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改错。

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unlockable
2023-05-04 16:57:28 +08:00
parent 0aa4306eb5
commit 672b1c9659
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15曲面的表示与逼近.tex
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@@ -49,7 +49,7 @@
\[\bvec{n} \parallel \dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0)\] \[\bvec{n} \parallel \dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0)\]
进一步假设$\dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0) \neq \bvec{0}$即两向量不共线，则可取$S$在$P$点法向$\bvec{n} = \dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0)$，得到切平面方程 进一步假设$\dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0) \neq \bvec{0}$即两向量不共线，则可取$S$在$P$点法向$\bvec{n} = \dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0)$，得到切平面方程
\[\brak{\dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0), \bvec{r} - \bvec{r}_0}\] \[\brak{\dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0), \bvec{r} - \bvec{r}_0} = 0\]
利用行列式也可以得到切平面方程 利用行列式也可以得到切平面方程
\[\begin{vmatrix} \[\begin{vmatrix}
x - x_0 & y - y_0 & z - z_0\\ x - x_0 & y - y_0 & z - z_0\\