# GPU friendly compression of 2D signal

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Hey

I want to try shade particles by compute a "small" number of samples, e.g. 10, in VS. I only need to compute the intensity of the light, so essentially it's a single piece of data in 2 dimensions.

Now I want to compress this data, pass it on to PS and decompress it there (the particle is a single quad and the data is passed through interpolators). I will accept a certain amount of error as long as there are no hard edges, i.e. blurred.

The compressed data has to be small and compression/decompression fast. Does anyone know of a good way to do this?

Maybe I could do something fourier based but I'm not sure of what basis functions to use.

Thanks

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Combine the results of the samples using Spherical Harmonics and output that in the VS.

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If you want it only for 2D, SH is more than necessary, but i'm unsure what you try to do.

However, i use code below to calculate the curvature directions of a mesh. The problem here is that curvature direction is the same on opposite sides, e.g. vec2(0.7, 0.7) equals vec2(-0.7, -0.7) so i can not simply add vectors to get average curvature direction.

Instead i express directions with a sine wave that has two lobes pointing forwards and backwards, phase is direction and amplitude is intensity. Now adding two sine waves always results in another single sine wave and this way i get an accurate result from summing any number of samples. (Same principle is used in SH and Fourier Transform).

So, if this sounds interesting to you, you could do the same for lighting, but you would want the lobe pointing only in one direction and not the opposite as well, which means replacing factors of 2 with 1 and adjusting some other things as well.

But: For lighting i would just sum up vector wise and accept the error coming from that. Also note that my approach does not have a constant band like SH, so the same amount of light coming from right and left would result to zero - might be worth to add this for lighting.

	struct Sinusoid
{
float phase;
float amplitude;

Sinusoid ()
{
phase = 0;
amplitude = 0;
}

Sinusoid (const float phase, const float amplitude)
{
this->phase = phase;
this->amplitude = amplitude;
}

Sinusoid (const float *dir2D, const float amplitude)
{
this->amplitude = amplitude;
phase = PI + atan2 (dir2D[1], dir2D[0]) * 2.0f;
}

float Value (const float angle) const
{
return cos(angle * 2.0f + phase) * amplitude;
}

void Add (const Sinusoid &op)
{
float a = amplitude;
float b = op.amplitude;
float p = phase;
float q = op.phase;

phase = atan2(a*sin(p) + b*sin(q), a*cos(p) + b*cos(q));
float t = a*a + b*b + 2*a*b * cos(p-q);
amplitude = sqrt(max(0,t));
}

float PeakAngle () const
{
return phase * -0.5f;
}

float PeakValue () const
{
return Value(PeakAngle ());
}

void Direction (float *dir2D, const float angle) const
{
float scale = (amplitude + Value (angle)) * 0.5f;
dir2D[0] = sin(angle) * scale;
dir2D[1] = cos(angle) * scale;
}

};

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Thanks for the replies!

SH could be an option and it did cross my mind. It's 2D indeed. The domain when using SH is usually a sphere. In my case I want to use it on a quad. Would that have an impact? I understand that spherical coords can be regarded as a square. I'm just wondering if the domain has any impact & if there would be some other basis functions more suited for an actual quad.

@JoeJ your suggestion looks similar to a fourier series which also crossed my mind. The fact that sin/cos operations are expensive on GPUs made me a little less keen. The general idea of treating the problem as some sort of curve is good though. I could use something like a power function, that could be encoded in 4 params - uv intensity multiplier & uv exponent, given that I pass on the actual colour of 1 of the corners (on the other hand this approach would only be able to depict gradients).

I'm not 100% of how much detail I need to encode in the quad but preferably as much as possible for as little cost

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2 hours ago, 51mon said:

Thanks for the replies!

SH could be an option and it did cross my mind. It's 2D indeed. The domain when using SH is usually a sphere. In my case I want to use it on a quad. Would that have an impact? I understand that spherical coords can be regarded as a square. I'm just wondering if the domain has any impact & if there would be some other basis functions more suited for an actual quad.

You can warp fourier transform around a circle, and traet the circle as a square. You can then decice how much bands you need: 1st. Band is a constant term, 2nd can encode a lode towards a single directions, adding more bands means you can approximate multiple lights more accurate.

SH is similar: The smallest 2 band version has one number for the constant term (1st band), and a 3D vector (2nd band) for a directional bump. (This band tells you the dominant light direction if you gather many samples, similar to my curvature example.)

So for 2D you should need 3 numbers: Constant term, and a 2D direction (or angle and amplitude like i did, but direction avoids the trig functions when decoding).

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