Dynamic Graffiti Stylisation with Stochastic Optimal Control

We present a method for the interactive generation of stylised letters, curves and motion paths that are similar to the ones that can be observed in art forms such as graffiti and calligraphy. We define various stylisations of a letter form over a common geometrical structure, which is given by the spatial layout of a sparse sequence of targets. Different stylisations are then generated by optimising the trajectories of a dynamical system that tracks the target sequence. The evolution of the dynamical system is computed with a stochastic formulation of optimal control, in which each target is defined probabilistically as a multivariate Gaussian. The covariance of each Gaussian explicitly defines the variability as well as the curvilinear evolution of trajectory segments. Given this probabilistic formulation, the optimisation procedure results in a trajectory distribution rather than a single path. It is then possible to stochastically sample from the distribution a possibly infinite number of dynamically and aesthetically consistent trajectories, which mimics the variability that is typically observed in human drawing or writing. We demonstrate how this system can be used together with a simple user interface, in order to explore different stylisations of interactively or procedurally defined letters.