Example systems and related methods relate to rendering using smooth shading. A computing device can receive information about an image, the information including one or more patches, where a particular patch of the one or more patches is specified using a plurality of non-linear equations. The computing device can determine one or more linear approximations to a particular non-linear equation of the plurality of non-linear equations. The computing device can update the particular patch to replace the particular non-linear equation with at least one linear approximation of the one or more linear approximations. The computing device can render at least part of the image by at least rendering the updated particular patch. The computing device can generate an output that includes the rendered at least part of the image.