# From BIM to Scan Planning and Optimization for Construction Control

^{*}

## Abstract

**:**

## 1. Introduction

- To compare two methods of scan position distribution (grid-based and triangular-based) and select the one that shows the most robust behavior.
- To design a method adapted to the building complexity.
- To consider acquiring vertical elements, such as beams, from a two-dimensional perspective.
- To implement a route calculation and optimization method that joins scan positions avoiding obstacles.

## 2. Related Work

#### 2.1. Scan-Planning in Indoor Environments

#### 2.2. Discretization of the Navigable Space

## 3. Methodology

#### 3.1. From 3D to 2D

_{dis}needed to represent the entire line. In elements represented geometrically by a central point and radius, such as circles and arcs, the discretization points E are generated according to the angular resolution defined by the following equation:

#### 3.2. Discretization of the Navigable Space

_{sec}determined by the robotic unit dimensions. The distance d

_{sec}is defined by the user as the minimal distance between central point of the platform and the nearest obstacle. In case of rooms connected by doors, the door width must ensure accessibility.

**P**(Figure 3a). Polygons are defined by a set of vertices organized in counterclockwise direction V = {v

_{1}, …, v

_{n}}. In case of the existence of holes in the navigable space, vertices are defined clockwise. This representation is typical from early stages of the construction process in which rooms are not still constructed, and holes are caused by the planning of stairs, elevators, pipes, etc. If rooms are represented,

**P**is decomposed in smaller navigable polygons P

_{n}(Figure 3b). This subdivision only indicates when constructed walls separate different spaces. In which case, polygons define navigable space P = {P

_{0}, …, P

_{r}}, where P

_{i}with i = 0, …, r corresponds to the polygon that represents the room i. As well as P, each P

_{i}can be defined by its vertices V

_{i}= {V

_{i1}, …, V

_{im}}, where m is the number of vertices each room/corridor.

#### 3.2.1. Grid-Based Distribution

_{n}(Figure 4a). If rooms P

_{n}are represented in the DXF, the space partition is carried out separately by each room. A local coordinate system is adopted to distribute the candidate scan positions and grid resolution is adjusted to room size (Figure 4b).

_{cand}= Vc. Grid-based methods yield uniform and dense space divisions. However, the size of candidate positions obtained from this distribution may involve higher computational costs, especially in larger scenes. The existence of holes H and a security distance d

_{sec}defined by the robotic unit are used for filtering final candidate scan positions $\left\{{S}_{cand}:{S}_{cand}\cap H\right\}\leftarrow \varnothing $ and $\{{S}_{cand}:\left|{S}_{cand},E\right|<{d}_{sec}\}\leftarrow \varnothing $, those in which the system can be placed to perform acquisition (Figure 4).

#### 3.2.2. Triangulation-Based Distribution

_{e}are necessary to generate a Voronoi diagram. Vertices V of lines defining building elements (i.e., walls) and centers of circles C (i.e., circular cross-section columns) are used as seed points for Voronoi process ${\mathrm{S}}_{\mathrm{e}}\leftarrow \left\{\mathrm{V},\mathrm{C}\right\}$. In case the distance between input points is higher than d

_{max}, new seed points S

_{e}are generated. The Euclidean distance d of each segment is calculated and compared with a distance d

_{max}. Segments d > d

_{max}are split generating new evenly spaced points. Figure 6 shows a schema of the seed generation approach. In the case of an early stage of the construction, in which the floor plan is not divided into rooms, floor contour vertices and column centers are considered as seed points. In the case of an indoor scene divided into rooms P

_{i}, each room is individually processed, analogue to Section 3.2.1. In the Voronoi process, new seed S

_{i}points in the interior of the room are generated. S

_{e}and S

_{i}are used as input for the discretization process based on a Delaunay Triangulation. This step is essential for a good distribution of candidate scan positions, especially in big rooms with simple geometry.

_{e}, S

_{i}} are obtained and Delaunay Triangulation is implemented, candidates to scan positions S

_{cand}are filtered in order to discard those candidates out of the navigable space or representing low-interest areas (Figure 7). In the first case, triangles whose centroid are outside of the navigable space are removed from the selection. This happens mainly in concave spaces. In the second case, triangles with very small angles and sides are discarded considering by angle α

_{min}Equation (2), being ${l}_{min}$ the minor side of the triangle. Also, the candidate positions must fulfil with the constrains of dimension and mobility of the robotic unit.

_{cand}and the polygon area containing them. In order to ensure an acceptable density, triangulation is iterated for those rooms with density inferior to dens

_{min}, generating new candidates.

#### 3.3. Visibility Analysis

_{cand}. This process is based on a ray tracing algorithm that simulates the laser beam and establishes the surface theoretically acquired by a laser scanner taking into account scanner range r and field of view v.

_{x},I

_{y}). Then, the cells crossed by rays simulated between laser position and target cells (all cells in the field of view and range of the laser) are calculated by Bresenham´s line algorithm [52]. After this step, visible cells for each candidate to scan position are obtained Iv.

#### 3.4. Scan Optimization

_{scan}for avoiding the acquisition of repetitive data, an optimization is performed by using a backtracking algorithm [53]. Final scan positions are determined considering the theoretical surface acquirable a from each position (Figure 9). The best scan position is the one from which a larger number of cells are visible. The rest of the scan positions are being selected based on the number of visible cells that can provide to the already selected positions ${S}_{scan}\leftarrow \{{S}_{cand}:\mathrm{max}\left(a\right)\}$. The process is repeated until a minimum of coverage c

_{min}is accomplished (stopping criteria). Since semantic information is preserved from the BIM model, scan optimization can be directed to the control of specific elements in the scene.

#### 3.5. Optimal Routing

_{scan}have to be obtained, and for this purpose, a navigable graph G = {N,E} is created. As grid-based graphs are more suitable for route calculation than triangulation-based graphs [31], the construction of the navigable graph is based on a regular grid.

_{scan}may not coincide with the location of navigable nodes N, previously calculated because this process is independent of candidate generation. In this case, scan positions are relocated to the nearest navigable nodes ${S}_{scan}\leftarrow \left\{N:min\left|N,{S}_{scan}\right|\right\}$ in order to calculate the optimal route (Figure 10b). In this way, accessibility is ensured.

_{p},E

_{p}} between each pair of scan positions is calculated using Dijkstra algorithm [56]. This information is used to create a simplified graph in which just nodes representing scan positions and distances between them are represented (Figure 11). This simplified graph G

_{s}= {N

_{s},E

_{s}} is used to implement the Ant colony optimization algorithm for obtaining the optimal path.

## 4. Results and Discussion

#### 4.1. Instruments and Data

#### 4.2. Results

#### 4.2.1. Parameters and Values

_{min}is given by the ratio of theoretical area that must be acquired from all visible area of interest. The c

_{min}parameter supposes the stop criterion in the selection of the best scanning positions. The process ends when the ratio of structural acquired elements is greater than or equal to c

_{min}.

#### 4.2.2. From 3D to 2D

#### 4.2.3. Distribution of the Navigable Space

#### 4.2.4. Visibility Analysis

#### 4.2.5. Scan Optimization

#### 4.2.6. Optimal Route

#### 4.3. Application in A Real Case Study

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Building elements considered in this work, (

**b**) elements after discretization in equidistant points.

**Figure 3.**Geometric representation of navigable space (

**a**) in case of the existence of holes and columns (blue lines), (

**b**) in case of the existence of rooms.

**Figure 4.**Schema of discretization process when using a grid-based structure (

**a**) in case of the existence of one floor space including a hole and three columns (blue lines) (

**b**) in case of the existence of rooms. Final candidate positions are in green, while discarded candidate positions are in red. Local coordinate systems are represented.

**Figure 6.**Generation of seed points S

_{e}(in blue) for triangulation process for: (

**a**) column, (

**b**) polygon with side < d

_{min}and (

**c**) polygon with side < d

_{min}.

**Figure 7.**Navigable space is partitioned by applying Delaunay triangulation process. (

**a**) Since the polygon that contains navigable space may be concave, some positions obtained after the division can fall out of navigable space (orange). Small triangles are discarded according the parameters l

_{min}and α

_{min}(yellow). (

**b**) A filtering process is conducted to retrieve positions are inside navigable space (points generated by Voronoi process are included). Subsequently, points near obstacles are discarded (red) according to the defined security distance.

**Figure 8.**Bresenham algorithm is used to determinate the map cells that are crossed by simulated beam (gray) in visibility analysis. (

**a**) target cell (red) is wrongly classified as visible since it is not occluded by other cells representing building elements, (

**b**) target point (green) is correctly classified as occluded in the ray-casting process.

**Figure 9.**Scan optimization process is carried out from candidate positions (green points) to obtain scanning positions (red points). In each iteration the candidate position is selected which maximizes the theoretically acquirable surface (red lines). The black lines represent the surface theoretically acquired from the previously selected positions.

**Figure 10.**(

**a**) Graph nodes are 8-connected by edges and the ones intersecting with any no-navigable space are removed (magenta). (

**b**) Scanning positions (red points) are relocated to nearest nodes to them (blue points with red contour).

**Figure 11.**(

**a**) A navigable graph composed by navigable (blue) and scanning (red) nodes is generated. Then, navigable nodes are abstracted from graph and (

**b**) a simpler one is represented only with scanning nodes (red).

**Figure 12.**(

**a**) A subgraph is generated separately for each room. (

**b**) The global graph consists of all subgraphs joined by new nodes corresponding to door positions (yellow).

**Figure 14.**Candidate positions generated by both discretization methods in case study 1: (

**a**) grid-based method in structural phase, (

**b**) triangulation-based method in structural phase, (

**c**) grid-based method with rooms and (

**d**) triangulation-based method with rooms. Horizontal and vertical elements are displayed in magenta and black respectively. Green points represent position reachable by robotic system, unreachable positions are depicted in red.

**Figure 16.**Visibility analysis results obtained from candidates generated in case study 1: (

**a**) grid-based candidate distribution in structural phase, (

**b**) triangulation-based candidate distribution in structural phase, (

**c**) grid-based candidate distribution with rooms and (

**d**) triangulation-based candidate distribution with rooms. Elements determined as visible for analysis process are depicted in green, black points represent no visible elements.

**Figure 18.**Visibility analysis of case study 1 original (

**a**) and rotated (

**b**). Visible elements are coloured in green, while black zones correspond to areas of element to be acquired are not visible from any candidate position.

**Figure 19.**Optimization scan position result in case study 1: (

**a**) grid-based method, (

**b**) triangulation-based method, (

**c**) grid-based with scan positions in doors and (

**d**) triangulation-based method with scan positions in doors. Color code: scan positions (red points), candidates scan positions (gray points), acquired elements (green), non-acquired elements (black).

**Figure 21.**Optimal route calculated in case study 1 whose scanning positions were obtained by: (

**a**) grid-based method in structural phase, (

**b**) triangulation-based method in structural phase, (

**c**) grid-based method with rooms and (

**d**) triangulation-based method with rooms. Horizontal and vertical elements are displayed in magenta and black respectively. Green points represent start and end scanning position, the remaining ones are depicted in red.

**Figure 23.**Optimal route calculated in case study 1 with scan positions at doorways in (

**a**) and without scan position at doorways in (

**b**). Color code: scan positions (red points), graph nodes (gray points), start-end positions (green points), scanning-door positions (orange).

**Figure 24.**Workflow of the entire process from Building Information Model (BIM) to the acquired point cloud tracking scanning plan generated by the proposed algorithm.

Type of Parameter | Parameter | Abbreviation | Value |
---|---|---|---|

Discretization resolution | d_{dis} | 50 mm | |

Laser range | r | 5 m | |

Field of view | v | 360º | |

General | Security Distance | d_{sec} | 0.7 m |

Coverage | c_{min} | 90% | |

Specifics | Resolution grid | r_{grid} | 1.0 m |

Door accessibility | door_access | 0.7 m | |

Doors as scanning position | door_scan | True/False |

Scenario | BEAMS | COLUMNS | STAIRS | WALLS | TOTAL |
---|---|---|---|---|---|

Case 1 (Structural) | 9066 | 1038 | 891 | - | 10995 |

Case 1 (Rooms) | - | 1038 | 891 | 6296 | 8225 |

Case 2 (Structural) | 6044 | 491 | 682 | - | 7217 |

Case 2 (Rooms) | - | 491 | 682 | 5690 | 6863 |

Case of Study | Scenario | Distribution | Number of Candidates | Reachable Candidates | Time (s) |
---|---|---|---|---|---|

Case 1 | Structural | Grid-based | 374 | 247 | 0.83 |

Triangulation-based | 131 | 80 | 0.33 | ||

Rooms | Grid-based | 297 | 163 | 0.83 | |

Triangulation-based | 368 | 229 | 1.06 | ||

Case 2 | Structural | Grid-based | 214 | 182 | 0.80 |

Triangulation-based | 65 | 35 | 1.10 | ||

Rooms | Grid-based | 183 | 105 | 0.79 | |

Triangulation-based | 233 | 138 | 0.68 |

Scenario | Units To Be Acquired | Method | Candidate Positions | Visible Units | Time (s) | Avg. Time (s) |
---|---|---|---|---|---|---|

Case 1 (structural) | 10104 | Grid-based | 247 | 9864 | 15.66 | 0.063 |

Triangulation-based | 80 | 9714 | 4.73 | 0.059 | ||

Case 2 (structural) | 6535 | Grid-based | 182 | 6230 | 7.73 | 0.042 |

Triangulation-based | 35 | 6173 | 1.53 | 0.043 | ||

Case 1 (Rooms) | 7334 | Grid-based | 163 | 3940 | 2.45 | 0.015 |

Triangulation-based | 229 | 4260 | 3.78 | 0.017 | ||

Case 2 (Rooms) | 6181 | Grid-based | 105 | 3193 | 1.69 | 0.016 |

Triangulation-based | 138 | 3417 | 2.18 | 0.016 |

l_rng | 5 m | 10 m | |
---|---|---|---|

Grid-based | units of visible elements | 9864 units | 9967 units |

time consumed | 15.66 s | 89.59 s | |

Triangulation-based | units of visible elements | 9714 units | 9963 units |

time consumed | 4.73 s | 21.18 s |

Scenario | Method | Candidate Positions | Scanning Positions | Acquired (%) | Time (s) |
---|---|---|---|---|---|

Case 1 (structural) | Grid-based | 247 | 10 | 90.67 | 1.94 |

Triangulation-based | 80 | 10 | 90.71 | 0.58 | |

Case 2 (structural) | Grid-based | 182 | 7 | 90.48 | 0.92 |

Triangulation-based | 35 | 7 | 90.07 | 0.17 | |

Case 1 (Rooms) | Grid-based | 163 | 17 | 90.36 | 1.36 |

Triangulation-based | 229 | 19 | 90.71 | 2.19 | |

Case 2 (Rooms) | Grid-based | 105 | 13 | 92.48 | 0.71 |

Triangulation-based | 138 | 14 | 90.31 | 0.97 |

Scenario | Method | Scanning Positions | Time Graph Generation (s) | Route Distance (m) | Time Route Calculation (s) |
---|---|---|---|---|---|

Case 1 (structural) | Grid-based | 10 | 2.35 | 55.61 | 0.15 |

Triangulation-based | 10 | 2.38 | 57.02 | 0.15 | |

Case 2 (structural) | Grid-based | 7 | 1.58 | 42.42 | 0.06 |

Triangulation-based | 7 | 1.55 | 44.59 | 0.05 | |

Case 1 (Rooms) | Grid-based | 17 | 3.02 | 103.99 | 0.63 |

Triangulation-based | 19 | 4.27 | 100.34 | 0.94 | |

Case 2 (Rooms) | Grid-based | 13 | 1.87 | 88.10 | 0.29 |

Triangulation-based | 14 | 1.89 | 87.27 | 0.35 |

© 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**

Frías, E.; Díaz-Vilariño, L.; Balado, J.; Lorenzo, H. From BIM to Scan Planning and Optimization for Construction Control. *Remote Sens.* **2019**, *11*, 1963.
https://doi.org/10.3390/rs11171963

**AMA Style**

Frías E, Díaz-Vilariño L, Balado J, Lorenzo H. From BIM to Scan Planning and Optimization for Construction Control. *Remote Sensing*. 2019; 11(17):1963.
https://doi.org/10.3390/rs11171963

**Chicago/Turabian Style**

Frías, Ernesto, Lucía Díaz-Vilariño, Jesús Balado, and Henrique Lorenzo. 2019. "From BIM to Scan Planning and Optimization for Construction Control" *Remote Sensing* 11, no. 17: 1963.
https://doi.org/10.3390/rs11171963