Localised Topology Correction for Hypertextured Terrains

Terrains for computer graphics have traditionally been modelled with height fields. In the case of procedurally defined terrains, the height field is generated by a displacement map z = f (x,y). Displacement maps, however, do not allow the formation of such terrain features as overhangs, arches or caves. The most flexible approach to model procedural terrain is to consider it as an implicit surface, given by f (x,y,z) = 0. Hypertexturing can be used to add terrain features to an initially smooth implicit surface. The main drawback of modelling terrains as hypertextures is that terrain fragments can easily become disconnected. A topology correction method is presented that is able to remove all topologically disconnected fragments of a hypertextured terrain, leaving only the main surface of the terrain. The method works in the context of a ray casting algorithm for implicit surfaces and for any given terrain point indicates whether it is connected or not. The method is localised because it only needs to examine the terrain inside a neighbourhood of sufficiently small size around the point that is being tested in order to determine its connectivity state. This localised connectivity test allows the modelling of procedural terrains over wide areas such as terrains defined over an infinite horizontal plane. Our method works with terrains that are C continuous and uses Morse theory to find the critical points of the terrain. The method follows the separatrix lines joining the critical points to isolate disconnected fragments.