Procedural modelling of terrains with constraints

Terrain is an essential part of any outdoor environment and, consequently, many techniques have appeared that deal with the problem of its automatic generation, such as procedural modeling. One form to create terrains is using noise functions because its low computational cost and its random result. However, the randomness of these functions also makes it difficult to have any control over the result obtained. In order to solve the problem of lack of control, this paper presents a new method noise-based that allows procedural terrains creation with elevation constraints (GPS routes, points of interest and areas of interest). For this, the method establishes the restrictions as fixed values in the heightmap function and creates a system of equations to obtain all points that they depend this restrictions. In this way, the terrain obtained maintains the random noise, but including the desired restrictions. The paper also includes how we apply this method on large terrain models without losing resolution or increasing the computational cost excessively. The results show that our method makes it possible to integrate this kind of constraints with high accuracy and realism while preserving the natural appearance of the procedural generation