Résumé: We propose a new stochastic sampling method for implicit surfaces based on an Ito-type stochastic di!erential equation with the converging constraint. The equation can realize a stationary state in which the probability distribution becomes uniform over the whole area of a constraint surface. A hypothetical stochastic particle described by the equation performs Brownian motion, i.e. random walk, being con"ned on a constraint surface, i.e. an implicit surface. Therefore its trajectory gives us sample points on it. The stochastic sampling method is fast and widely applicable to implicit surfaces de"ned with twice di!erentiable constraint functions. It is applicable to non-polynomial surfaces and surfaces with branches, too. It does not require an initial sample point on a sampled surface to start sampling. It works well with a single-particle system without necessity of introducing interaction between particles. It also has advantageous features at the rendering stage.

Langue: Anglais