臺灣博碩士論文加值系統

因為頭髮的高硬度, 使得模擬頭髮相當地困難, 容易造成數值上的不穩定而需要較小的時間步驟來進行數值模擬.
我們觀察到一個施在一條線一端的力會轉移到其他部份產生線的變形力矩, 我們把這個行為模組化成力的移動流程, 並且簡化了特別Cosserat原理來模擬不延展的線. 我們的實驗證明我們可以穩定地模擬頭髮的動力學, 並且使得頭髮的模擬及互動可以在即時完成

Simulating hair motion is difficult due to their high-stiffness property, which usually
causes numerical stability problem and needs the numerical simulation be
performed at a small time step. We observed that a force applied to one part of
a strand will transport to other parts of the strand where the force can contribute
the deformation of the strand. We model this force transport process and simplify
the special Cosserat Theory to simulate inextensible hair strands. Our experiments
show that the proposed approach can simulate hair dynamics robustly and
efficiently such that hair simulation with user interaction can be executed in real
time.

1 Introduction 1
2 Related Work 3
2.1 Spring-Damper Model . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Rigid-body Chain Model . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Cosserat Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Strand Simulation 5
3.1 The Cosserat Model and Special Cosserat Theory . . . . . . . . . 5
3.2 Representing the State if Rod using Reduced Coordinate . . . . . 7
3.3 Force Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3.1 Tangential Force . . . . . . . . . . . . . . . . . . . . . . 9
3.3.2 Normal Force . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 Discretization and Dynamics Equation of the strand . . . . . . . 12
3.5 Dynamics Integration . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Hair Simulation 15
4.1 Hair Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Guide Hair Interpolation with GPU . . . . . . . . . . . . . . . . . 16
4.3 Collision Detection and Response . . . . . . . . . . . . . . . . . 16
5 Experiment and Result 18
5.1 Single Strand Test . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1.1 Statics Test . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1.2 Dynamics Test . . . . . . . . . . . . . . . . . . . . . . . 19
5.1.3 Curliness Test . . . . . . . . . . . . . . . . . . . . . . . . 20
5.1.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . 20
5.2 Hair Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.1 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . 21
5.3 Other Demo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 Conclusion 29
7 Appendix 30

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