Inverse dynamic hair modeling with frictional contact

Abstract

Figure 1: Our inversion method makes the hair synthesis pipeline consistent: (a) Raw hair geometry (a set of polylines) resulting from the manual design or the automatic capture of a static hairstyle (here, a capture from [Herrera et al. 2012]); (b) Input geometry is automatically converted into a dynamic hair model (a set of super-helices) at equilibrium under gravity and frictional hair-body and hair-hair contact forces; Unlike classical hair simulators (c) which ignore surrounding forces when initializing the hairstyle and are thus prone to undesired sagging, our simulator (b) exactly matches the original hair geometry at initial state and (d) yields a realistic, character-specific hair animation. AbstractIn the latest years, considerable progress has been achieved for accurately acquiring the geometry of human hair, thus largely improving the realism of virtual characters. In parallel, rich physics-based simulators have been successfully designed to capture the intricate dynamics of hair due to contact and friction. However, at the moment there exists no consistent pipeline for converting a given hair geometry into a realistic physics-based hair model. Current approaches simply initialize the hair simulator with the input geometry in the absence of external forces. This results in an undesired sagging effect when the dynamic simulation is started, which basically ruins all the efforts put into the accurate design and/or capture of the input hairstyle. In this paper we propose the first method which consistently and robustly accounts for surrounding forcesgravity and frictional contacts, including hair self-contacts -when converting a geometric hairstyle into a physics-based hair model. Taking an arbitrary hair geometry as input together with a corresponding body mesh, we interpret the hair shape as a static equilibrium configuration of a hair simulator, in the presence of gravity as well as hair-body and hair-hair frictional contacts. Assuming that hair parameters are homogeneous and lie in a plausible range of physical values, we show that this large underdetermined inverse problem can be formulated as a well-posed constrained optimization problem, which can be solved robustly and efficiently by leveraging the frictional contact solver of the direct hair simulator. Our method was successfully applied to the animation of various hair geometries, ranging from synthetic hairstyles manually designed by an artist to the most recent human hair data automatically reconstructed from capture.

Computational design of stable planar-rod structures

“…Derouet-Jourdan [2013] treated hair shape as a static equilibrium configuration of a hair simulator and solve an inverse problem for finding a physically valid rest shape for a given hairstyle. Twigg and Kačić-Alesić [2011] proposed a solution to the inversion problem with contact of mass-springs systems to reduce sagging in animations through nonlinear optimization.…”

An asymptotic numerical method for inverse elastic shape design

“…Derouet-Jourdan et al [2010] proposed an inverse design method for 2D dynamic curves to convert a userinput sketch into a dynamic rod model and then optimize the natural curvatures to achieve certain equilibrium states. Derouet-Jourdan et al [2013] proposed a constrained optimization method for solving the inverse static equilibrium problem of hairs subject to gravity and frictional contacts. These methods were specifically designed for slender structures.…”

“…For applications of animation control, initial shapes are often computed using fast models such as spring-mass systems [Twigg and Kačić-Alesić 2011], which are efficient but less accurate, and thus not applicable to predictive computational design tasks such as those in 3D fabrication. For rod-like geometries, solutions can be efficiently found using reduced kinematic models (e.g., [Hadap 2006;Derouet-Jourdan et al 2010;Derouet-Jourdan et al 2013]), yet no such method exists for general volumetric elastic objects. Thus existing methods for computational design and 3D fabrication (e.g., Skouras et al 2012]) typically formulate the rest shape computation as a nonlinear (constraint) optimization problem solved by a Newton-type iterative solver.…”

Capturing braided hairstyles

“…To avoid the daunting task of manipulating individual hair fibers, these systems usually provide some kinds of geometric proxy, such as guide strands or polygonal surfaces for more intuitive design and manipulation of hair [Choe and Ko 2005;Fu et al 2007;Wither et al 2007;Yuksel et al 2009;Ghoniem and Museth 2013]. Further realism can be achieved through physical simulation as a post-process [Selle et al 2008;Derouet-Jourdan et al 2013]. While it is possible to manually create braided hairstyles from scratch as demonstrated in [Yuksel et al 2009], complex and realistic ones are very difficult and time consuming to produce (often requiring up to several weeks for a skilled artist).…”