We introduce Delaunay Painting, a novel and easy-to-use method to flat-color contour-sketches with gaps. Starting from a Delaunay triangulation of the input contours, triangles are iteratively filled with the appropriate colors, thanks to the dynamic update of flow values calculated from color hints. Aesthetic finish is then achieved, through energy minimisation of contour curves and further heuristics enforcing the appropriate sharp corners. To be more efficient, the user can also make use of our color diffusion framework which automatically extends coloring to small, internal regions such as those delimited by hatches. The resulting method robustly handles input contours with strong gaps. As an interactive tool, it minimizes user's efforts and enables any coloring strategy, as the result does not depend on the order of interactions. We also provide an automatized version of the coloring strategy for quick segmentation of contours images, that we illustrate with an application to medical imaging.