Method and apparatus for the interactive enhancement of 2D art with 3D geometry. A surface inflation tool may be used to create a 3D shape by inflating the surface that interpolates the input boundaries. The surface inflation tool may, for example, obtain a closed 2D boundary as input, triangulate the area within the boundary to generate an initial surface, and inflate the surface while maintaining a fixed boundary. Using surface normal values and/or mean curvature values specified at boundary vertices as constraints, the tool may control the inflated surface efficiently using a single linear system. Embodiments handle both smooth and sharp position constraints. Position constraint vertices may also have constraints specified for controlling the inflation of a local surface.