## Real-time surface manipulation with C<sup>1</sup> continuity through simple and efficient physics-based deformations

**Authors: **Wang, S., Xiang, N., Xia, Y., You, L. and Zhang, J.

**Journal:** Visual Computer

**Volume:** 37

**Issue:** 9-11

**Pages:** 2741-2753

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-021-02169-4

**Abstract:**

We present a novel but simple physics-based method to interactively manipulate surface shapes of 3D models with C1 continuity in real time. A fourth-order partial differential equation involving a sculpting force originating from elastic bending of thin plates is proposed to define physics-based deformations and achieve C1 continuity at the boundary of deformation regions. In order to obtain real-time physics-based surface manipulation, we construct a mapping relationship between a deformation region in a 3D coordinate space and a unit circle on a 2D parametric plane, formulate corresponding C1 continuous boundary conditions for the unit circle, and obtain a simple analytical solution to describe the physics-based deformation in the unit circle caused by a sculpting force. After that, the obtained physics-based deformation is mapped back to the 3D coordinate space, and added to the original surface to create a new surface shape with C1 continuity at the boundary of the deformation region. We also develop an interactive user interface as a plug-in of the 3D modelling software package Maya to achieve real-time surface manipulation. The effectiveness, easiness, real-time performance, and better realism of our proposed method is demonstrated by testing surface deformations on several 3D models and comparing with other methods and ground-truth deformations.

http://eprints.bournemouth.ac.uk/35698/

**Source:** Scopus

## Real-time surface manipulation with C-1 continuity through simple and efficient physics-based deformations

**Authors: **Wang, S., Xiang, N., Xia, Y., You, L. and Zhang, J.

**Journal:** VISUAL COMPUTER

**Volume:** 37

**Issue:** 9-11

**Pages:** 2741-2753

**eISSN:** 1432-2315

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-021-02169-4

http://eprints.bournemouth.ac.uk/35698/

**Source:** Web of Science (Lite)

## Real-time surface manipulation with C1 continuity through simple and efficient physics-based deformations

**Authors: **Wang, S., Xiang, N., Xia, Y., You, L. and Zhang, J.

**Journal:** Visual Computer

**Volume:** 37

**Pages:** 2741-2753

**ISSN:** 0178-2789

**Abstract:**

We present a novel but simple physics-based method to interactively manipulate surface shapes of 3D models with C1 continuity in real time. A fourth-order partial differential equation involving a sculpting force originating from elastic bending of thin plates is proposed to define physics-based deformations and achieve C1 continuity at the boundary of deformation regions. In order to obtain real-time physics-based surface manipulation, we construct a mapping relationship between a deformation region in a 3D coordinate space and a unit circle on a 2D parametric plane, formulate corresponding C1 continuous boundary conditions for the unit circle, and obtain a simple analytical solution to describe the physics-based deformation in the unit circle caused by a sculpting force. After that, the obtained physics-based deformation is mapped back to the 3D coordinate space, and added to the original surface to create a new surface shape with C1 continuity at the boundary of the deformation region. We also develop an interactive user interface as a plug-in of the 3D modelling software package Maya to achieve real-time surface manipulation. The effectiveness, easiness, real-time performance, and better realism of our proposed method is demonstrated by testing surface deformations on several 3D models and comparing with other methods and ground-truth deformations.

http://eprints.bournemouth.ac.uk/35698/

**Source:** BURO EPrints