Two-dimensional compositing that preserves the curvatures of non-flat surfaces is disclosed. In some embodiments, a mapping is associated with a two-dimensional rendering that maps a potentially variable portion of the two-dimensional rendering to a canvas. The mapping is generated from a three-dimensional model of the potentially variable portion of the two-dimensional rendering. The potentially variable portion of the two-dimensional rendering is dynamically modified according to the mapping to reflect content comprising the canvas or edits received with respect to the canvas.