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Summer 2017
2D Line Drawing of a Cube. Skewed Symmetry Hyperbola of Gradient Equation Rotated 3D Cube Constructed from Line Drawing

Construction of 3D Cuboids from Line Drawings
Tyler Nowicki
University of Waterloo
February 23, 2015

This is a presentation on three methods for inferring 3D information from line drawings by assuming right angles at a 3-line intersection. The first method is the cubic corner method that relates the slope of each line at the intersection to the three angles that are observed between the intersecting lines. If the angles of the intersecting lines are not precise however, the slopes may be very large, or a solution may be impossible. The skewed-symmetry method infers the slope of each visible planar surface from the intersection. The least tilted surface is used to construct the 3D corner. This method is computes a good 3D corner even with small imperfections in the drawing. The last method is optimization which fits a cuboid to the line intersection by minimizing a combination of several visual cues such as line parallelism, face planarity, corner orthogonality, etc. However, this approach is slow and doesn't always converge on a nice cuboid.

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