# Three-Dimensional Engine-Based Geometric Model Optimization Algorithm for BIM Visualization with Augmented Reality

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### BIM-AR Integration

## 2. Background

#### 2.1. Model Optimization Methods

#### 2.1.1. Quadrics Error Metrics Method

#### 2.1.2. Curvature Calculation-based Check Method for Border Mesh

_{1}) and Q(v

_{2}) are the quadrics related to vertices v

_{1}and v

_{2}, respectively; W

_{b}is a user-defined weight factor; k(v

_{1}) and k(v

_{2}) are the curvatures of the boundary at vertices v

_{1}and v

_{2}, respectively; and Q

_{bcp}is a quadric of the boundary constraint plane at the edge (v

_{1},v

_{2}).

## 3. Materials and Methods

#### 3.1. Geometric Model Optimization for BIM

#### 3.1.1. Mesh Reconstruction Method

#### 3.1.2. Barycentric Coordinates-Based Triangle Centroid Formula

#### 3.2. Test-Bed Specifications and 3D Modeling

## 4. Results

#### 4.1. Validation of Mesh Reconstruction Method for Bridge

#### 4.2. Validation of Mesh Reconstruction Method for Building

#### 4.3. AR Visualization Test of the Optimized Models

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Conceptual framework of 3D engine-based geometry optimization for augmented reality (AR) visualization.

**Figure 5.**Triangle centroid formulation by Abraham Albert Ungar in August 2010 [35].

**Figure 6.**Three-dimensional modeling process for SKKU steel bridge and No. 2 engineering building. Real environment: (

**a**) bridge, and (

**b**) building. Model in Revit: (

**c**) bridge, and (

**d**) building. Model in Unity: (

**e**) bridge, and (

**f**) building.

**Figure 7.**SKKU steel bridge models and internal glass structure (mesh-form): (

**a**) original and (

**b**) optimized.

**Figure 8.**SKKU No. 2 engineering building models and internal round-column structure (mesh form): (

**a**) original, and (

**b**) optimized.

Model | Category | Original | Optimized | Improvement (%) |
---|---|---|---|---|

SKKUsteel bridge | Number of vertices | 590,942 | 255,625 | ↓56.7 |

Number of triangles | 335,564 | 107,573 | ↓67.9 | |

File size (KB) | 50,535 | 13,451 | ↓73.4 |

Model | Category | Original | Optimized | Improvement (%) |
---|---|---|---|---|

SKKU No. 2 engineering building | Number of vertices | 4,183,198 | 2,235,879 | ↓46.6 |

Number of triangles | 3,231,090 | 1,336,165 | ↓58.6 | |

File size (KB) | 364,761 | 124,173 | ↓66.0 |

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**MDPI and ACS Style**

Aung, P.P.W.; Choi, W.; Kulinan, A.S.; Cha, G.; Park, S.
Three-Dimensional Engine-Based Geometric Model Optimization Algorithm for BIM Visualization with Augmented Reality. *Sensors* **2022**, *22*, 7622.
https://doi.org/10.3390/s22197622

**AMA Style**

Aung PPW, Choi W, Kulinan AS, Cha G, Park S.
Three-Dimensional Engine-Based Geometric Model Optimization Algorithm for BIM Visualization with Augmented Reality. *Sensors*. 2022; 22(19):7622.
https://doi.org/10.3390/s22197622

**Chicago/Turabian Style**

Aung, Pa Pa Win, Woonggyu Choi, Almo Senja Kulinan, Gichun Cha, and Seunghee Park.
2022. "Three-Dimensional Engine-Based Geometric Model Optimization Algorithm for BIM Visualization with Augmented Reality" *Sensors* 22, no. 19: 7622.
https://doi.org/10.3390/s22197622