1. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Growth of crystals governed by a metric field that specifies a spatially varying distribution of growth speeds: (a) ellipses are used to represent the metric field; and (b) growth of the crystal boundaries Figure Legend:

2. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Voronoi regions generated by crystal growth in the absence of boundaries. The figures on the left represent the metric field by ellipses and those on the right are the shapes of the crystals, i.e., the Voronoi regions: (a) and (b) constant isotropic metric field; (c) and (d) constant anisotropic metric field; and (e) and (f) variable metric field. Figure Legend:

3. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Boundary conditions for crystal growth: (a) wet contact; and (b) dry contact Figure Legend:

4. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Labelle–Shewchuk example re-interpreted: (a) the metric distribution which is assumed to be constant within the Voronoi region of a seed; (b) the Voronoi regions obtained using the method proposed here. It can be observed that no “orphan” regions are generated, but some “isolated” Voronoi regions have only one neighbor region. Figure Legend:

5. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Labelle–Shewchuk example re-interpreted: (a) the spatial distribution of metric tensors (thin lines) has been interpolated from the previous metric tensors (thick lines) to obtain a continuous metric field that does not produce “isolated” regions; (b) the corresponding spatial partition into Voronoi regions Figure Legend:

6. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 A complex domain: (a) prescribed anisotropic metric field and (b) boundary-conforming Voronoi partition Figure Legend:

7. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Comparison of the distribution of the isotropic (a) and anisotropic (b) metric fields and corresponding Voronoi partitions (c) and (d), respectively, obtained for a domain around a symmetric aerofoil Figure Legend:

8. Date of download: 6/26/2016 Copyright © ASME. All rights reserved. From: A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics J. Comput. Inf. Sci. Eng. 2014;14(3):031007-031007-7. doi:10.1115/1.4027698 Comparison of the Delaunay triangulations obtained for a domain around a symmetric aerofoil using isotropic (left) and anisotropic (right) metric fields: (a) and (b) whole mesh; and (c) and (d) enlargement near the wake of the aerofoil. Notice how the introduction of anisotropy in the metric field aligns the triangles with the wake as required. Figure Legend: