Quadratic interpolation in hardware Phong shading and texture mapping

Rendering systems often represent curved surfaces as a mesh of planar polygons that are shaded to add realism and to restore a smooth appearance. To increase the rendering speed, complex operations, such as the evaluation of the local illumination model or texture transformation, are executed for just a few knot points, and the values at other points are interpolated. Usually, a linear transformation is used, since it can be easily implemented in hardware. However, the colour distribution and texture transformation may be strongly nonlinear, so a linear interpolation may introduce severe artifacts. Thus, this paper proposes two-variate quadratic interpolation to tackle this problem and demonstrates that it can be implemented in hardware. A software simulation and a VHDL description of the shading hardware are also presented.