Plausible cloth animation using dynamic bending model (2008) Progress in Natural Science
Abstract
Simulating the mechanical behavior of a cloth is a very challenging and important problem in computer animation. The models of bending in most existing cloth simulation approaches are taking the assumption that the cloth is little deformed from a plate shape. Therefore, based on the thin-plate theory, these bending models do not consider the condition that the current shape of the cloth under large deformations cannot be regarded as the approximation to that before deformation, which leads to an unreal static bending. [This paper introduces a dynamic bending model which is appropriate to describe large out-plane deformations such as cloth buckling and bending, and develops a compact implementation of the new model on spring-mass systems. Experimental results show that wrinkles and folds generated using this technique in cloth simulation, can appear and vanish in a more natural way than other approaches.]
1. Introduction
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Decouple the buckling deformation into two different types:
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shearing buckling
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by stretching
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structural buckling
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by compression
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A new dynamic bending model
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derived from the thin-shell theory
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describe the structural buckling
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An implementation of the model
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by the dynamic stiffness method
2. Problems in the existing cloth simulation approaches
the cloth usually shows a strong resistance to stretch and shear, but a weak resistance to bending
the bending deformation along one direction of a thin-sheet material will change the bending stiffness along other directions
Fig. 1. Different bending stiffness along the vertical direction is formed by the same piece of soft and thin material in three different shapes. (a) Very weak bending stiffness; (b) medial bending stiffness; (c) strong bending stiffness.
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the bending model
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derived from the thin-plate theory
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assumes that the new shape is just warped from a planar plate so that a constant bending stiffness is adopted
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However, taking this assumption limits the computational model to be only true to small warping
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When this model is used to simulate cloth animation which always involves large warping, the generated wrinkles and folds are fake
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derived from the thin-shell theory (Our new dynamic bending model)
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more appropriate to model large warping deformation
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a dynamic stiffness method (=implementation)
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to implement the dynamic bending model on the spring-mass systems
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which is compact and easy to integrate into the current available cloth simulator
3. Bending analysis based on thin-shell theory
There are several methods in solid mechanics to model the bending behavior of thin and soft elastic models accurately (e.g., thin-shell elements in Finite Element Analysis). However, these approaches are seldom adopted in the computer animation applications mainly for two reasons: (1) the computation is too time-consuming, and (2) it is hard to interact with other processes like collision handling.
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In the particles (or spring-mass system) based approaches
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the bending
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linear spring (the usual practice)
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converted into a linear deformation
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simulated by adding a linear spring linking the particles on two triangles sharing the same edge
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For the discretization with quadrilateral faces
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such a linear bending spring is added on the diagonal of two facets sharing only one node
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drawbacks in such simplification
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linear springs can only present the one-dimensional relationship between stress and strain but cannot mimic the two-dimensional deformation
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using a linear spring can only simulate the relationship between the bending deformation and the forces in small deformation as the relationship is actually nonlinear in large rotation and bending
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the bending deformation for cloth animation is dynamic
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During the simulation, we need to consider about the variation of bending stiffness led by the change of shape (e.g., the same material but with different shapes as shown in Fig. 1 will have different bending stiffness).
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the thin-plate theory
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widely employed in the previous cloth simulation approaches
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cons
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can only model the static bending deformation
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assumption
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every shape is just slightly deformed from a thin-plate
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the thin-shell theory
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pros
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simulate the dynamic bending
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based on the current shape of the objects
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Moment = bending stiffness * curvature = Elastic modulus *
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Young’s modulus?
Fig. 2. The bending deformation in different configurations. (a) Bending from a plate; (b) bending from a warped shell that is approximated by a cylinder, where g and g′ are the centroid, and x is the inertia axis.
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Assumptions
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that the plate is warped around the 1 axis only
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The width-thickness ratio (w/h), which is an important parameter in the later analysis of bending, usually falls in the range between 5 and 50
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The thickness (h) of fabrics is usually between 0.15 and 2 mm, and each quadrilateral facet after tessellation is with the width (w) between 1 and 2 cm
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Choosing different values for w/h will greatly affect the bending deformation result as it changes the value of inertial moment.
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the buckling of fabrics after bending is much greater than the thickness of fabrics
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simplifies the computation of inertial moments after bending
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Comparison of the bending deformations of a cylinder-shape cloth falling down by its own weight – all are with the same grids. (a) The result by Ref. [8], (b) the result by Ref. [4] with small Young’s modulus in bending, (c) the result by Ref. [4] with large Young’s modulus bending, (d) our result by the dynamic stiffness method – the small Young’s modulus as (b) is used in bending and w/h = 6 is chosen, (e) our result with w/h = 12 and the large Young’s modulus in bending as (c), and (f) our result by increasing the value of w/h from 6 to 24 while keeping all other parameters in (d).
Screen-shots from the catwalk simulation of Qipao.