Rasterization vs Ray Tracing Overview

Rasterization vs Ray Tracing

• Rasterization projects the primitives (e.g., triangles) onto the view plane and checks if each pixel overlaps with the primitive.
• Ray tracing casts a ray from each pixel into the scene and checks for collisions with primitives.

Rasterization: Why?

• Rasterization is generally faster than ray tracing, mainly due to better convergence when projecting and optimized GPUs.
• The technique used depends on the scene complexity and optimization techniques in use.

Rasterization: Algorithm

• The algorithm involves two stages:
  • Projection stage: Projects 3D geometry onto the 2D view plane.
  • Rasterization stage: Checks each pixel in the 2D view plane for overlap with projected geometry.

Rasterization: Coordinate Systems

• Raster/Screen Space, Normalized Raster Space and NDC Space are coordinate systems used in rasterization.
• Specific coordinates (0.0, 0.0), (screenWidth, 0.0), (0.0, screenHeight), (screenWidth, screenHeight) etc define the boundaries of Raster/Screen space.

Rasterization: Rasterization Stage

• The stage involves defining triangles with NDC (normalized device coordinates) and checking if a pixel is inside those triangles. NDC coordinates range from (-1, -1) to (1, 1).
• NDC coordinates are converted to screen space using formula to match screen resolution.

Rasterization: Rasterization Stage

• The formulas converted from screen space to view plane are inverted when testing if a pixel is inside a triangle.
• Pixel is represented as a Vector2 with (px + 0.5, py + 0.5).
• Vertices are represented in screen space with a third (z) coordinate representing depth.
• The z coordinate is ignored during the cross product calculations.

Rasterization: Rasterization Stage

• Loops over all triangles in NDC space.
• Loops over all pixels inside a triangle.
• Colors a pixel white if it's inside the triangle.

Rasterization: Projection Stage

• Object models are first defined in model space, with vertices relative to the model's axis origin at the center.
• Vertices are transformed from model space to world space using transformation matrices (to handle translation, rotation and scaling).

Rasterization: Projection Stage

• The projection stage transforms 3D world space to 2D normalized device coordinates (NDC) to prepare for rasterization.

Rasterization: Projection Stage

• The transformation from world to camera space involves multiplying vertices with the inverse of the camera-to-world matrix.
• The transformation from camera to a normalized coordinate system requires further transformations.

Rasterization: Projection Stage

• Coordinates are translated and transformed, including considering the projection matrix and viewport transformation.
• Projecting 3D points onto a 2D view plane involves the perspective divide operation to handle perspective distortion.

Rasterization: Projection Stage

• The z-component of the projected point is stored unchanged.
• The converted coordinates are in projection space.
• Screen dimensions and FOV are used to adjust coordinates.

Rasterization: Barycentric Coordinates

• Barycentric coordinates are weights representing how a point relates to a triangle's vertices.
• These weights are calculated from the signed areas of sub-triangles formed by connecting the point to triangle vertices.
• The normalized weights sum to 1, and determine the color to display using interpolation.

Rasterization: Barycentric Coordinates

• Barycentric coordinates can be used to determine the location of a point within a triangle, based on areas of sub-triangles formed by connecting to the vertices and a particular point.
• The calculation of these weights is determined by the cross product of vectors connecting the vertices of the triangle and the point into consideration.
• The normalized weights of barycentric coordinates sum to 1 and can be used to derive the final color of a pixel inside the triangle.

Rasterization: Barycentric Coordinates

• Barycentric coordinates are unique up to scaling. Meaning for any positive a, the coordinates (λa, λb, λc) are the same.
• To normalize the coordinates, divide each weight by the total sum of weights (which is always 1).
• They're useful for calculating the color of a pixel by interpolating vertex colors based on these weights.

Rasterization: Barycentric Coordinates

• To calculate the weights to draw a line between the center of mass point and the vertices , we need to calculate the area of the three small triangles made by drawing lines connecting every vertex to the center of mass point.

Rasterization: Barycentric Coordinates

• The ratio of the area of the triangle opposed to a vertex, divided by the total area of the original triangle equals the weight of that vertex, which tells us exactly where the point is relative to the vertex.

Rasterization: Depth Buffer

• Depth buffer is a separate array that stores the depth (z-value) of each pixel in the scene.
• When a pixel is inside a triangle, its depth is compared to the stored depth value in the depth buffer.
• The pixel is drawn if the current pixel's depth is less than the value in the depth buffer, updating the depth buffer with the new value if the test is successful. This is used to detect and resolve depth issues, which means to prevent ZFighting.

Rasterization: Optimizations

• Calculating bounding boxes for each triangle determines the minimum and maximum x/y coordinate values.
• The rasterization process iterates over pixels inside this bounding box rather than the entire screen.
• This improves performance, especially when rendering complex scenes with smaller triangles.