viewProj

The viewProj matrix, often referred to as the view–projection matrix, is a fundamental construct in 3D computer graphics. It represents the combination of a camera's view transformation and the projection transformation that converts 3D world coordinates into 2D screen coordinates. By multiplying a vertex’s position first by the view matrix—accounting for camera position, orientation, and target—and then by the projection matrix—determining perspective or orthographic projection—the viewProj matrix condenses both steps into a single matrix operation. This consolidation reduces computational load in shaders and improves pipeline efficiency.

In practice, the view matrix is derived from the camera’s eye position, look-at point, and up vector, forming a right-handed coordinate system. The projection matrix is defined by field of view, aspect ratio, near and far clip planes, or, for orthographic views, the bounds of the view volume. The resulting viewProj matrix is commonly passed to vertex shaders via uniform variables and applied to vertex positions in clip space. Because of its extensive use, many graphics APIs and shader languages expose standard functions to compute or multiply viewProj efficiently. Misapplication of the matrix—such as swapping row-major and column-major conventions—can lead to inverted perspective, incorrect depth ranges, or skewed geometry. Understanding the mathematical relationship between view and projection, and carefully managing coordinate system conventions, ensures correct rendering across different platforms and shading pipelines.