Géraldine Morin, Ron Goldman

• Blossoming is a powerful tool for studying and computing with Bézier and B-spline curves and surfaces - that is, for the investigation and analysis of polynomials and piecewise polynomials in geometric modeling. In this paper, we define a notion of the blossom for Poisson curves. Poisson curves are to analytic functions what Bézier curves are to polynomials - a representation adapted to geometric design. As in the polynomial setting, the blossom provides a simple, powerful, elegant and computationally meaningful way to analyze Poisson curves. Here, we define the analytic blossom and interpret all the known algorithms for Poisson curves - subdivision, trimming, evaluation of the function and its derivatives, and conversion between the Taylor and the Poisson basis - in terms of this analytic blossom.