perspectivecorrect

Perspective-correct interpolation is a technique in computer graphics used to interpolate attributes across a polygon in screen space so that the results are consistent with the scene’s perspective projection. It is essential for rendering textures and other per-vertex attributes without introducing geometric distortion when parts of a polygon lie at different depths.

The core idea is that affine interpolation in screen space does not align with perspective, causing textures and colors to appear warped. To achieve perspective correctness, attributes are first divided by the homogeneous depth (or w) at each vertex. For a vertex i with attribute a_i and depth w_i, compute a_i' = a_i / w_i and w_i' = 1 / w_i. During rasterization, a_i' and w_i' are interpolated linearly across the triangle using the usual barycentric weights. At a fragment, the original attribute is recovered as a = a'/w'.

In practice, this method is most commonly applied to texture coordinates (u, v) to produce undistorted texturing, but it also applies to other per-vertex attributes such as colors and normals. Modern GPUs perform perspective-correct interpolation automatically within the rasterization pipeline, ensuring accurate texture mapping and shading on polygons of varying depth.

Advantages of perspective-correct interpolation include accurate texture mapping and reduced distortion in projected geometry. Limitations are primarily numerical: finite precision can introduce artifacts, especially on very large triangles or when depth buffers have limited precision. Some systems offer affine interpolation as a faster but less accurate alternative when performance is critical or when depth variation is minimal.

Historically, perspective correction became standard with the advent of texture mapping and modern rasterization pipelines, where it is implemented as part of the rendering hardware and shader stages.