### AFFINE FUNCTION IN 2D + 3D

**Ax+By+C** : an affine function of 2 variables.

**Ax+By+Cz+D** : an affine function of 3 variables.
The function in 2D:
Ax+By+C

If c = 0, then the function level line Ax+By is equal constant.

**Ax+By = 0
**

[A,B].[x,y] = 0

[A,B] is perpendicular to [x,y]

The level line is a curve where a function has a single value.

The "curve" with Ax+By=0 is the line through the origional point and perpendicular to [A,b]

**Ax+By = C
**

Axo+Byo = C

(x-xo)+(y-yo) = 0

This means all the level lines of Ax+By are all perpendicular to [A,B],

the distance from the line Ax+By=0 where C>0 is C/(square root of A^2 + B^2).

**The way to calculate the distance:**

if we have function Ax+By=C1 and Ax+By=C2

the signed distance between them =** (C1-C2)/(square root of A^2+B^2)**

**Wave in Crests:**

If time = 0, then the wave height = **Acos(Ax+By+Cz)**

where (a,b,c) is related to lambda,the wave length vector.

The wave height and lambda are prependicular to each other.