Quadric Surfaces - 二次曲面

椭球面 / Ellipsoid

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1\quad (a, b, c>0)

单叶双曲面 / Hyperboloid of one sheet

轴沿 z：
\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1

双叶双曲面 / Hyperboloid of two sheets

轴沿 z：
-\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1

椭圆抛物面 / Elliptic paraboloid

开口沿 z：
\frac{z}{c}=\frac{x^2}{a^2}+\frac{y^2}{b^2}

双曲抛物面（马鞍面）/ Hyperbolic paraboloid (saddle)

\frac{z}{c}=\frac{x^2}{a^2}-\frac{y^2}{b^2}

椭圆锥面（双圆锥）/ Elliptic cone (double cone)

\frac{z^2}{c^2}=\frac{x^2}{a^2}+\frac{y^2}{b^2}