1. Approximation by Constraints Why do we need approximation/interpolation? –Record values at some finite set of points in space and time. –Does not capture the entire continuously changing surface. –Need to interpolate: approximation of the value at a given place and time from values at other places and time.

2. Advantage of representing approximation by constraint databases. Interpolation functions is usually represented by constraints. Data compression: constraint representation requires fewer tuples and less compute memory than the original representation. Queries can often be evaluated much faster on the constraint approximation.

3. Triangulated Irregular Networks Often used in GIS to approximate the surface of a landscape. Landscape surfaces –Hard to represent in database systems: infinite number of points. –TIN approximation: take a sample of points on the surface find a triangulation of the sample points