DescreeptionScalar field.png	English: Abstract example of a scalar field.
Date	29 Julie 2012
Soorce	Ain wirk
Author	Lucas Vieira
Permission (Reuisin this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions	Animation of a line integral over this field 3D version

The field

The field is a superposition of several 2D gaussian surfaces.

Define ${\displaystyle {\mbox{G}}(x,y)=e^{-(x^{2}+y^{2})}}$

Then, the field f used is given by the following function:

${\displaystyle f(x,y)=-{\tfrac {4}{10}}S(x,y)+{\tfrac {3}{2}}}$

Where S is the sum of the following:

${\displaystyle S(x,y)={\begin{aligned}\\{\mbox{G}}(2x,2y)\\-{\tfrac {8}{10}}{\mbox{G}}(2x+1.25,2y+1.25)\\+{\tfrac {1}{2}}{\mbox{G}}(2x-1.25,4y+1.25)\\-{\tfrac {1}{2}}{\mbox{G}}(3x-1.25,3y-1.25)\\+{\tfrac {7}{20}}{\mbox{G}}(2x+1.25,2y-1.25)\\-{\tfrac {1}{2}}{\mbox{G}}(x-1.25,3y+1.5)\\+{\tfrac {6}{5}}{\mbox{G}}(x+1.25,3y-1.85)\end{aligned}}}$

Evaluated from -1 to 1 in both x and y directions.

3D version