Methods and apparatus for specifying and interpolating hierarchical procedural models

Methods and apparatus for procedural modeling are described for generating procedural models and exploring procedural model space. Common procedural components (models, modules, and methods) and a hierarchical framework are described that may be used to construct hierarchical procedural models. A model may comprise a hierarchy of one or more modules. Each module includes a sequence of methods and an optional geometry for display. A method may be controlled by one or more parameters. The values of the parameters may be specified via curves. A module description may be condensed into a single array of values for parameters of the module. Thus, a model or module may be specified by filling in values for arrays of parameters for the sequence of methods. An interpolation technique for interpolating between models is described in which models are matched according to a cost function so that ancestry is preserved.