BeskrywingScalar field.png	English: Abstract example of a scalar field.
Datum	29 Julie 2012
Bron	Eie werk
Outeur	Lucas Vieira
Toestemming (Hergebruik van die lêer)	Public domainPublic domainfalsefalse Ek, die outeursreghouer van hierdie werk, stel dit hiermee in die publieke domein vry. Dit geld wêreldwyd. In sommige lande is dit dalk nie wettiglik moontlik nie. Indien so: Ek verleen aan enigiemand die reg om hierdie werk te gebruik vir enige doel, sonder voorwaardes, tensy sulke voorwaardes deur die wet vereis word.
Ander weergawes	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