Title :
2D Shape Manipulations with Holomorphic Coordinates
Author :
Li, Zheng ; Liu, Chengming
Author_Institution :
Sch. of Comput., Guangdong Univ. of Technol., Guangzhou, China
Abstract :
Cage-based deformation methods require an enclosing cage to deform a shape, which is not user-friendly. In this paper, we propose holomorphic coordinates that directly take user-specified shape points as handles to produce visually promising conformal deformations for 2D shapes. Based on the theory of holomorphic functions, holomorphic coordinates promise the interpolation and smoothness properties on the shape. Namely, handle points can be moved to the exact locations that the user specifies, and the deformations are smooth all over the shape. We also suggest an algorithm to solve holomorphic coordinates on a grid in a least-squares sense by constructing harmonic and conjugate constraints. Experiments have shown that the numerical errors are close to zero, and deformed shapes can be obtained at an interactive rate.
Keywords :
computational geometry; deformation; interpolation; least squares approximations; 2D shape manipulations; 2D shapes; cage-based deformation methods; conformal deformations; conjugate constraints; harmonic constraints; holomorphic coordinates; holomorphic function theory; interpolation properties; numerical errors; smoothness properties; user-specified shape points; Conformal mapping; Equations; Green products; Harmonic analysis; Interpolation; Mathematical model; Shape; conformal deformations; coordinates; holomorphic functions; shape manipulations;
Conference_Titel :
Digital Home (ICDH), 2012 Fourth International Conference on
Conference_Location :
Guangzhou
Print_ISBN :
978-1-4673-1348-3
DOI :
10.1109/ICDH.2012.26