We propose a sketch-based modeling system where all user input is performed from a unique viewpoint. The strokes drawn by the user must not then be restricted to the drawing plane: their orientation in the 3D space is automatically determined by the system. The desired surface is reconstructed from a grid made of two groups of similar lines, that are considered co-planar. The orientation of the two sets of planes is determined by assuming that at the intersection of a representative line of each group, those two lines are perpendicular.

We propose a new method to recover scene points from a single calibrated view using a subset of distances among the points. This paper first introduces the problem and its relationship with the perspective n point problem. Then the number of distances required to uniquely recover scene points are explored. The result is then developed into a practical vision algorithm to calculate the initial points' coordinates using distance constraints. Finally SQP (Sequential Quadratic Programming) is used to optimize the initial estimations. It can minimize a cost function defined as the sum of squared reprojection errors while keeping the specified distance constraints strictly satisfied. Both simulation data and real scene images have been used to test the proposed method, and good results have been obtained.