Direct 3D coordinate transformation based on the affine invariance of barycentric coordinates

Coordinate transformation is indispensable to unify the three-dimensional (3D) points between different coordinate systems. Traditional methods are generally two-step work: transformation parameter estimation and coordinate transformation. Unlike traditional methods, this paper proposes a direct 3D coordinate transformation method based on the affine invariance of barycentric coordinates. The proposed method avoids solving transformation parameters and requires neither the initial values nor the iterations. Experiments based on LiDAR point cloud registration and coordinate transformation demonstrate that the proposed method can reach or even outperform traditional methods, and is suitable for both similarity and affine transformation of 3D points with strong anisotropic scaling.