Abstract
We present a novel but simple physics-based method to interactively manipulate surface shapes of 3D models with C^1 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 C^1 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 C^1 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 C^1 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.
Highlights
Surface manipulation, known as surface or mesh editing, is the fundamental research topic in geometric modelling and computer-aided design
A popular physicsbased surface manipulation method is physics-based NURBS [7,8,9], which allows users to manipulate the surface shapes in Fig. 11, the deformation created by our proposed method well keeps the features of the boundary shapes
We obtain different deformations on each model by moving the cursor with different directions and positions to generate various shapes. These results indicate that our method is effective and convenient to create various surface shapes
Summary
Known as surface or mesh editing, is the fundamental research topic in geometric modelling and computer-aided design. In order to improve the efficiency and capability of surface manipulation, free-from deformation (FFD) methods were developed, which embed an object within a 3D lattice and simulate the deformations by moving lattice control points [3,4] Another widely used surface manipulation method is Laplacian coordinates [5,6], which describes the relation of each vertex to its local neighbourhood and modifies the derivatives of the surface to find the best-fit positions of vertices by solving a system involving the Laplacian. Since purely geometric surface manipulation methods do not follow any underlying physical laws, the quality of deformed shapes depends on the personal skills and perceptions of users, and different users may create somewhat different shapes for the same model. Physics-based methods usually involve heavy numerical calculations and slow responding time of real-time operations
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