Beyond Triangles: A Novel Quadrilateral Rendering Approach

Real-time computer graphics has long relied on triangles due to GPUs' native support for hardware-accelerated rasterization of triangles only. This leads to C^1 discontinuities in vertex attributes like texture coordinates and normals along the shared edge when quadrilaterals are split into triangles. This article presents a novel method that preserves C^1 continuity across the common edge of two triangles generated from convex quadrilaterals using an algebraic solution for bilinear interpolation coefficients expressed in barycentric coordinates. The method is implemented across Geometry, Tessellation, and Mesh shaders, significantly improving rendering quality with negligible computational overhead.