Lecture 10: Anti-aliasing

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]

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;

[5]

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

Gamma-correction

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.

\[{GammaRGB}={LinearRGB}^{\frac{1}{\gamma}}\]

[6]

Off topic

public static Matrix4x4 GetJitteredPerspectiveProjectionMatrix(Camera camera, Vector2 offset)
{
    float near = camera.nearClipPlane;
    float far = camera.farClipPlane;
    float vertical = Mathf.Tan(0.5f * Mathf.Deg2Rad * camera.fieldOfView) * near;
    float horizontal = vertical * camera.aspect
    offset.x *= horizontal / (0.5f * camera.pixelWidth);
    offset.y *= vertical / (0.5f * camera.pixelHeight);
    var matrix = camera.projectionMatrix;
    matrix[0, 2] += offset.x / horizontal;
    matrix[1, 2] += offset.y / vertical;
    return matrix;
}

Lab: 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

Homework

1. Implement all ray tracing labs
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

Due date: Friday, 18 February 2022, 12:00 AM