DirectX Documentation

The Rasterizer Stage

The rasterizer is a crucial fixed-function component of the DirectX graphics pipeline responsible for converting geometric primitives (like triangles and lines) into a set of pixels that can be rendered on the screen. It takes the output from the vertex shader and performs the necessary calculations to determine which screen-space pixels are covered by each primitive.

Core Functionality

  • Primitive Assembly: Takes processed vertices and forms primitives (triangles, lines, points).
  • Clipping: Removes primitives (or parts of primitives) that lie outside the view frustum or viewport.
  • Perspective Divide: Divides vertex coordinates by their 'w' component to transform from homogeneous clip space to normalized device coordinates.
  • Viewport Transformation: Maps normalized device coordinates to screen coordinates (pixels).
  • Triangle Traversal: For triangles, determines which pixels are inside its boundaries. This is often done using barycentric coordinates.
  • Attribute Interpolation: Calculates the interpolated values of vertex attributes (like color, texture coordinates) for each pixel based on barycentric coordinates.
  • Depth Testing (Early-Z): Compares interpolated depth values to the depth buffer to discard pixels that are occluded by closer primitives before pixel shading.

Barycentric Coordinates

For triangles, the rasterizer commonly uses barycentric coordinates. For any point P inside a triangle with vertices A, B, and C, P can be expressed as a weighted sum:

P = uA + vB + wC

where u + v + w = 1 and u, v, w ≥ 0. The values u, v, and w are the barycentric coordinates. These coordinates are used to interpolate vertex attributes across the triangle's surface.

Triangle Rasterization Algorithm (Simplified)

A common approach involves the following steps:

  1. Determine the bounding box of the triangle in screen space.
  2. Iterate through each pixel within the bounding box.
  3. For each pixel, calculate its barycentric coordinates with respect to the triangle.
  4. If the barycentric coordinates indicate the pixel is inside the triangle (u, v, w ≥ 0), then:
    • Interpolate the vertex attributes (color, texture coordinates, normals, etc.) using the barycentric coordinates.
    • Perform depth testing. If the pixel is visible, it proceeds to the pixel shader.

Example: Barycentric Coordinate Calculation (Conceptual)

Given a pixel at screen coordinates (x, y) and triangle vertices A(xA, yA), B(xB, yB), C(xC, yC):


    // Area of the triangle ABC
    float totalArea = 0.5 * (-xB*yA + xC*yA + xA*yB - xC*yB - xA*yC + xB*yC);

    // Calculate barycentric coordinates
    float u = 0.5 * ( (yB - yC)*(x - xC) + (xC - xB)*(y - yC) ) / totalArea;
    float v = 0.5 * ( (yC - yA)*(x - xA) + (xA - xC)*(y - yA) ) / totalArea;
    float w = 1.0 - u - v;

Note: This is a simplified representation. Actual implementations handle edge cases and optimizations.

Performance Considerations

The rasterizer is a highly optimized hardware unit. Its performance is critical for achieving high frame rates. Techniques like tile-based rendering and early depth testing are employed to minimize redundant calculations and memory accesses.