Angle-Based Representation of Triangulated Surfaces

We propose a novel algorithm for determining the vertex coordinates of triangle meshes from angles with given triangle connectivity. Our algorithm is capable of handling noise interior and dihedral angles by employing spectral analysis. More precisely, we formulate the shape reconstruction as an eigenvalue problem. The reconstructed shape is determined up to an affine transformation. We fix the affine transformation through a simple voting strategy. Finally, we offer an optional gradient descent to further reduce the deviation of the reconstructed angle from the input. We show the efficiency and effectiveness of our method in numerical tests.