Our goal is to implement an ornamental calligraphic pen that enriches the stroke of a pressure-sensitive digital pen with perfectly adjusted ornamental content while the stroke is drawn. For this, we propose an algorithm that calculates a local coordinate system within the stroke using the graphics processing unit. The fast calculations on the GPU make it possible that the calculation progress is made visible and that the user can observe the ornamental content flow dynamically into its intended position. The result of our algorithm is close to conformal—meaning that the map of the ornamental content to the local coordinate system within the stroke preserves angles and infinitesimal shapes.