# Interactive Blow and Burst of Giant Soap Bubbles

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Related Work in Human Interaction Using Kinect

#### 2.2. Related Work in Soap Bubble Simulation

#### 2.3. Related Work in Air Effects

## 3. System Overview

## 4. User Interaction

#### 4.1. Hand Position Acquisition

#### 4.2. Hand Trajectory

#### 4.3. Hand Velocity

## 5. Soap Bubble Simulation

#### 5.1. Surface Tension

Algorithm 1 Pseudo-code for surface tension and damping force |

1: for all springs do2: ${x}_{i}$, ${x}_{j}$: position of connected particle by spring 3: ${\overrightarrow{\mathrm{f}}}_{i}^{s}={E}_{i}\left(\Vert {x}_{i}-{x}_{j}\Vert -l\right)\frac{{x}_{i}-{x}_{j}}{\Vert {x}_{i}-{x}_{j}\Vert}$ 4: ${\overrightarrow{\mathrm{f}}}_{j}^{s}={E}_{j}\left(\Vert {x}_{j}-{x}_{i}\Vert -l\right)\frac{{x}_{j}-{x}_{i}}{\Vert {x}_{j}-{x}_{i}\Vert}$ 5: ${\overrightarrow{\mathrm{f}}}_{i}^{d}={k}_{d}\left({v}_{j}-{v}_{i}\right)\xb7\frac{{x}_{j}-{x}_{i}}{\Vert {x}_{j}-{x}_{i}\Vert}$ 6: ${\overrightarrow{\mathrm{f}}}_{j}^{d}=-{\overrightarrow{\mathrm{f}}}_{i}^{d}$ 7: end for |

#### 5.2. Air Effects

#### 5.2.1. Air Inflow

#### 5.2.2. Air Flow Transfer

Algorithm 2 Pseudo-code for Air Flow Transfer |

1: if air inflow is created2: assign $\overrightarrow{ai{r}_{i}}$ to the end particles 3: for each particle ${\mathrm{p}}_{i}$ do4: if particle ${\mathrm{p}}_{i}$ has air flow then5: for each particle ${\mathrm{p}}_{j}$ $\in $ one-ring neighborhood particles of particle ${\mathrm{p}}_{i}$ do6: if ${a}_{dir}$ > ${\lambda}_{air}$ then7: add ${\overrightarrow{\mathrm{air}}}_{i}^{f}$ to ${\overrightarrow{\mathrm{air}}}_{j}^{f}$ 8: end for9: delete ${\overrightarrow{\mathrm{air}}}_{i}^{f}$ 10: end for |

#### 5.2.3. Air Pressure

#### 5.3. Time Integration

## 6. Soap Film Bursting

#### 6.1. Hole Opening Propagation

Algorithm 3 Pseudo-code for Soap Film Bursting |

1: Capture particles of which the thickness are thinner than ${\lambda}_{thi}$ 2: Set up these particles as bursting particles. 3: Set one-ring neighborhood of bursting particles as next-bursting particles 4: Remove bursting particles and their springs. 5: if all three particles constituting the triangle are removed then6: Remove the corresponding triangle from the mesh. 7: Copy next-bursting particles to bursting particles. 8: Remove next-bursting particles. 9: Repeat step 3~8 until all particles have burst. |

#### 6.2. Position-Dependent Draining

## 7. Soap Solution Control

## 8. Experimental Results and Analysis

## 9. Conclusions and Future Work

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Photographs of a real giant soap bubble blowing and bursting. When using a tool with (

**a**) two wands and (

**b**) single wand.

**Figure 4.**(

**a**) Input hand trajectories; (

**b**) interpolated hand trajectories; and (

**c**) wand trajectories. Left hand (

**red**

**curve**), right hand (

**blue**

**curve**).

**Figure 6.**Schematic diagram of air flow transfer (starting with the end particles of the soap film, air is introduced into the adjoining soap film particles).

**Figure 10.**Simulation results (

**left**), left wand trajectory (

**middle**), right wand trajectory (

**right**). Input hand trajectory (

**dotted line**), wand trajectory (

**full line**), starting point (

**+**), end point (

**×**), current point (

**square**). When the user's hands movements are gentle (

**a**–

**c**). When user's hands movements are sudden (

**d**–

**f**).

**Figure 11.**Simulation results by our soap film bursting method. (

**a**) When using a tool with two wands; and (

**b**) when using a tool with single wand.

**Figure 13.**Results of the color coding of the strength of the air flow in Figure 12b.

**Figure 14.**Comparison of simulation results and real footage. (

**a**) The real footage and (

**b**) simulation result, respectively, when using a tool with two wands. (

**c**) The real footage and (

**d**) simulation result, respectively, when using a tool with single wand.

Example | Avg. Particle Size | Avg. Triangle Size | Avg. Time (fps) (Including Rendering) |
---|---|---|---|

Figure 10a | 9452 | 15,324 | 31.2 |

Figure 10b | 9088 | 12,542 | 35.0 |

Figure 10c | 9868 | 21,036 | 28.5 |

Figure 10d | 9252 | 14,282 | 31.3 |

Figure 10e | 16,020 | 32,568 | 20.1 |

Figure 10f | 13,882 | 28,324 | 22.5 |

Figure 11a | 13,056 | 28,112 | 23.1 |

Figure 11b | 25,650 | 41,208 | 18.1 |

Figure 12a | 10,026 | 20,328 | 26.5 |

Figure 12b | 11,328 | 23,580 | 27.3 |

Notation | Parameter Name | Range |
---|---|---|

${w}_{\mathrm{E}}$ | Varying elasticity coefficient (Section 5.1) | [12.0~13.0] |

${w}_{e}$ | Area weight (Section 5.1) | [0.02~0.05] |

${\lambda}_{air}$ | Air direction threshold (Section 5.2.2) | [0.5~0.7] |

$h$ | Time step (Section 5.3) | 0.02 |

${\lambda}_{thi}$ | Thickness threshold (Section 6.1) | [20~50] |

$Sticky$ | Viscosity of the soap solution (Section 6.2) | [20.0~30.0] |

${\lambda}_{col}$ | Colliding threshold (Section 8) | [1.5~2.0] |

© 2017 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/).

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**MDPI and ACS Style**

Kim, N.; Park, K.
Interactive Blow and Burst of Giant Soap Bubbles. *Symmetry* **2017**, *9*, 56.
https://doi.org/10.3390/sym9040056

**AMA Style**

Kim N, Park K.
Interactive Blow and Burst of Giant Soap Bubbles. *Symmetry*. 2017; 9(4):56.
https://doi.org/10.3390/sym9040056

**Chicago/Turabian Style**

Kim, Namjung, and Kyoungju Park.
2017. "Interactive Blow and Burst of Giant Soap Bubbles" *Symmetry* 9, no. 4: 56.
https://doi.org/10.3390/sym9040056