In the realm of computer graphics, particularly in game development, triangles play a pivotal role. From rendering intricate 3D models to defining the simplest shapes, understanding triangle rasterization is fundamental. This article explores the mechanics of triangle rasterization in game engines, the significance of vertex ordering, and why triangles are the preferred shape in computer graphics.
What is Triangle Rasterization?
Triangle rasterization is the process of converting the vertices of a triangle into a series of pixels (or fragments) that can be displayed on a screen. This process is essential in rendering 3D models and scenes in game engines, transforming abstract geometric data into visually stunning graphics.
The Rasterization Process

Vertex Processing: Vertices of a triangle are first processed through the vertex shader, transforming them from model space to screen space.

Edge Function Evaluation: The edges of the triangle are evaluated to determine which pixels fall within the boundaries of the triangle.

Fragment Generation: The rasterizer generates fragments for each pixel inside the triangle. These fragments are then processed by the fragment shader, determining the final color and texture.

Depth Testing and Blending: The fragments undergo depth testing to handle visibility and blending to mix colors correctly.
Why Triangles?
Every 3D model that you see in a computer is made up of triangles. Triangles are the fundamental building blocks of computer graphics for several reasons:

Planar Simplicity: A triangle is the simplest polygon that can represent a surface in 3D space. Any three noncollinear points form a triangle, making them inherently planar.

Mathematical Stability: Triangles are mathematically stable. They always define a single plane and do not suffer from the complexities and ambiguities that can arise with higherorder polygons (e.g., quads or ngons).

Efficiency in Rendering Pipelines: Graphics hardware is optimized for triangles. The fixed number of vertices (three) allows for highly efficient processing and rasterization. Triangles also facilitate easier interpolation of vertex attributes (like color and texture coordinates).

Versatility: Complex shapes and surfaces can be decomposed into triangles, enabling detailed modeling and rendering. This process, known as tessellation, allows for the representation of intricate models while leveraging the simplicity of triangles.
Clockwise and CounterClockwise Order: Determining Front and Back Faces
In computer graphics, the order in which the vertices of a triangle are defined determines its orientation—whether it’s considered a front face or a back face. This orientation is crucial for rendering and culling processes.

Clockwise Order (CW): If the vertices of a triangle are defined in a clockwise order, it is typically considered a back face.

CounterClockwise Order (CCW): Conversely, if the vertices are defined in a counterclockwise order, the triangle is considered a front face.
Although this direction can be inversed and is only a rule that should be followed through the development process. Game engines use this distinction to optimize rendering. By default, back faces can be culled (not rendered) because they are typically not visible to the camera. This process, known as backface culling, improves rendering efficiency by reducing the number of triangles processed by the fragment shader.
Let’s visualize this concept with a simple example using an image of a triangle with three vertices labeled A, B, and C.
Imagine a triangle with vertices A, B, and C. We will illustrate two different orderings: ABC (counterclockwise) and CBA (clockwise). When vertices are defined in a counterclockwise order (ABC), the triangle is considered a front face. This is the default orientation in many graphics systems, including OpenGL, where the front face is typically what the camera sees.
When vertices are defined in a clockwise order (CBA), the triangle is considered a back face. Back faces are usually culled (not rendered) to optimize performance since they are often not visible to the camera.
Conclusion
Triangles are the base of the computer graphics. Knowing how they are processed and how to mathematically work with them is essential for every game developer. In the future articles I will focus more on this subject and we will dive deeper into the computer graphics.