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In computer graphics, triangle setup is the rasterization stage that prepares a screen-space triangle for coverage testing and interpolation. It computes information such as edge equations and gradients so later stages can determine which pixel samples lie inside the triangle and calculate values such as depth and shading attributes. The phrase is also used for a Brazilian jiu-jitsu technique; this article covers the graphics meaning.
What triangle setup does
Once a triangle’s vertices have been transformed into screen or window coordinates, the rasterizer needs a way to test positions against its edges and determine how values change across the triangle. Triangle setup computes the data needed for those tasks. Real-Time Rendering, Fourth Edition describes the stage this way: “In this stage the differentials, edge equations, and other data for the triangle are computed” (authors’ resources for the book; section 2.4.1, A K Peters/CRC Press, 2018).
Conceptually, the flow is:
- Screen-space vertices: the transformed triangle is ready to be processed in rasterization.
- Setup: edge-related data and interpolation gradients are calculated.
- Traversal and coverage: sample positions are tested to determine whether they are covered, producing fragments for covered samples.
- Interpolation: values defined at the vertices are evaluated for the resulting fragments, providing data such as depth and shading attributes to later pixel-processing stages.
Setup prepares information; it does not mean that the triangle’s pixels have already been shaded. The textbook treats setup and traversal as separate conceptual stages.
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How the rasterizer determines whether a sample is inside
Edge equations provide a compact way to evaluate a sample’s position relative to a triangle’s boundaries. During traversal, the rasterizer uses edge-related information to classify sample positions as inside or outside the triangle, applying rules for positions that lie exactly on an edge.
The coverage result depends on the sampling method. A simple example tests the pixel center, but that is not a universal rule. Multisampling and supersampling evaluate multiple sample positions. Conservative rasterization uses a different criterion: a pixel is considered inside when at least part of it overlaps the triangle. These approaches can therefore classify coverage differently. For broader context on setup, traversal, and rasterization, see Real-Time Rendering, Fourth Edition.
What data setup can compute
Depending on the implementation, setup data can include edge equations or slopes, differentials, and depth gradients. These values support coverage tests and interpolation of information that varies across the triangle. The specific fields and how they are calculated or organized depend on the GPU architecture; there is no single internal implementation that applies to every GPU.
A graphics-processor patent provides one implementation example: its setup block sorts vertices by x and y, assigns triangle descriptors, computes edge slopes and depth gradients, and supplies data to downstream processing. That example illustrates possible responsibilities, not a standard specification for all graphics hardware (patent database).
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Triangle setup is not the whole rasterization process
The useful distinction is between calculating the triangle’s setup information and using that information to process samples. Setup supplies edge and interpolation data; traversal tests coverage and produces fragments; interpolation derives fragment-level values from vertex data. The stages are related, but saying “triangle setup shades the pixels” collapses separate work into one and is misleading.
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