diff --git a/15曲面的表示与逼近.tex b/15曲面的表示与逼近.tex index 46e259f..6a09cda 100644 --- a/15曲面的表示与逼近.tex +++ b/15曲面的表示与逼近.tex @@ -49,7 +49,7 @@ \[\bvec{n} \parallel \dfrac{\partial \bvec{r}}{\partial u}(u_0, v_0) \times \dfrac{\partial \bvec{r}}{\partial v}(u_0, v_0)\] 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 \[\begin{vmatrix} x - x_0 & y - y_0 & z - z_0\\