Humans have the ability to intuitively realize the 3D geometry from a given 2D sketch. On the contrary, a computer-aided design program encounters sketches as a 2D configuration of lines, without any geometric depth information and requires mathematical criteria to establish if a sketch is realizable, i.e., if it is the projection of a 3D model. Research on the field of “ Sketch realizability” aims at providing geometric, algebraic, or computational criteria/conditions that determine whether a sketch identifies with the projection of a valid polyhedron.
My research on this field focuses on the development of an algebraic model of the “cross-section” geometric realizability criterion, which was first introduced by Whiteley in “Weavings, sections and projections of spherical polyhedral, Discrete Applied Mathematics, 32(3), 1991, 275-294″.
The proposed algebraic model describes explicitly the constraints that are involved within the cross-section criterion and forms the basis for an algorithmic implementation of the latter: the developed algorithm constructs a cross-section from a given wireframe sketch in order to evaluate the realizability of it. The realizability evaluation is based on the calculation of a “distance parameter”, which verifies the compatibility of the generated cross-section with the given sketch. The proposed algorithm can also handle inexact sketches, i.e., sketches with noisy vertices.
The proposed algorithm can be effectively employed within a “sketch-to-solid” algorithm in order to (a) facilitate the process of the “hidden geometry determination” that is required for natural sketches, (b) correct the geometry of a given wireframe sketch, and (c) generate a compatible cross-section for constructing the trihedral polyhedron from a given sketch.
Related to this research Publications:
- A hybrid-optimization method for assessing the realizability of wireframe sketches, P. Azariadis, S. Kyratzi, N.S. Sapidis, 3D Research, 4(1), Article: 3, 2013.
- Realizability of a Sketch: An Algorithmic Implementation of the Cross-Section Criterion, S. Kyratzi, P. Azariadis, N.S. Sapidis, Computer Aided Design and Applications, 8(5), 665-679, 2011.
- From Sketch to Solid: An Algebraic Cross-Section Criterion for the Realizability of a Wireframe Sketch, S. Kyratzi, N.S. Sapidis, Journal of Computing, 86(2-3), 219-234, 2009.