This project focuses on the implementation of Green Coordinates in 2D and extends its contributions by introducing an algorithm for Green Coordinates in 3D. Green Coordinates, as proposed by Yaron Lipman in his research paper, provide a user-friendly tool for cage-based deformation in graphics modeling, texturing, and geometric modeling.
The primary objective of this project is to develop an efficient algorithm for implementing Green Coordinates in 2D scenarios. The 2D implementation enables shape-preserving space deformations through conformal mappings. The project involves the derivation of closed-form expressions for the coordinates, resulting in a straightforward and efficient algorithm. The effectiveness of the implemented algorithm is evaluated by comparing it with other barycentric coordinate techniques for mesh deformation.
In addition to the 2D implementation, the project extends its scope by implementing the algorithm for Green Coordinates in 3D. This algorithm utilizes Green Coordinates to achieve quasi-conformal mappings in 3D space. Closed-form expressions for the coordinates are derived, enabling a simple and efficient algorithm for cage-based space deformation in three dimensions.
- Implementation of Green Coordinates in 2D for shape-preserving space deformations.
- Extension to Green Coordinates in 3D for quasi-conformal mappings.
- Derivation of closed-form expressions for efficient algorithms in both 2D and 3D scenarios.
- Evaluation of algorithm effectiveness through comparisons with other barycentric coordinate techniques for mesh deformation.
The project provides valuable insights and tools for graphics modeling, texturing, and animation in computer graphics applications. Users can explore the implemented algorithms for both 2D and 3D scenarios and evaluate their effectiveness in comparison to alternative techniques.
To use the project, follow these steps:
- Clone the repository:
git clone https://github.com/your-username/green-coordinates-project.git - Navigate to the project directory:
cd green-coordinates-project - Explore the source code and documentation to understand the implemented algorithms.
- Run the provided examples or integrate the algorithms into your graphics applications.
Contributions, bug reports, and feature requests are welcome! Feel free to open issues or submit pull requests.
This project is under the MIT License.