Generates mesh deformation using cage-based or variational deformation methods based on Polynomial Green Coordinates. The repository contains the source code for the research paper: http://staff.ustc.edu.cn/~fuxm/projects/CurvedGreen/Poly3DGreen.pdf

• Eigen (Recommended version: 3.3.8)
• OpenMesh (Recommended version: 10.0 static)
• Qt (Recommended version: 5.14.2)
• Boost (Recommended version: 1.86.0)

git clone -b master git@github.com:xiongyuwu\PolynomialGreenCoordinate.git
cd PolynomialGreenCoordinate

Edit lines 14-16 of CmakeLists.txt to set the values of EIGEN_PATH,OPENMESH_PATH and OPENMESH_LIB_PATH.

Edit line 23 of CmakeList.txt to set the value of CMAKE_PREFIX_PATH to help find Qt.

Edit line 34 of CmakeList.txt to set the value of BOOST_ROOT to help find Boost.

To avoid modifying CMakeLists.txt, you can install the required libraries in the following default locations:

Eigen 3.3.8: D:/ProgramFiles/eigen-3.3.8

OpenMesh 10.0 (Static): D:/ProgramFiles/OpenMesh 10.0 static

Qt 5.14.2: D:/ProgramFiles/Qt/5.14.2

Boost 1.86.0: D:/ProgramFiles/boost_1_86_0

mkdir build && cd build
cmake -A x64 ..

To view more information and outputs, enable Debug mode:

mkdir build && cd build
cmake -A x64 -DDEBUG_MODE=ON ..

Open PolynomialGreenCoordinate.sln, select PolynomialGreenCoordinate as the startup project, and run.

Store the cage mesh as "cage.obj" in the \PolynomialGreenCoordinate\build directory.

The default deformed cage uses 3rd-order Bézier facets. To change the facet order, modify the variable "control_point_per_edge" in \PolynomialGreenCoordinate\src\MeshViewer\PGC.h.

For variational deformation, place all constraint files ("fixed_vertices.txt", "position_constraints.txt", "polyline.off", "orientation_constraints.txt") in the \PolynomialGreenCoordinate\build directory.

To generate cage-based deformation using precomputed control points, store the control points data in "deformed_control_points.obj" and place it in the \PolynomialGreenCoordinate\build directory.

• Select File → Open to load the controlled mesh (.obj/.off/.ply/.stl)
• Click "Change Cage Mode Tri/Quad" button if the cage is a triangular mesh
• Click "Read Cage From File" button to load the cage
• Click "Draw Control Point" button to visualize control points
• Click "Draw Cage" button to visualize the cage
• Click "Draw Move Vertices Action" button to visualize position constraints
• Click "Generate Deformed Mesh" for cage-based deformation using current control points
• Click "Record Origin Mesh" button to compute and save integral parameters for cage-based deformation
• Click "Compute Para For Control Points" button to compute integral parameters for variational deformation
• Click "Read Integral Para From Files" button to load precomputed parameters
• Click "Generate Deformation By Control Points" button to generate cage-based deformation from "deformed_control_points.obj"
• Click "Optimize Control Points" button to generate variational deformation from constraints
• Click "Generate Variational Deformation" button to generate deformation with SVD decomposition
• Click "Generate Para Complete Flow" button for complete variational deformation workflow
• Click "Move Control Point" button for real-time cage deformation by moving control points
• Click "Move Position Constraints" button for real-time variational deformation
• Click "Select Move Control Points" button to select multiple control points, then use "Move Control Points" button to deform
• Click "Clear Selected Points" button to clear selections

Real-time cage-based deformation (triangular cage):

1. Place "cage.obj" in \PolynomialGreenCoordinate\build
2. Load controlled mesh
3. Click "Change Cage Mode Tri/Quad"
4. Click "Read Cage From File"
5. Click "Record Origin Mesh"
6. Click "Read Integral Para From Files"
7. Click "Draw Control Point" and "Draw Cage"
8. Click "Move Control Point" and drag control points

Real-time variational deformation (triangular cage):

1. Place "cage.obj" and constraint files in \PolynomialGreenCoordinate\build
2. Load controlled mesh
3. Click "Change Cage Mode Tri/Quad"
4. Click "Read Cage From File"
5. Click "Generate Para Complete Flow"
6. Click "Draw Move Vertices Action"
7. Click "Move Position Constraints" and drag constraints

fixed_vertices.txt

#One line of integers, strore mesh vertex indices that need to fixed
0 1 2 3 4 5 6

position_constraints.txt

#Lines of integers and floats. For each line, the first number is an integer that represents a mesh vertex index, and the following three floats represents the corresponding target position.
0 0.0 0.0 0.0
1 1.0 2.0 3.0
10 3.0 2.0 1.0

polyline.off

#An off file that contains points that represents the medial axis of mesh. This will be used as rigidity constraints in variational deformation.
OFF
0 0 0
0 0 0.5
0 0 1
0 0 1.5
0 0 2

orientation_constraints.txt

#Lines of integers and floats. For each line, the first number is an integer that represents a mesh vertex index, and the following nine floats represents the corresponding target orientaion matrix.
0 1.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 3.0
10 2.0 0.0 0.0 0.0 0.5 -0.866 0 0.866 0.5

Sample datasets are available in the model directory. Each dataset includes a mesh and its control cage. Some also contain deformed control points (for cage-based deformation) or constraints (for variational deformation). These resources enable reproduction of our paper's results.

The demo directory contains giraffe.png (reference figure from our paper) and a script to generate its corresponding mesh. Run demo.exe to verify results, with outputs saved in deformed_mesh.obj.