Warning

This repo is still very much work in progress.

A set of grasshopper components to quadrangulate tri-meshes by merging faces using a graph-matching approach.

This stems from the need to get quad based meshes for FE-analysis. Many good tools exist to do smooth adaptable triangulations in gh but few offer "sofistik" style FE-suitable meshes. This can be done through the process of Triangulation -> Quadrangulation -> Smoothing.

The process works as follows. Given a quality triangulated mesh (in this case provided using the remeshing in this toolkit), the quadrangulation works by constructing a graph for the face connectivity, and walking this graph according to a breadth-first or depth-first search, finding a set of matchings, pairs of triangles that can be merged into quads.

An example of the process is shown below.

To generate a quadrangulated FE mesh, create a triangulation, and do a quadrangulation, followed by a smooth. Make sure to fix the nodes used for supports or edges in the smoothing process. An example file can be found in the example folder which shows the following geometry.

Left is the triangular mesh, middle the quadrangulated and right the smooth quad-mesh. The red points are pinned during the process.

This is quite work in progress still, and may be extended to feature more graph based mesh processing algorithms in the future; beyond what's needed for quadrangulation.

The repo has two projects.

• MeshGraphLib
• MeshQuadrangulationGH

The first one features a graph data structure and the processing algorithms, along with some conversion helpers to and from Rhino geometry.

The second is the gh-plugin, which for now only has two component: Quadrangulate Meshes and Laplacian Smooth

• Base graph structure
• Quadrangulation algorithm
• Laplacian smoothing (with option to fix points)
• Handle loops (faces) in graph structure
• Catmull-Clark algorithm (with option to fix points) for smoothing
• Handle non-convex matching cases.
• Expose explicit steps in process as gh components
• Implement Blossom algorithm for computing matchings.
• Grasshopper Icons
• Make algorithms etc. more modular