^{10} (\frac14 (\cos (\frac{31 \pi k}{10000} + \frac{25 \pi}{32}))^ {20} + \frac1{20} (\cos(\frac{31 \pi k}{10000}))^2) \\ & + \frac1{30} (\frac32 - (\cos(\frac{62 \pi k}{10000}))^2) \end{split}