TopoLite

TopoLite is a cross-platform tool for creating topological interlocking shell structures. It supports surface tiling, contact detection, globally interlocking verification, rigid body equilibrium, and topological interlocking block generation.

Complete documentation about the software is provided here

Abstract

We study assemblies of convex rigid blocks regularly arranged to approximate a given freeform surface. Our designs rely solely on the geometric arrangement of blocks to form a stable assembly, neither requiring explicit connectors or complex joints, nor relying on friction between blocks. The convexity of the blocks simplifies fabrication, as they can be easily cut from different materials such as stone, wood, or foam. However, designing stable assemblies is challenging, since adjacent pairs of blocks are restricted in their relative motion only in the direction orthogonal to a single common planar interface surface. We show that despite this weak interaction, structurally stable, and in some cases, globally interlocking assemblies can be found for a variety of freeform designs. Our optimization algorithm is based on a theoretical link between static equilibrium conditions and a geometric, global interlocking property of the assembly-that an assembly is globally interlocking if and only if the equilibrium conditions are satisfied for arbitrary external forces and torques. Inspired by this connection, we define a measure of stability that spans from single-load equilibrium to global interlocking, motivated by tilt analysis experiments used in structural engineering. We use this measure to optimize the geometry of blocks to achieve a static equilibrium for a maximal cone of directions, as opposed to considering only self-load scenarios with a single gravity direction. In the limit, this optimization can achieve globally interlocking structures. We show how different geometric patterns give rise to a variety of design options and validate our results with physical prototypes.

Please check our Topo2019SigA paper for more technical details.

GUI Interface

Compilation

Clone the repository, run CMake to generate Makefiles or CMake/Visual Studio project files, and the rest should just work automatically.

MacOS:

Xcode >= 11.5 (C++ 17)

$ brew install ipopt
$ mkdir build
$ cd build
$ cmake -DCMAKE_BUILD_TYPE=Release ..
$ make -j 16

Ubuntu(Linux):

gcc >= 7.5.0 (C++ 17)

$ sudo apt-get install libglu1-mesa-dev
$ sudo apt-get install libxxf86vm-dev
$ sudo apt-get install libxrandr-dev
$ sudo apt-get install libxinerama-dev
$ sudo apt-get install libxcursor-dev
$ sudo apt-get install libxi-dev
$ sudo apt-get install libx11-dev
$ sudo apt-get install coinor-libipopt-dev

$ mkdir build
$ cd build
$ cmake -DCMAKE_BUILD_TYPE=Release ..
$ make -j 16

the integer following make -j is the number of threads supported by your CPU architecture. Replace it with your optimal value.

Windows: currently unavailable.

Documenting the code

MacOS/Linux

pip install sphinx
cd docs/
make html

The generated documents is in docs/_build

License

MIT License

Copyright (c) 2020 LGG Computer Graphics and Geometry Laboratorty, EPF Lausanne

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

tangbohu / RigidBodyEquilibrium