vector-field-calculus

vector field visualizer, using love2d

Red channel represents relative divergence of the vector field
Blue channel represents relative curl of the vector field
Green channel represents relative magnitude of each vector

Example of functions:

    P(x,y) = ( y*cos(x/2 + 2.8), x*sin(y/2 + 2.8) )

   P(x,y) = ( (x*y + x*x), (x*y - y*y) )

    P(x,y)  =  ( x*sin(y/2),  y*cos(x/2) )

Making your own functions

To see your own functions in action, set the values for F and G at the top of main.lua as seen below. The operations used must be valid lua AND valid GLSL. (math module has been exported to global)

list of cool-ish functions:

where vector field P is defined as:

P(x,y) = ( F(x,y),  G(x,y) )

local F = '  sin(y) - cos(x*x)  ' 
local G = '  cos(x) - sin(y*y)  '

local F = '  cos(x*x*y) + y/5   '
local G = '  sin(y*y*x) + x/5   '

REALLY cool functions:

local F   =  ' x*y + x*x '
local G   =  ' x*y - y*y '


local F   =  ' x*sin(y/2) '
local G   =  ' y*cos(x/2) '

how this works:

Component functions are defined as a string in lua, and loaded into shader and as a lua function.

The divergence and curl is calculated naturally in the GPU using finite difference to simulate derivatives.

In the CPU, the divergence, curl, and magnitude of vectors are calculated with ~200,000 (x,y) positions over the given vector field. The variance for each property is then calculated from all the positions iterated, as is the mean value. Variance and mean values for each property for vectors over the field are sent to the GPU, and from there, the properties are used to offset the values that were calculated previously, and are reduced to a range of 0 -> 1.

TODO:

Lots to do.

Particle sym maybe?

Normalize vectors in vector field, so if you scale up to 100 it doesnt look weird