Technical sectionFast energy-based surface wrinkle modeling
Introduction
Wrinkle modeling techniques are indispensable in numerous applications, e.g. characters in animations, clothing simulation, freeform modeling in computer aided design, etc. These techniques are particularly necessary since the users always intend to greatly enhance the modeling results with finer detail. Often, a sequence of sculpting operations performed on the existing object would lead to the desired shapes, which are encountered in many real-life objects. In many problems, this set of operations is a critical modeling component. For example, in the animation industry, computer artists need to create skin wrinkles on digital characters to make them more realistic; in a digital fashion show, realistic simulation of clothing on the characters are represented via various wrinkled shapes; a toy designer constructing and editing his work on a 3D CAD system usually enhances its model by adding wrinkles.
In all the applications of surface wrinkle modeling, we encounter two major problems: (1) the realistic representation of the wrinkled shape; and (2) the speed of wrinkle modeling. For the previous problem, the physically based modeling techniques provide very good solutions. Many energy models were developed for research in physically based modeling. These models can be loosely classified into three categories: continuum models, mass-spring models, and particle models.
The full continuum model of a deformable object considers the equilibrium of a general body acted on by external forces, such as the model proposed in some pioneering work [1], [2], [3]. Moreover, for shape editing in CAD, many authors adopt FEM with various element types and interpolation functions to solve the continuum models with more robustness and accuracy, e.g. see [4], [5]. Easier to implement and faster than FEM, other works adopt mass-spring models which are extensively used for animation of dynamic behaviors, e.g. [6], [7], [8]. However, even by the fastest mass-spring models, it is still difficult to achieve an interactive speed for the modeling of surface wrinkles, especially when the number of mesh vertices is greatly increased for more realistic models. Therefore, the later problem appears. In this paper, we are going to present a fast energy-based surface wrinkle modeling approach which can achieve the interactive speed.
We create wrinkles on the mesh surface by a curve driven shape-editing approach. It could be more clearly described by examples. As illustrated in Fig. 1, with the help of sketching tools, users can rapidly define a base curve on the surface of the given mesh (the curve in Fig. 1b); after that, another stroke for a region curve, crossing the base curve, is applied to specify the influence region (see Fig. 1c, where the influence region is illustrated by dashed lines). A governing curve is then constructed according to the base curve, where the governing curve is actually a list of particles linked by polygonal edges. The underlying energy function which represents the physical material properties of deformable objects is applied to the governing curve. To direct the wrinkle shape, users are requested to input the expected length of the governing curve and a parameter indicating the material stiffness. By computing the minimum curve energy, we can modify the geometry of a governing curve and mimic the wrinkle shape with different material properties. Figs. 1d and e shows the shapes of the governing curve before and after energy releasing. The shape of the governing curve is next propagated on the base curve and the given mesh surface through geometry-oriented techniques. The final surface wrinkles interpolate the governing curve and are attenuated while they gradually move close to the boundary of the influence region to achieve the smoothness. During the propagation, adaptive mesh refinement is integrated to enhance the wrinkle effects. The surface wrinkle is actually constructed by a set of curves (a base curve, a region curve, and a governing curve) and two parameters (the target length of governing curve and the stiffness coefficient for wrinkle shape).
Our wrinkle modeling method achieves a realistic surface wrinkle shape representing the various materials of non-rigid objects without the shortcoming of the high cost in physically based modeling. This is achieved by using the energy-based simulation to obtain the target wrinkle shape on the governing curve and the propagation of deformation via a few desirable geometry-oriented techniques. Actually, the interactive wrinkle modeling tool provided here achieves a balance of the aforementioned two problems—realistic modeling and speed, which is the major contribution of our work.
The remainder of the paper is organized as follows: we first discuss previous related work. Then we introduce the overall algorithm of our wrinkling approach, which is followed by the detailed descriptions of the particle-based curve energy model and the surface wrinkling propagation techniques. Finally, we illustrate some experimental results and show the applications of our approach to process complex models.
Section snippets
Related work
The pioneer work in computer graphics to animate deformable objects was introduced by Terzopoulos et al. [1], [3] using finite differences for the integration of energy-based Lagrange equations. Their energy functions were derived using a continuum formulation. Departing completely from continuum models, particle-based models formulate the energy function on discrete primitives. Our energy model for simulating the governing curve is essentially a particle-based curve model. The first particle
Wrinkling algorithm
The wrinkling algorithm includes two stages to perform the wrinkling deformation of the given mesh surface: (1) wrinkle shape construction and (2) surface propagation. In this section, we take the example shown in Fig. 2 to help explain the overall algorithm.
In the first stage, which is typically computed once, a base curve and a region curve are specified on the given mesh surface M (see Figs. 2a and c). These curves can be specified by either the traditional 3D curve input methods in
Particle curve model
In this section, we introduce our discrete energy model for piecewise curves. A sequence of particles is associated with a piecewise linear polygonal curve defined as governing curve as shown in Fig. 3a. The particles are assumed to be sequentially connected by rotational springs, which simulate the elastic flexure properties of curve and resist the deformation inspired by customized external energy. The model presented in this section is akin to the work of Breen et al. [8] which
Surface wrinkle modeling
As mentioned in the section of overall algorithm, the surface wrinkle is constructed in a customized region by propagating the energy functional generated governing curve. Two options to define the influence region are developed for different applications. As a mesh processing technique for finer details, the adaptive refinement is critical and offered in our approach to achieve enhanced results. Our approach also allows the manipulation with multiple sets of wrinkling curves to obtain results
Applications and experimental results
Wrinkles and creases can greatly enhance the realism of deformable objects. This section illustrates the versatility of our wrinkling tool with several experimental results that demonstrate different aspects of our wrinkle deformation technique. These results depict how our wrinkling curve is used to control the deformation, propagation on a surface, and localized to increase surface detail. Our approach is a hybrid of physically based and geometry-oriented modeling. All the operations of
Conclusion and discussion
The paper presents an energy-based approach that generates the distinct wrinkle shapes to represent the different material properties of non-rigid objects at an interactive speed. This effective technique is based on the integration of physically based and geometric-oriented modeling to achieve visually realistic results. The surface wrinkle is generated by deforming the given mesh surface according to the shape change of a user-specified governing curve on the surface. An energy function is
Acknowledgments
The authors would like to acknowledge the financial support from HKUST6234/02E project to graduate student Yu Wang during the course of this research, and thank the anonymous reviewer for the helpful comments.
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