# A Method to Compute Shadow Geometry in Open Building Information Modeling Authoring Tools: Automation of Solar Regulation Checking

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. An Overview of Shading Factor Computation

#### 2.1.1. Shadow Geometry Computation

#### 2.1.2. Shading Factor

#### 2.2. A New Method to Compute Shadow Geometry: Solid Clipping

- Identification of the building walls or elements that can cast a shadow regarding sun exposition, as in Figure 3a;
- Extrusion of a three-dimensional (3D) sun path in the direction of the wall where shadows have to be evaluated, as in Figure 3b;
- Calculation of 3D intersections of the sun path with the building to identify the parts that can generate shadows on the considered walls, as in Figure 3c;
- Extrusion of previous 3D intersections, reduced to intersection surfaces, up to the considered walls to trace and calculate the shadows, as in Figure 3d.

Algorithm 1: Algorithm to compute shadow |

**Line 1**- The $\overrightarrow{sun}$ points downward, i.e., from the sun through the face of interest F. F is extruded to the infinite along $-\overrightarrow{sun}$ to create the “solid of light” $Light$. It represents the light flux without obstruction, as shown in Figure 3a.
**Line 2**- The Boolean intersection between the solid $Light$ and all the other solid of the BIM model ($Building$) is computed and stored in $CatchedLight$. Shown in black in Figure 3c.
**Line 5 to 8****Line 10**- The Boolean union of all the $PartialShadowSurface$ (dark blue in Figure 3d) defines the face shadow ${F}_{shadow}$.

## 3. Application: Checking the RTAADOM on BIM Models

#### Validation of RTAADOM Shading Factor Computed Using BIM

## 4. Conclusions and Perspectives

#### 4.1. Extending Regulation Using BIM

#### 4.2. Research Directions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Checking of a regulation based on shading factor computation is split into three stages: (1) shadow geometry computation, (2) shading factor computation, and (3) checking regulation.

**Figure 2.**RTAADOM geometric model: (

**a**) configuration and parameters to describe overhang, (

**b**) configuration and parameters to describe fins, and (

**c**) snapshot of the translated protected spreadsheet implementing the model with overhang in orange, vertical left fin in green and vertical right fin in yellow.

**Figure 3.**Successive stages of computation for a simple 2D model: (

**a**) The model of interest with a window and a few wall elements that can cast a shadow. The vector is plotted. (

**b**) Extrusion. (

**c**) Intersection with $volumeIntersection$ in black. (

**d**) Face selection (red), extrusion of faces along (dark yellow), intersection with F gives ${F}_{shadow}$ as a patch of surface (dark blue).

**Figure 4.**(

**a**) Snapshot of a window with an overhang of depth d. (

**b**) Shading factor ${S}_{R}$ as a function of the overhang depth d for the four cardinal orientations (color) and the two computation methods (line style).

**Figure 5.**(

**a**) Snapshot of a window with an overhang and rectangular vertical fins of depth d. (

**b**) Shading factor ${S}_{R}$ as a function of the overhang and vertical fins depth d for the four cardinal orientations (color) and two computation methods (line style).

**Figure 6.**(

**a**) Snapshot of a window with an overhang and triangular vertical fins of depth d. (

**b**) Shading factor ${S}_{R}$ as a function of the overhang and triangular vertical fins depth d for the north orientation is represented by the dotted curve (labeled $ht$). The overhang with (labeled $hr$) and without (labeled h) vertical rectangular fins is added for comparison.

**Figure 7.**Snapshot of shadow computed by solid clipping for original solar protection design: (left) curved boundary parametrized by a spline, (right) rectangular shape with holes.

**Table 1.**Shading factor values computed with the spreadsheet (left) and with our approach (right) for solar protection with overhang.

Reference | BIM | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

d | North | South | East | West | d | North | South | East | West | |

0.1 | 0.91 | 0.94 | 0.95 | 0.96 | 0.1 | 0.92 | 0.96 | 0.96 | 0.96 | |

0.2 | 0.80 | 0.90 | 0.88 | 0.89 | 0.2 | 0.82 | 0.89 | 0.94 | 0.91 | |

0.3 | 0.72 | 0.88 | 0.81 | 0.83 | 0.3 | 0.75 | 0.83 | 0.92 | 0.85 | |

0.4 | 0.67 | 0.86 | 0.76 | 0.78 | 0.4 | 0.70 | 0.78 | 0.91 | 0.80 | |

0.5 | 0.64 | 0.84 | 0.70 | 0.73 | 0.5 | 0.67 | 0.73 | 0.90 | 0.76 | |

0.6 | 0.61 | 0.82 | 0.66 | 0.69 | 0.6 | 0.66 | 0.74 | 0.90 | 0.77 | |

0.7 | 0.60 | 0.81 | 0.63 | 0.66 | 0.7 | 0.65 | 0.69 | 0.89 | 0.72 | |

0.8 | 0.60 | 0.80 | 0.60 | 0.63 | 0.8 | 0.65 | 0.67 | 0.89 | 0.70 | |

0.9 | 0.59 | 0.79 | 0.58 | 0.61 | 0.9 | 0.64 | 0.66 | 0.88 | 0.68 | |

1.0 | 0.59 | 0.78 | 0.56 | 0.59 | 1.0 | 0.64 | 0.64 | 0.88 | 0.66 |

**Table 2.**Shading factor values computed with the spreadsheet (left) and with our approach (right) for solar protection with overhang and vertical fins.

Reference | BIM | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

d | North | South | East | West | d | North | South | East | West | |

0.1 | 0.66 | 0.71 | 0.80 | 0.81 | 0.1 | 0.70 | 0.84 | 0.79 | 0.87 | |

0.2 | 0.54 | 0.64 | 0.70 | 0.73 | 0.2 | 0.56 | 0.74 | 0.71 | 0.78 | |

0.3 | 0.47 | 0.59 | 0.63 | 0.66 | 0.3 | 0.46 | 0.65 | 0.64 | 0.70 | |

0.4 | 0.42 | 0.56 | 0.56 | 0.60 | 0.4 | 0.40 | 0.58 | 0.59 | 0.64 | |

0.5 | 0.38 | 0.52 | 0.51 | 0.55 | 0.5 | 0.36 | 0.53 | 0.56 | 0.58 | |

0.6 | 0.37 | 0.50 | 0.47 | 0.51 | 0.6 | 0.33 | 0.48 | 0.53 | 0.53 | |

0.7 | 0.35 | 0.48 | 0.44 | 0.47 | 0.7 | 0.32 | 0.45 | 0.50 | 0.49 | |

0.8 | 0.34 | 0.47 | 0.41 | 0.44 | 0.8 | 0.31 | 0.42 | 0.48 | 0.46 | |

0.9 | 0.34 | 0.45 | 0.38 | 0.42 | 0.9 | 0.30 | 0.39 | 0.47 | 0.43 | |

1.0 | 0.33 | 0.44 | 0.37 | 0.40 | 1.0 | 0.29 | 0.37 | 0.45 | 0.40 |

Wall Orientation | Overhang | Overhang and Fins |
---|---|---|

North | 0.037 | 0.030 |

East | 0.045 | 0.018 |

South | 0.064 | 0.036 |

West | 0.044 | 0.028 |

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## Share and Cite

**MDPI and ACS Style**

Voivret, C.; Bigot, D.; Rivière, G.
A Method to Compute Shadow Geometry in Open Building Information Modeling Authoring Tools: Automation of Solar Regulation Checking. *Buildings* **2023**, *13*, 3120.
https://doi.org/10.3390/buildings13123120

**AMA Style**

Voivret C, Bigot D, Rivière G.
A Method to Compute Shadow Geometry in Open Building Information Modeling Authoring Tools: Automation of Solar Regulation Checking. *Buildings*. 2023; 13(12):3120.
https://doi.org/10.3390/buildings13123120

**Chicago/Turabian Style**

Voivret, Charles, Dimitri Bigot, and Garry Rivière.
2023. "A Method to Compute Shadow Geometry in Open Building Information Modeling Authoring Tools: Automation of Solar Regulation Checking" *Buildings* 13, no. 12: 3120.
https://doi.org/10.3390/buildings13123120