Make It Balance

In this program, we implemented a methodology to modify 3D objects in order to balance them on defined balance points. The methodology is described in detail in the paper: Make it stand: balancing shapes for 3D fabrication [1].

This project was built from scratch, forked from the libigl example project.

Program

A 3D object printed out, in reality, may not balance as we want it. Our program helps a user create a balanced 3D object given a specified point-of-balance and object orientation. Our program selects regions within the object that it decides will be empty when printed. As a result, this adjusts the center of mass for the object and balances it. We assume that the objects we are working with solid objects (not hollow).

Once the program is running, we can begin choosing our balancing options using the Make It Stand menu on the left. First, we configure the point of balance by clicking on object. The selected balance point will appear as a yellow dot.

Next, we adjust the rotation of the object. Rotation is defined in terms of yaw, pitch, and roll. Note that the plane shown on the screen represents the ground.

Now that we defined how our object will look statically. We can begin the carving process to make a balanced object. At first, nothing is carved, meaning that the inside of the object is full/solid.

Click the Carve button run one iteration of carving. Click the Finish Carving button to complete the carving of the image.

Implementation of Balancing

The first step to balancing an object is to discretize the object into voxels — commonly known as voxelization. Converting the object into voxels simplies the problem so that we can carve an object by removing a voxel. An important constraint to follow is that voxels within a certain distance from the border of the mesh should not be removed. This maintains the object's integrity when printed.

Next, we want to carve the object to adjust its center of mass. Having a center of mass directly above the point-of-balance would mean the object is balanced. To carve the object, we draw a plane on the point-of-balance. This plane is parallel to the direction of gravity, and perpendicular to the point-of-balance to center-of-mass vector. An illustration is shown in the paper.

One side of this plane contains the object's current center of mass. This is the side we want to remove voxels from because removing a voxel will potentially bring the center of mass closer to the plane and balance point, and make the object more balanced. Removing a voxel from the other side of the plane will always make the shape more unbalanced.

Code Summary

main.cpp

• Displays mesh objects and balancing options
• Controls the workflow of balance properties selection

inner_void_mesh.h and inner_void_mesh.cpp

• InnerVoidMesh class holds the current state of carving; e.g. holds a list of voxels, whether they are removed, etc.
• Voxel holds the definition for a voxel
• Voxalizes the mesh
• Decides which voxel to carve

list3d.h and list3d.cpp

• 3D vector wrapper. Used to hold the 3D list of voxels

center_of_mass.h and center_of_mass.cpp

• Computes the center of mass of an object

grid_util.h and grid_util.cpp

• Helper functions to help transform (translate, scale, rotate) and voxelize objects

Next Step

This implementation of 3D balancing could be improved by introducing deformation to balance the object, allowing the use of points of balance, and using polygons as bases of balance. These were features described in the paper and were left out in consideration of time.

Dependencies

The only dependencies are stl, eigen, libigl and the dependencies of the igl::opengl::glfw::Viewer.

The cmake build system will attempt to find libigl according to environment variables (e.g., LIBIGL) and searching in common desitinations (e.g., /usr/local/libigl/). If you haven't installed libigl before, we recommend you to clone a copy of libigl right here:

cd libigl-example-project/
git clone https://github.com/libigl/libigl.git

Make sure to use the --recursive flag if you're cloning this project. This will clone the submodules for this project — specifically, LIBIGL.

Compile

Compile this project using the standard cmake routine:

mkdir build
cd build
cmake ..
make

This should find and build the dependencies.

Run

From within the build directory just issue:

./make-it-stand

A glfw app should launch displaying the default bunny mesh with menu options to select the balancing options.

References

[1] Romain Prévost, Emily Whiting, Sylvain Lefebvre, and Olga Sorkine-Hornung. 2013. Make it stand: balancing shapes for 3D fabrication. ACM Trans. Graph. 32, 4, Article 81 (July 2013), 10 pages. DOI: https://doi.org/10.1145/2461912.2461957