Lecture #10. Anti-aliasing

Computer graphics in Game development

Ivan Belyavtsev


Aliasing issue

Aliasing issue

Kotelnikov theorem (aka Nyquist–Shannon sampling theorem)

If a function \(x(t)\) contains no frequencies higher than \(B\) hertz, it is completely determined by giving its ordinates at a series of points spaced \(1/2B\) seconds apart. [1]

Super-sampling anti-aliasing

  1. Trace 4 uniform rays per pixel
  2. Blend resulted colors [2]

Temporal anti-aliasing for rasterization

  1. Render scene with subpixel jitter
  2. Reproject the pixel to world-space using depth buffer
  3. Use world space to find previous screen space position
  4. Offset previous position using motion vectors
  5. Use this to look up the previous color
  6. Blend resulting colors with the previous result[3]

Halton sequence

Halton sequence is a quasi-random number sequence which actively use for Monte-Carlo simulation. [4]

From: https://en.wikipedia.org/wiki/Halton_sequence#/media/File:Halton_sequence_2_3.svg

Halton sequence generator

float2 result{0.0f, 0.0f};
constexpr int base_x = 2;
int index = frame_id + 1;
float inv_base = 1.0f / base_x;
float fraction = inv_base;
while (index > 0)
    result.x += (index % base_x) * fraction;
    index /= base_x;
    fraction *= inv_base;
constexpr int base_y = 3;
index = frame_id + 1;
inv_base = 1.0f / base_y;
fraction = inv_base;
while (index > 0)
    result.y += (index % base_y) * fraction;
    index /= base_y;
    fraction *= inv_base;
return result - 0.5f;


Temporal anti-aliasing for ray tracing

  1. Find the next jitter value
  2. Cast camera rays with the jitter
  3. Blend the result image with the previous one


During accumulation you’ll find the intensity of the light is reducing proportional the number of accumulated frames. To compensate the energy lost lets apply a gamma-correction.



Lab: 2.06 Anti-aliasing

  1. Implement get_jitter method of raytracer class
  2. Add history resource in raytracer class
  3. Implement TAA in ray_generation method of raytracer class
  4. (Bonus) Adjust closest_hit_shader for Monte-Carlo light tracing


  1. Implement all ray tracing labs (Fix all TODO 2.01 - 2.06)
  2. Mark your final commit with raytracing tag
  3. Push your implementation and the raytracing tag
  4. Make sure that an instructor has access to your repo (djbelyak on github)
  5. Submit your implementation in Moodle with the repo URL and short description of your creative task

Due date: 21.10.2022


Kotel’nikov V.A. On the transmission capacity of ’ether’ and wire in electric communications // Usp. Fiz. Nauk. Uspekhi Fizicheskikh Nauk, 2006. Vol. 176, № 7. P. 762–770.
Shirley P. Ray tracing in one weekend. second. Amazon.com Services LLC, 2019. Vol. 1.
Karis B. High quality temporal anti-aliasing [Electronic resource]. 2014. URL: https://de45xmedrsdbp.cloudfront.net/Resources/files/TemporalAA_small-59732822.pdf.
Halton J.H. Algorithm 247: Radical-inverse quasi-random point sequence // Commun. ACM. New York, NY, USA: Association for Computing Machinery, 1964. Vol. 7, № 12. P. 701–702.
NVIDIA. NVIDIA DLSS [Electronic resource]. 2018. URL: https://developer.nvidia.com/dlss.
McKesson J.L. Linearity and gamma [Electronic resource] // Learning modern 3D graphics programming. 2015. URL: https://paroj.github.io/gltut/index.html.
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