- 高度场(Height)
\[P(x,y,t) = (x,y,H(x,y,t))
\]
- 副切线(BiTangent)
\[\begin{aligned}
B(x,y,t)
&= \left( \frac{\partial x}{\partial x}, \frac{\partial y}{\partial x}, \frac{\partial H(x,y,t)}{\partial x} \right) \&= \left( 1, 0, \frac{\partial H(x,y,t)}{\partial x} \right) \\end{aligned}
\]
- 切线(Tangent)
\[\begin{aligned}
T(x,y,t)
&= \left( \frac{\partial x}{\partial y}, \frac{\partial y}{\partial y}, \frac{\partial H(x,y,t)}{\partial y} \right) \&= \left( 0, 1, \frac{\partial H(x,y,t)}{\partial y} \right) \\end{aligned}
\]
- 法线(Normal)
\[\begin{aligned}
N(x,y,t)
&= B(x,y,t) \times T(x,y,t) \&= \left( -\frac{\partial H(x,y,t)}{\partial x}, -\frac{\partial H(x,y,t)}{\partial y}, 1 \right)
\end{aligned}
\]
\[\begin{aligned}
\nabla h(\overrightarrow x, t)
&= \left(\frac{\partial h}{\partial x}, \frac{\partial h}{\partial y} \right) \&= \nabla \sum_{\overrightarrow k} \tilde h (\overrightarrow k, t) e^{j \overrightarrow k \cdot \overrightarrow x} \&= \sum_{\overrightarrow k} \tilde h (\overrightarrow k, t) \nabla e^{j \overrightarrow k \cdot \overrightarrow x} \&= \sum_{\overrightarrow k} \tilde h (\overrightarrow k, t) \nabla e^{j(k_x x + k_z z)} \&= \sum_{\overrightarrow k} \tilde h (\overrightarrow k, t) \left( e^{j(k_x x + k_z z) }jk_x, e^{j(k_x x + k_z z) }jk_z \right) \&= \sum_{\overrightarrow k} \tilde h (\overrightarrow k, t) j \overrightarrow k e^{j \overrightarrow k \cdot \overrightarrow x} \\end{aligned}
\]
