关键词: 变形网格, 织物模拟, 织物悬垂, 悬垂系数, 悬垂不匀

Abstract:

Objective In allusion to the stitch of constrained fabric simulation, this paper proposes a deformable mesh for reproducing the drape profile of fabric. Aiming to represent the dynamic process rather than static form of the fabric drape, the mesh model is featured with kinetic parameters and an evolution process to enable shape change over time.

Method In the mesh model, the constraints inside the fabric were built up through a constraint factor as well as an attenuation factor, and the contact between the fabric flexible body and the rigid plane was performed with a Touch-Counteract mechanism. The forces on the particles in the mesh, which were calculated with mesh deformation, were then used to generate the further displacement of the mesh. The evolution of the mesh was brought up by step-by-step iteration to introduce draping kinetics of the virtual fabric.

Results The drape profile of virtual fabric is achieved as the evolution processs meets its steady state. The drape coefficient is then worked out through identifying and quantifying the projection area of the mesh. The impact of the constraint factor and the attenuation factor on the drape coefficient are investigated, which has revealed the features and range of the model parameters capability. With lower attenuation factor (e=0.6), larger drape coefficient can be brought about while the range of the drape is narrow, and the drape is mainly affected by the attenuation factor and the effect from the constraint factor is relatively minor. When the attenuation factor grows (e=1.2 or e=2.4), smaller drape can be achieved while the range of the drape gets broader, and the constraint factor becomes more influential. When the attenuation factor goes up to 3.6 plus, the range of the drape turns to shrink, and the influence from the constraint factor recedes again. The upper limit of the range for the drape approximates 1.0 when the attenuation factor gets close to zero, and the lower limit of the range approaches 0 when the attenuation factor grows. Therefore, the theoretical range (0,1) of the drape coefficient gets fully covered with the mesh. Concerning the unevenness ripples, the reason for real fabric is discussed and reduced into the mechanical anisotropy. By emulating anisotropy through the differentiated constraint factors, the uneven appearance along the draping surface is manipulated and manifested. Finally, the precise of the model is boosted with respect to the mesh scale as well as the evolution algorithm, and a sensible mesh scale value 57 has been figured out for balancing between the simulation effect and the resource consumption. By employing the third-order Tylor expansion, the computational error is minished and the precision of the evolution algorithm is raised up to O(Δt⁴).

Conclusion It has turned out in the simulation experiments this mesh to be a simple, fast and precise model for expressing fabric draping. In the mesh model, the constraint factor and the attenuation factor together have been testified to be a compact approach to expressing the mutual effects between different parts of the real fabric. By recognizing and quantifying the projection area, the drape coefficient of the virtual fabric well meet the theoretic range of it. The drape coefficient has been found positively related to the constraint factor, and negatively related to the attenuation factor, and the latter has comparatively more impact on the drape coefficient. There are two kinds of precision involved in this model, i.e., the mesh precision and the algorithm precision. The former is determined by the mesh scale, and an appropriate scale has proved to be a trade-off between precision and efficiency considering the rapid growth of computational resource demand along the scale. While the algorithm precision can be improved significantly with the third-order Tylor expansion.

Key words: deformable mesh, fabric simulation, fabric drape, drape coefficient, drape unevenness