Diary of a Path Tracer – Texture Sampling And Bump Mapping

Index: https://cranberryking.com/2020/08/22/diary-of-a-path-tracer-the-beginning/

Intro

In our last post, we looked at the various utilities used by cranberray. in this post we’re going to return to the world of graphics and take a look at cranberray’s texture sampling and bump mapping strategy.

Texture Sampling

Cranberray takes inspiration from graphics APIs and splits texture sampling into 2 parts. The sampler and the texture.

The sampler in cranberray stores information such as sample type (nearest, bilinear) and some other useful flags such as gamma_to_linear to convert our textures stored in sRGBA to linear RGBA. Textures store pixel data and simply support sampling a single point in them.

Sampling a texture in cranberray is quite simple, you take your UV coordinates and convert them to an array index.

static cv4 sample_r_u8(cv2 uv, uint8_t* cran_restrict image, uint32_t width, uint32_t height, uint32_t offsetX, uint32_t offsetY)
{
	float readY = uv.y * (float)height;
	float readX = uv.x * (float)width;

	uint32_t y = (uint32_t)floorf(readY) + offsetY;
	y = y >= height ? height - 1 : y;
	uint32_t x = (uint32_t)floorf(readX) + offsetX;
	x = x >= width ? width - 1 : x;
	uint32_t readIndex = y * width + x;

	float f = (float)image[readIndex] / 255.0f;
	return (cv4) { f, f, f, f };
}

Once your can retrieve distinct pixel values, you can either sample nearest of use bilinear interpolation between 4 different samples.

if (sampleType == sample_type_nearest)
{
	color = samplers[texture->format](uv, texture->data, texture->width, texture->height, 0, 0);
}
else if (sampleType == sample_type_bilinear)
{
	cv4 s00 = samplers[texture->format](uv, texture->data, texture->width, texture->height, 0, 0);
	cv4 s01 = samplers[texture->format](uv, texture->data, texture->width, texture->height, 0, 1);
	cv4 s10 = samplers[texture->format](uv, texture->data, texture->width, texture->height, 1, 0);
	cv4 s11 = samplers[texture->format](uv, texture->data, texture->width, texture->height, 1, 1);

	float wf = cf_frac((float)texture->width * uv.x);
	float hf = cf_frac((float)texture->height * uv.y);
	wf = wf < 0.0f ? 1.0f + wf : wf;
	hf = hf < 0.0f ? 1.0f + hf : hf;
	color = (cv4)
	{
		cf_bilinear(s00.x, s01.x, s10.x, s11.x, wf, hf),
		cf_bilinear(s00.y, s01.y, s10.y, s11.y, wf, hf),
		cf_bilinear(s00.z, s01.z, s10.z, s11.z, wf, hf),
		cf_bilinear(s00.w, s01.w, s10.w, s11.w, wf, hf)
	};
}

And that’s pretty much it for how cranberray samples its textures!

Bump Mapping

Bump mapping is a bit more fun than texture sampling.

A very important and interesting point about the tangent frame is that it is the set of vectors that represent the basis for our texture coordinates. Originally, I believed that any tangent and bitangent could be selected as long as they were orthonormal. In the context of bump mapping, this is not correct. We actually want to select our tangent and bitangent so as to have them represent the flow of the U and V coordinates in space. ([2] has an excellent visualization for this)

To construct your tangent and bitangent, you can imagine that your triangle edge is a construction of the tangent and bitangent vectors.

Once you know you can construct your edges from some contribution of the tangent and bitangent, you can solve for your tangent and bitangent vectors with a little bit of algebra.

// e0=du0T+dv0B (1)
// e1=du1T+dv1B (2)
// solve for B
// (e0-du0T)/dv0
// plug into (2)
// e1=du1T+dv1(e0-du0T)/dv0
// solve for T
// e1=du1dv0T/dv0+dv1e0/dv0-dv1du0T/dv0
// dv0e1=du1dv0T+dv1e0-dv1du0T
// dv0e1-dv1e0=du1dv0T-dv1du0T
// dv0e1-dv1e0=T(du1dv0-dv1du0)
// T = (dv0e1-dv1e0)/(dv0du1-dv1du0)

Calculating tangent frames caused a surprising amount of issues with degenerate triangles and NaNs. Be careful here.

And now that you have your tangent and bitangent vectors, you can “bump” them using the partial derivatives of a height map. To bump your tangent and bitangent vectors, you add a scaled normal to the tangent and bitangent vectors and recalculate the normal using the cross product of said vectors.

cv3 normal = cv3_normalize(inputs.normal);
{
	cv4 partialDerivative = sampler_sample(&scene->textureStore, microfacetData.bumpSampler, microfacetData.bumpTexture, inputs.uv);
	normal = cv3_cross(cv3_add(inputs.tangent, cv3_mulf(normal, partialDerivative.x)), cv3_add(inputs.bitangent, cv3_mulf(normal, partialDerivative.y)));
	normal = cv3_normalize(normal);
	cran_assert(cv3_dot(normal, inputs.normal) >= 0.0f);
}

Conclusion

And that’s it! This part of cranberray is quite simple but was fun to write!. Next time we’ll look at the iterative path tracing of cranberray. Until then, happy coding!

Future Work

I would like to add a few things to the texture sampling system as it’s quite barebones. Things such as mip map selection, trilinear interpolation as well as add a texture caching system. (Currently cranberray keeps all textures resident in memory)

References

[1] http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf

[2] https://learnopengl.com/Advanced-Lighting/Normal-Mapping

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