Hermite Interpolation of Heightmaps

Abstract

Heightmaps are ubiquitous in real-time computer graphics. They are used to describe geometric detail over an underlying coarser surface. Various techniques, such as parallax occlusion mapping and relief mapping, use heightmap textures to impose mesostructural details over macrostructural elements without increasing the actual complexity of the rendered geometries. We aim to improve the quality of the fine resolution surface by incorporating the gradient of the original function into the sampling procedure. The traditional representation consists of simple height values stored on a regular grid. During rendering, bilinear filtering is applied. We propose to store the partial derivatives with the height values and use Hermite interpolation between the samples. This guarantees a globally C1 continuous heightfield instead of the C0 -continuity of bilinear filtering. Moreover, incorporating higher order information via partial derivatives allows us to use lower resolution heightmaps while retaining the appearance of a higher resolution map. In parallax mapping, surface normals are often stored alongside the height values, as such, our method does not require additional storage, since normals and partial derivatives can be calculated from one another. The exact normals of the reconstructed cubic Hermite surface can also be calculated, resulting in a storage efficient replacement for normal mapping with richer visual appearance.