Rendering 3D paintings can be done by compositing strokes embedded in space. Users input strokes and other image elements using an input device that specifies a 2D view of the element, and the system provides the 3D position of the element based on rules and processes, some of which allow for user input of high level parameters, thereby allowing for intuitive and quick entry of 3D elements, and a 3D scalar field. The artist can treat the full 3D space as a canvas. Strokes painted in a 2D viewport window are embedded in 3D space in a way that gives creative freedom to the artist while maintaining an acceptable level of controllability. The canvas need not be tied to any particular object already in a scene, but the canvas can be dependent on, or a function of, another object. An implicit canvas can be defined by the 3D scalar field.