There is considerable recent progress in physically-based simulations, driven by the high demands in computer animated movies. Realistic animations of rigid bodies, fluid, deformable objects and couplings among different objects became possible. However, simulating wetting effects between solid objects and water is still relatively in its infancy despite the fact that it is a common phenomenon in the real world. The main cause is the complexity of physical mechanism of the wetting effects. The wetting effects are interesting effects in our daily life and could greatly enrich the realism of games and animations.

An object that has water absorbency is called a porous medium. An internal structure of the porous medium consists of a solid part of the medium mixing with a vast number of pores. These pores result in the capillary action where water is absorbed into and flows through the medium. Pores inside porous media such as cloth and sponge have their locations fixed in the media, while pores in porous media such as granular material and hair are dynamically and temporally arise from complex contact regions among the media. This dissertation categorizes the former porous structure as a rigid porous structure and the latter as a deformable porous structure. Recently, novel approaches for wetting effects in the rigid porous structure have been proposed in the computer graphics field. However, only a few studies have been introduced for the deformable porous structures. Accordingly, this dissertation targets wetting effects in the deformable porous structures, especially, wetting effects in sands and hair strands which are the objects in our daily life and important in CG.

When granular material comes into contact with water, water is absorbed into pores among granular particles and diffused from particle to particle throughout the material by the influence of capillary action. Then, wet granular particles stick together due to liquid bridges that are formed between particles. The liquid bridges subsequently disappear when there is too much water penetrates into the material. The similar physical mechanism occurs in the case of hair as well. However, the wetting effects of hair are more complicated. There are three main differences from the granular material. First, a single hair strand is also a kind of porous medium. Water is absorbed not only into small contact regions among hair strands, but also into the inner layer of each hair strand. When water percolates into the inner layer of hair strand, a chemical reaction inside the strand causes the shape of the hair strand to temporally change. Second, the contact regions among hair strands are costly to examine, since a hair strand is a long cylindrical deformable object. Third, hair is an anisotropic porous medium, as water diffuses more in the hair strand direction.

To develop models for the wetting effects, the underlying simulation models for granular material and hair strands are also important. While well-studied particle systems can be used for simulating fine-scale of granular material, simulation of hair is still a challenging problem in computer graphics. Traditional simulation techniques handle hair as clumps or continuum for efficiency; however, the visual quality is limited because they cannot represent the fine-scale motion of individual hair strands. Although a recent mass-spring approach tackled the problem of simulating the dynamics of every strand of hair, it suffered from high computational cost and required a complicated setting of springs. The morphological shape transformation of wet hair requires a model that can easily modify the shape of hair, thus the recent models are not suitable. In this dissertation, the hair simulation model on such a fine-scale is built up from a novel single strand simulation model. Strand-like objects in our daily lives have a wide variety of materials, e.g., extensible and inextensible strands, rubber, threads, plastic. Such strand-like objects also exhibit interesting behaviors such as bending, twisting, tearing (by stretching or twisting), and bouncing back when pulled and released.

This dissertation presents a strand simulation model that enables these behaviors, handles wide variety of materials, and is suitable for building a hair simulation model for wetting effects. Specifically, this dissertation offers the following four contributions. First, this dissertation introduces a strand simulation model that based on Lattice Shape Matching (LSM), which has been successfully used for simulating deformable objects. Each strand is represented as a chain of particles, and its deformation are handled by geometrically-derived forces of the chain based on shape matching. The shape matching can simulate a stiff strand in a numerically stable way. This benefits in handling stiff hairstyles such as curly hair and afro. Second, this dissertation introduces a method for handling twisting effects with both uniform and non-uniform torsional rigidities. Third, this dissertation presents a method for estimating the tension acting on inextensible strands in order to reproduce tearing and flicking (bouncing back), whereas the tension for an extensible object can be computed via stretched length. The length of an inextensible object is maintained constant in general, and thus, a novel approach is needed. Fourth, this dissertation introduces an optimized grid-based collision detection for accelerating the computation. In the simulation of a large number of hair strands, this dissertation develops a GPU-based simulator which achieves visually-plausible animations consisting of several tens of thousands of hair strands at interactive rates.

For the wetting effects in granular material, this dissertation introduces a wetness value for each granular particle and integrates wet behaviors dependent on the wetness value into a simple particle-based framework. Using this method, a GPU-based simulator can achieve dynamic animations of granular material including wetting effects at interactive rates. For the wetting effects of hair, this dissertation introduces a simulation model that reproduces interactions between water and hair as a dynamic anisotropic porous medium. An Eulerian approach is utilized for capturing the complex deformable porous structure of hair and the wetting effects are efficiently handled using a Cartesian bounding grid. The proposed model and simulation generate many interesting effects of interactions between fine-detailed dynamic hair and water, i.e., water absorption and diffusion, cohesion of wet hair strands, water flow within the hair volume, water dripping from the wet hair strands and morphological shape transformations of wet hair.

本論文は7章からなり、第1章は導入として、様々な物体の吸湿現象とComputer Graphics(以下、CG)による吸湿現象についての重要性と本論文の研究テーマの位置づけ、論文における貢献について述べられている。第2章は関連研究として、従来のCGにおける吸湿現象を考慮したシミュレーション法について十分に調査し、まとめている。第3章は基礎となる手法を述べられている。

提案手法は4章から6章に亘って述べられている。第4章は、線状物体のシミュレーション法を提案している。髪の毛のような線状物体をシミュレートするために、1次元変形物体のシミュレーションモデルから構成され、一本ずつの動きをシミュレートする手法を提案している。そして、ケーブル、プラスチック糸、ゴム糸などの様々な線状物体の伸び縮み、ねじれ、断裂、および伸長時から急激に収縮するといった性質を実現する手法を提案している。また、第4章では高速化した衝突判定を提案し、高度な並列計算を得意とするグラフィックス・プロセッシング・ユニット(以下、GPU)を使用したシミュレータを開発し、数万本の髪の毛のアニメーションを対話的な速度で生成することができている。提案法は線状物体の興味深い動きを詳細でシミュレートことが可能になったことが認められる。

第5章は、吸湿現象を考慮した粒状物体について述べられている。粒状物体の各粒子に対して、水分量の値を導入し、その値に応じた粒状物体の挙動を、粒子ベースシミュレーションのフレームワークに統合する手法を提案している。また、提案手法はGPUを用い、 吸湿現象を考慮したダイナミックなアニメーションを対話的な速度で生成することができる。従来の湿現象を考慮した粒状物体のシミュレーションとは違ったより高速で詳細なシミュレーションができることが認められる。

第6章は、吸湿現象を考慮した線状物体について述べられている。髪のような線状物体を異方性の変形多孔質媒体として、水との相互作用を再現するシミュレーション法を提案している。髪を格子化することにより、髪の複雑な変形多孔質構造を扱う。直交座標系のバウンディング・グリッドを使用し、効率的に吸湿現象を実現できている。本研究では、髪の毛の吸水、水分の伝播、髪の毛が束になる様子、水がしたたり落ちる様子、濡れた髪の毛の形状変化を扱う。提案法は、詳細な髪の毛と水の相互作用の多様な興味深い効果を再現することを成功しており、その新規性と難題への挑戦は評価に値する。

最後の第7章はまとめと今後の課題について述べられている。今後の課題は、読者に適度な問題提起を残しており、研究テーマとしての拡張性と可能性を感じさせるものであった。

以上の論文内容と審査を実施した結果、論文内に記された論文提出者の主張が妥当であることを評価できる。すなわち、本論文では、吸湿現象を考慮した粒状および線状物体のシミュレーションを実現するために、適切な線状物体のシミュレーション法と粒状および線状物体の吸湿現象を扱う手法を提案している。これによりCGの分野に従来であまり考慮しなかった吸湿現象を導入し、新たな興味深い現象を再現することが可能になったことが認められる。

なお、本論文第4章は、Napaporn Metaaphanon、坂東 洋介、Bing-Yu Chen、金森 由博、西田 友是との、第5章はZoltan Szego、金森 由博、西田 友是との、第6章は、金森 由博、西田 友是との共同研究であるが、論文提出者が主体となって分析及び検証を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、博士(科学)の学位を授与できると認める。