Heightfields

Heightfields are a common representation of a three-dimensional surface used widely in computer graphics, geographic information systems, and terrain modeling. A heightfield is typically a two-dimensional grid where each grid cell stores a single scalar height value. The resulting surface is the graph of a function z = f(x, y) over a regular domain, often interpreted as terrain elevation. Heightfields are usually stored as 2D arrays or grayscale images, with height increasing with brighter intensities (or based on a separate height array). The grid has defined spacing dx and dy and an extent in the x and y directions.

Rendering and use: To render, adjacent grid points are connected to form a mesh of quads or triangles; shading, lighting, and texturing are applied. Heightfields support real-time rendering and are used for terrain in video games and simulations. They also serve in GIS as digital elevation models (DEMs) and in architectural visualization.

Data sources and generation: Heights can come from real-world measurements (LiDAR, radar, stereo imagery, satellite altimetry) or be generated procedurally with noise, fractal algorithms, and erosion simulations. Preprocessing may include regridding, gap filling, and smoothing.

Interpolation and limitations: Accessing heights at arbitrary x, y is done via interpolation (bilinear, bicubic, etc.). A key limitation is that heightfields represent surfaces without overhangs or voids; they cannot model caves or cliffs that descend beneath or rise above surrounding points without special techniques. They scale well in memory and speed but can be memory-intensive at high resolutions.