-------------------------------------------------------------------- Integer-Grid Maps for Reliable Quad Meshing – Supplementary Material -------------------------------------------------------------------- Authors : David Bommes, Marcel Campen, Hans-Christian Ebke, Pierre Alliez, Leif Kobbelt WWW: http://www.rwth-graphics.de ---------------------------------------- File Naming Scheme ---------------------------------------- File names have the form (as a Perl regexp): (.*)_(in|out)_(cf|tri|quad)(_scaled)?(_enhanced)?.(ndf|off) The first capture is the model name, the second capture specifies whether the file acts as input or as output to the algorithm (cross fields and triangle meshes are input, quad meshes are output). The third capture specifies the type of data (cf = cross field, tri = triangle mesh, quad = quad mesh). The optional fourth capture is present in quad meshes obtained from the parametrization scaled by a factor of 10 (see below). The optional fifth capture is present in the enhanced cross fields from Figure 8 as well as in the output quad meshes corresponding to these cross fields. Note that all coarse results where obtained without up-sampling (see Section 3.4). Consequently, artifacts of the decimated input geometry are visible in some of the results, especially in those obtained from scaled parametrizations. Of course for quad layout construction in practice one would compute a new distortion reduced map that keeps the layout fix but subdivides non-uniformly into rectangles, as could easily be done. For all provided results, the target edge length h used to generate the results was chosen as specified in the paper. All meshes are represented by OFF files. All cross fields are represented by NDF files, the format of which is specified below. ---------------------------------------- Quad Meshes from Scaled Parametrizations ---------------------------------------- Those quad meshes with a "_scaled" in their file name were obtained from the same parametrization as their non-scaled pendant except the parametrization was scaled by a factor of 10 prior to the quad mesh extraction. Thus, they basically represent a subdivided version of the non-scaled quad mesh. For very coarse quad meshes the scaled representations better approximate the original surface and thus are better suited for some visualization tasks. ---------------------------------------- The .ndf Format for Cross Fields ---------------------------------------- The cross fields are stored in a simple ini-file format. It can easily be parsed using e.g. QSettings from Nokias Qt-framework. A .ndf file usually contains 6 sections: [Comments] Here user comments and any other free text can be stored. [Information] Here general information about the mesh, e.g. #edges can be stored. [Pjumps] Refers to the integer jumps along an edge (see [1] Section 4.1 Equation (1)). The "values" string contains the integer jumps for all the edges in the mesh delimited by semi-colons and ordered in the same ordering as the edges. That is, the first integer corresponds to the first edge of the mesh and so on. [Theta] Refers to the angle \theta of a face (see [1] Section 4.1). The reference edge for the angle(s) is the first half-edge of the respective face. The angles in the "values" string are delimited by semi-colons, and ordered wrt the faces of the mesh. Hence, the first value corresponds to the angle in the first face of the mesh and so on. [Singularities] Similar to the section above, here the "indices" string refers to vertex indices of the mesh and "singularities" holds the index of the (singularitiy at the) respective vertex. Note: Our implementation uses www.openmesh.org as mesh datastructure. For reference half-edge of each face, we use the start half-edge of the FaceHalfedgeIter (fh_iter). For orientation between two faces we use the half-edges of the common edge, for example: face0 = face_handle( halfedge_handle( common_edge, 0)) face1 = face_handle( halfedge_handle( common_edge, 1)) [1] D. Bommes, H. Zimmer, and L. Kobbelt, “Mixed-integer quadrangulation,” in ACM SIGGRAPH 2009 papers, New York, NY, USA, 2009, pp. 77:1–77:10.