This paper presents an approach to automatically and transparently parallelize algorithms to build 2D or 3D virtual objects in geometric modeling: In particular, we show that subdivision and Iterated Function System constructions can be parallelized, without any explicit parallelization study by their developer. These operations are described in the framework Jerboa, where each operation is expressed as a graph transformation and objects are topologically described using generalized maps. All transformations are handled by a generic engine that can handle structure changes in parallel. The obtained results allow any designer of virtual environments to rely on modern multi-core and multi-processor architectures to get faster constructions of complex objects without any skills on parallelism.