Normal at a Point Using Gradient

Normal at a Point Using Gradient

For:

$$F(x,y)=0$$

the normal direction at $$(x_1,y_1)$$ is along:

$$\left(F_x(x_1,y_1),F_y(x_1,y_1)\right)$$

Hence the normal can be written as:

$$\frac{x-x_1}{F_x(x_1,y_1)}=\frac{y-y_1}{F_y(x_1,y_1)}$$

when the denominators are non-zero.

Usage

- Used to obtain the normal directly from an implicit equation.