# GPU-based Fast Motion Synthesis of Large Crowds Using Adaptive Multi-Joint Models

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Algorithms

#### 3.1. Motion Textures

#### 3.2. Pixel Coverage of Characters

#### 3.3. Motion Synthesis

**T**,

**R**, and

**S**represent the translation, rotation, and scaling matrix, respectively, while the ${p}_{f}^{h}$ and ${p}_{f}^{l}$ are the high and low speed motion, respectively, as follows:

#### 3.4. Motion Catching

## 4. Experimental Results

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Ijaz, K.; Sohail, S.; Hashish, S. A Survey of Latest Approaches for Crowd Simulation and Modeling using Hybrid Techniques. In Proceedings of the 17th UKSIM-AMSS International Conference on Modelling and Simulation, Cambridge, UK, 25–27 March 2015. [Google Scholar]
- Cooper, A.; Cooper, S.; Popovic, Z. Continuum Crowds. ACM Trans. Graph.
**2006**, 25, 3. [Google Scholar] - Helbing, D. A fluid dynamic model for the movement of pedestrians. Complex Syst.
**1992**, 6, 391–415. [Google Scholar] - Reynolds, C.W. Flocks, Herds, and Schools: A Distributed Behavioral Model. ACM SIGGRAPH Comput. Graph.
**1987**, 1, 25–34. [Google Scholar] [CrossRef] - Berg, J.; Patil, S.; Sewall, J.; Manocha, D.; Lin, M. Interactive Navigation of Individual Agents in Crowded Environments. In Proceedings of the Symposium on Interactive 3D Graphics and Games (I3D), Redwood City, CA, USA, 15–17 February 2008. [Google Scholar]
- Barnett, A.; Shum, H.; Komura, T. Coordinated Crowd Simulation with Topological Scene Analysis. Comput. Graph. Forum
**2016**, 35, 6. [Google Scholar] [CrossRef] - Karamouzas, I.; Skinner, B.; Guy, S. A universal power law governing pedestrian interaction. Phys. Rev. Lett.
**2014**, 113, 238701. [Google Scholar] [CrossRef] [PubMed] - Karamouzas, I.; Sohre, N.; Narain, R.; Guy, S. Implicit Crowds: Optimization Integrator for Robust Crowd Simulation. ACM Trans. Graph.
**2017**, 36, 4. [Google Scholar] [CrossRef] - Kwon, T.; Lee, K.; Lee, J.; Takahashi, S. Group Motion Editing. ACM Trans. Graph.
**2008**, 27, 3. [Google Scholar] - Kim, M.; Hyun, K.; Kim, J.; Lee, J. Synchronized Multi-Character Motion Editing. ACM Trans. Graph.
**2009**, 1, 28. [Google Scholar] - Lindstrom, P.; Koller, D.; Ribarsky, W.; Hodges, L.F.; Faust, N.; Turner, G. Real-time, Continuous Level of Detail Rendering of Height Fields. In Proceedings of the ACM SIGGARPH, New Orleans, LA, USA, 4–9 August 1996. [Google Scholar]
- Rose, C.; Cohen, M.; Bodenheimer, B. Verbs and Adverbs: Multidimensional Motion Interpolation. IEEE Comput. Graph. Appl.
**1998**, 18, 5. [Google Scholar] [CrossRef] - Meredith, M.; Maddock, S. Motion Capture File Formats Explained. Available online: http://www.dcs.shef.ac.uk/intranet/research/public/resmes/CS0111.pdf (accessed on 1 February 2019).
- Stang, G. Calculus, 3rd ed.; Wellesley-Cambridge Press: Wellesley, MA, USA, 2017; ISBN 978-0980232752. [Google Scholar]

**Figure 2.**A layout of motion texture: m is the number of frames, n is the number of joints, j

_{i}is the offset of the ith joint, p

_{0}is the global position, and o

_{i}is the orientation of the ith joint.

**Figure 5.**Algorithm for joint orientation estimation: This function returns a 4 × 4 orientation matrix for given three input parameters. The parent is the index number of parent joint, the frame is the frame number of motion data, and w is the speed parameter. To calculate a joint orientation in the hierarchical joint structure for the given parameters, the algorithm blends two input motions (i.e., slow and fast motion) from the current joint to the root joint. For the blending operation, spherical linear interpolation (SLERP) is used between two input joint orientations. All the joint orientations are represented as unit quaternions.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sung, M.; Kim, Y.
GPU-based Fast Motion Synthesis of Large Crowds Using Adaptive Multi-Joint Models. *Symmetry* **2019**, *11*, 422.
https://doi.org/10.3390/sym11030422

**AMA Style**

Sung M, Kim Y.
GPU-based Fast Motion Synthesis of Large Crowds Using Adaptive Multi-Joint Models. *Symmetry*. 2019; 11(3):422.
https://doi.org/10.3390/sym11030422

**Chicago/Turabian Style**

Sung, Mankyu, and Yejin Kim.
2019. "GPU-based Fast Motion Synthesis of Large Crowds Using Adaptive Multi-Joint Models" *Symmetry* 11, no. 3: 422.
https://doi.org/10.3390/sym11030422