VaryLab is a software developed at Berlin Institute of Technology by members of the geometry group. It is supported by DFG SFB/TR 109 Discretization in Geometry and Dynamics. It is designed to be an extensible and modular tool for experiments with discrete surfaces in pure mathematics and applications in industrial geometry.

The VaryLab User Interface |

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**Mesh Optimization **

VaryLab is all about mesh optimization, we say discrete surface optimization. That means you can modify a given mesh to have minimal energy in a certain sense. The energy in question is a combination of energies that are defined on the vertex positions of the input mesh. VaryLab implements various energies for discrete surfaces, e.g., planarity of faces, equal lengths of edges, curvature of parameter curves and many more.

The planar-quads energy

The planar-quads energy

before |

after |

before |

after |

During optimization watch the optimization core doing its job

### Data Visualization

Data visualization is one of most important tasks when doing surface optimization. On the basis of the analysis of data on a surface you decide which parameters go into the optimiza- tion and how the optimization core is performing.

Colors are a very effective way to represent scalar data on vertices, edges, and faces of a mesh. The nodes are colored using a color map.

This visualizer represents scalar functions on surfaces. In addition to the colors the sizes of the spheres indicate the values of the function.

The histogram shows a discrete density plot of scalar data on surface nodes. The color map can be adjusted to match the colors of a colored nodes or colored beads visualizer.

Vector data on surface nodes can be displayed with this visualizer. In VaryLab this is mainly used for the visualization of principle curvature directions and their singularities.

Feature Bundles:

### Parameterization

When speaking about parameterization of a discrete surface we mean the assignment of texture coordinates to the vertices of a mesh. This enables you to draw images on the surface and do processing in image space. You can do re-meshing by introducing new vertices at locations on the surface guided by patterns in image space, e.g., a quad or triangle pattern.

original mesh |

boundary aligned quad mesh |

boundary aligned triangle mesh |

boundary aligned hex mesh |

hybrid mesh |

### Online Program Start

The program features of the online version of VaryLab are roughly divided into bundles that can be selected when creating a new project. Currently available bundles include:The VaryLab for gridshells bundle contains optimization modules for the creation of meshes with constant edge length. Read more...

The Planar Quads bundle contains all modules needed to create meshes with planar quadrilaterals. You can do successive subdivision, remeshing and planarization, explore planar-by-definition meshes. Read more...

The Remeshing bundle contains the modules that create beautiful meshes from any shape that can be loaded into VaryLab. Improve the quality of triangles or quads. Convert between triangulations and quad meshes or hex meshes. Read more...

This bundle supports parameterizations of triangle meshes. Create conformal parameterizations with different boundary conditions and singularities. Read more...

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