02
Jul
09

### Borg 2D Polar Mapping

This is the Borg equation with polar coordinates.

Here’s the CIFilter Kernel code for cartesian and polar versions (I’ll let you work out sensible ranges for the various controls):

```/*
Borg equation in cartesian and polar varieties.
From 3D surface equation found here:
http://local.wasp.uwa.edu.au/~pbourke/geometry/borg/

Quartz Composer setup
toneburst 2009
https://machinesdontcare.wordpress.com
*/

kernel vec4 tb_borg_cartesian(sampler Image, vec2 NormFactor, float Z, vec2 Scale, vec2 Offset)
{
// Normalised coords of current pixel
vec2 xyNorm = samplerCoord(Image) * NormFactor;
xyNorm -= 0.5;
xyNorm *= Scale;
xyNorm += Offset;

float borg = sin(xyNorm.x * xyNorm.y) + sin(xyNorm.y * Z) + sin(Z * xyNorm.x);

// Sample image and return pixel
return vec4(vec3(1.0), borg);
}

kernel vec4 tb_borg_polar(sampler Image, vec2 NormFactor, float Phi, vec2 Scale, vec2 Offset)
{
// Normalised coords of current pixel
vec2 xyNorm = samplerCoord(Image) * NormFactor;
xyNorm -= 0.5;
xyNorm = abs(xyNorm);

// Cartesian to polar
vec2 polar;
polar[0] = length(xyNorm);				// R
polar[1] = atan(xyNorm.x/xyNorm.y);		// Theta

polar *= Scale;
polar += Offset;

float borg = sin(polar[0] * polar[1]) + sin(polar[1] * Phi) + sin(Phi * polar[0]);

// Sample image and return pixel
return vec4(vec3(1.0), borg);
}```

UPDATE:

#### 2 Responses to “Borg 2D Polar Mapping”

1. 1 Daniel
September 22, 2009 at 10:41 am

Nice.
I encountered a similar looking Moiré glitch recently:

I’d be happy to share the processing file if you are interested.

2. 2 toneburst
September 28, 2009 at 11:28 am

HI Daniel,

good to hear from you. The moire effect was kinda incidental, but I quite like it, now.
I’m afraid I don’t use processing, or have any experience of Java (though people keep telling me I should try it).

Good to have the URL of your Flickr collection. There’s some amazing stuff there! I especially like the Orthogonal Systems renderings.

Incidentally, did you happen to see any of the realtime volume renderings of the Borg and other surfaces I did?

https://machinesdontcare.wordpress.com/2009/07/06/more-raycaster-screenshots/
and moving examples:

I’m sure they’re not very useful as scientific visualisations, but they look quite nice… 🙂

a|x