This paper presents a novel approach for creating curvilinear, texture mapped, 3D scene models from a single painting or photograph with no prior internal knowledge about the shape. The new technique takes input as a sparse set of user-specified constraints, and generates a well-behaved 3D surface satisfying the parameters. As each constraint is specified, the system recalculates and displays the reconstruction in real time. In contrast to previous work in single view reconstruction, our technique enables high quality reconstructions of curved surfaces. A key feature of the approach is a novel hierarchical transformation technique for accelerating convergence on a non-uniform, piecewise continuous grid. The technique is interactive and updates the model in real time as constraints are added, allowing fast reconstruction of photorealistic scene models. The approach is shown to yield high quality results.