Toplet

Voxel-based topology optimization toy solver for Rhino.

Toplet is a toy solver intended for experimentation and learning. It is not numerically robust or validated for engineering use. It implements a simplified, voxel-based solver inspired by the classic Top99 algorithm (Ole Sigmund), adapted for interactive use directly inside the Rhino viewport.

The goal is not production-grade analysis, but a clear and flexible environment for exploring topology optimization concepts within a CAD workflow.

Status: active WIP, and honestly a bit messy under the hood — the solver internals have been rewritten several times chasing a setup that actually works, and that hasn't landed yet. The Rhino/Grasshopper-side workflow works end to end; the solvers themselves don't produce valid results yet — still tuning methods and parameters. See Commands below for what the plugin does, and Solver backends for what's still unresolved under the hood.

Commands

Toplet adds two Rhino commands:

• Toplet2D (Toplet2DCommand.cs) — takes a closed curve and voxelizes the region it encloses into a 2D grid.
• Toplet3D (Toplet3DCommand.cs) — takes a closed Brep and voxelizes its interior into a 3D grid.

Both then follow the same workflow: set point/face loads and supports on the voxelized domain, run a solve, and view the resulting material-density result in the Rhino viewport.

Solver backends

Each solve ultimately comes down to solving a large sparse linear system, and there are a few different ways to do that:

• Conjugate Gradient (CG) with an incomplete-Cholesky preconditioner — Eigen's built-in implementation. Straightforward, no setup cost, but doesn't scale well as grid size grows.
• Geometric multigrid (GMG), hand-rolled for this project, used as a CG preconditioner — builds an explicit coarse-grid hierarchy over the voxel domain to accelerate convergence at larger grid sizes.
• AMGCL — a vendored algebraic multigrid library (TopletSolverNative/include/amgcl/). Algebraic multigrid builds its hierarchy from the matrix itself rather than an explicit geometric grid, so it doesn't need the hand-tuned coarsening logic GMG does here.

Right now, solve_2d.cpp uses the first and solve_3d.cpp uses the second; AMGCL is vendored but not wired into either. That pairing isn't settled — which backend ends up serving which command is still an open question, not a deliberate or final choice. The one active comparison is GMG vs. AMGCL for the 3D backend specifically; neither has been declared a winner. The main open problem is getting a solve to converge to a valid result fast enough to be usable interactively, not just fast in isolation.

How it works

• TopOpt2D/ / TopOpt3D/ — Rhino command implementations (Toplet2DCommand.cs, Toplet3DCommand.cs) and their supporting types: domain/problem/result POCOs, voxelization (VoxelDomainBuilder3D), support-connectivity filtering, viewport display.
• Interop/ — the P/Invoke boundary to the native solver: marshals mask/force/constraint arrays across, runs the solve on a background task while a progress dialog owns the UI thread, and unpacks the result back into managed arrays.
• TopletSolverNative/ — the native C++ solver core (SIMP + optimality-criteria update + sensitivity filter), built as a separate DLL and loaded by the C# plugin at runtime. Eigen and AMGCL are vendored in include/ rather than pulled via a package manager, since there's no native C++ package manager as standard in the Rhino plugin ecosystem as NuGet is for .NET.

Building

• C# plugin: .NET Framework 4.8, RhinoCommon 7.0.20314.3001 (pinned in Toplet.csproj).
• Native solver: Visual Studio 2022 (v143 toolset), C++17, x64 only. Build this project first — the C# plugin P/Invokes the resulting TopletSolverNative.dll at runtime and won't find it otherwise.
• From the command line, build both with an explicit platform:

  MSBuild Toplet.sln /t:Restore,Build /p:Configuration=Debug /p:Platform=x64
  

  Toplet.sln only defines a Build.0 mapping for TopletSolverNative under x64 — omitting /p:Platform=x64 silently builds just the C# project and skips the native one with no error.
• Properties/launchSettings.json assumes Rhino is installed at its default location (C:\Program Files\Rhino 7 or Rhino 8) — edit the profile's executablePath if yours lives elsewhere.

Features

• Voxelized optimization domain from a closed curve (2D) or closed Brep (3D)
• Point and face-based constraints
• Point loads/supports for localized control
• Face loads/supports with distributed forces along surface normals
• Compliance-driven material distribution (SIMP-style)
• Direct Rhino interaction for geometry and constraint setup

Roadmap

1. Solver validity (current) — get 2D and 3D both converging to a physically sensible result; resolve the GMG-vs-AMGCL trade study for the 3D backend. Whether 2D should end up on the same backend as 3D is an open question, not yet decided.
2. Performance — once results are valid, get the solve loop fast enough for interactive use at useful grid resolutions.
3. Everything else — UI polish, more constraint types, is on hold until the solver itself is trustworthy.

License

MIT — see LICENSE. The vendored Eigen (MPL2) and amgcl (MIT) libraries under TopletSolverNative/include/ retain their own upstream licenses.

Attribution

Based on the Top99 topology optimization method: Ole Sigmund, A 99 line topology optimization code written in MATLAB.