Примеры графиков параметрических функций в пространстве

\[ x = \cos(u)\cos(v) \\ y = \sin(u)\cos(v) \\ z = \sin(v) \\ u \in [{-\pi}; \pi], \quad v \in \Big[{-\frac{\pi}{2}}; \frac{\pi}{2}\Big] \]

\[ x = \cos(u)\big(\cos(v) + 3\big) \\ y = \sin(u)\big(\cos(v) + 3\big) \\ z = \sin(v) \\ u \in [{-\pi}; \pi], \quad v \in [{-\pi}; \pi] \]

\[ x = \cos(u)\big(\cos(v) + 3\big) \\ y = \sin(u)\big(\cos(v) + 3\big) \\ z = \sin(v) + u \\ u \in [{-2\pi}; 2\pi], \quad v \in [{-\pi}; \pi] \]

\[ x = u\cos(u)\big(\cos(v) + 1\big) \\ y = u\sin(u)\big(\cos(v) + 1\big) \\ z = u\sin(v) \\ u \in [0; 3\pi], \quad v \in [{-\pi}; \pi] \]

\[ x = u\cos(u)\big(\cos(v) + 1\big) \\ y = u\sin(u)\big(\cos(v) + 1\big) \\ z = u\sin(v) - \Big(\frac{u + 3}{8}\pi\Big)^2 - 20 \\ u \in [0; 8\pi], \quad v \in [{-\pi}; \pi] \]

\[ x = \cos(u)\cos(v) + 3\cos(u)\Big(1,5 + \sin\frac{1,5u}{2}\Big) \\ y = \sin(u)\cos(v) + 3\sin(u)\Big(1,5 + \sin\frac{1,5u}{2}\Big) \\ z = \sin(v) + 2\cos(1,5u) \\ u \in [{-2\pi}; 2\pi], \quad v \in [{-\pi}; \pi] \]

\[ x = \cos(u)\sin(v) \\ y = \sin(u)\sin(v) \\ z = \cos(v) + \lg\Big(\tan\Big(\frac{v}{2}\Big)\Big) + 0,2u - 4 \\ u \in [0; 4\pi], \quad v \in [0,001; 2] \]

\[ x = \bigg(1 + \frac{v}{2}\cos\Big(\frac{u}{2}\Big)\bigg)\cos(u) \\ y = \bigg(1 + \frac{v}{2}\cos\Big(\frac{u}{2}\Big)\bigg)\sin(u) \\ z = \frac{v}{2}\sin\Big(\frac{u}{2}\Big) \\ u \in [0; 2\pi], \quad v \in [{-1}; 1] \]