DirectX Computational Graphics

Rasterization Fundamentals

Rasterization is a fundamental process in computer graphics responsible for converting vector graphics (geometric primitives like triangles) into a pixel-based representation (a bitmap image) that can be displayed on a screen. This tutorial explores the core concepts of rasterization within the DirectX pipeline.

What is Rasterization?

At its heart, rasterization is about transforming geometric shapes into a grid of pixels. For 3D graphics, this typically involves taking triangles defined in 3D space and determining which screen pixels each triangle covers. Each covered pixel is then assigned a color based on the triangle's properties and potentially interpolated data from its vertices.

The Stages of Rasterization

While modern GPUs have highly optimized hardware for rasterization, understanding the conceptual stages is crucial:

1. Triangle Setup: After the vertex shader processes vertices and they are transformed into screen space (clipping and perspective division), the rasterizer takes these clipped primitives. For triangles, this involves determining the edges and calculating edge functions.
2. Edge Walking/Scanline Conversion: The rasterizer determines which pixels lie inside the boundaries of the primitive. A common technique is edge walking, where the rasterizer traverses the screen from top to bottom (or left to right), determining the intersection of the primitive's edges with each scanline.
3. Fragment Generation: For each pixel that falls inside the primitive, a fragment is generated. A fragment is essentially a potential pixel to be colored. It holds interpolated attributes from the primitive's vertices, such as color, texture coordinates, and depth.
4. Clipping and Depth Testing: Fragments that lie outside the screen boundaries are discarded. Furthermore, for each fragment, a depth test is performed against the depth buffer. If the fragment is behind an existing fragment at the same pixel location, it is discarded. This ensures that objects closer to the camera obscure objects farther away.
5. Pixel Coloring: Fragments that pass all tests are then used to update the color buffer (the final image). The interpolated attributes are used by the pixel shader to determine the final color of the pixel.

Barycentric Coordinates

A key mathematical concept used in rasterization is barycentric coordinates. For a triangle with vertices A, B, and C, any point P inside the triangle can be expressed as a weighted average of the vertices:

P = u*A + v*B + w*C

where u + v + w = 1 and u, v, w >= 0. The values u, v, and w are the barycentric coordinates. These coordinates are linear and can be interpolated across the surface of the triangle. This is incredibly useful for interpolating vertex attributes (like color or texture coordinates) to each fragment.

Antialiasing

A common artifact of rasterization is "jaggies" or aliasing, where diagonal or curved edges appear blocky. Various antialiasing techniques are employed to mitigate this, often by sampling a primitive multiple times per pixel or by using coverage masks to determine how much of a pixel is covered by the primitive.

The Role in the DirectX Pipeline

In the DirectX pipeline, rasterization occurs after the geometry-related stages (vertex shader, tessellation, geometry shader) and before the pixel shader. The fixed-function hardware handles this complex process with incredible speed, allowing developers to focus on shader logic and visual effects.

Understanding rasterization is crucial for optimizing rendering performance, implementing effects like texture mapping, and comprehending how geometric data is translated into the final image you see on your screen.