Holomorphic Coordinates for Conformal Deformations Using Point Handles

摘要

A cage enclosing a shape is required by cage-based deformation methods to deform the shape. In order to avoid constructing such a cage, we propose holomorphic coordinates that directly take user-specified shape points as handles, and produce conformal deformations for 2D shapes. These handles move to the exact locations that the user specifies. We also propose an algorithm to solve these holomorphic coordinates in a least-squares sense by constructing harmonic and conjugate constraints defined in a grid. Our experiments have shown that numerical errors are close to zero, and the deformed shapes can be reconstructed at an interactive rate.