### Conceptual Model

### Spaces

Concept |
Denotation |
Discretization for the operational model |

Viewing Space | ||

The space of the possible viewpoints (people, cameras ...) | Set of points. Tendentiously all the points will represent the same amount of space, but they can have a different volume. And, as there can be some differences in the density of viewing agents per volume, there is also a weight attribute. | |

Viewed Space | ||

Surfaces | Surfaces of the objects in the 3D global volume | Set of points, centroids of little homomorphic triangles in which the triangles that shape the surfaces are divided. |

Global Volume | The entire 3D global volume | Set of points. Although data representation does not imposes any other restriction, the user interface guides to equal amount of space for each point. Global space is cut in axial (X, Y and Z) slices of equal thickness in each axis. Nevertheless, the thickness can be different from axis to axis. |

Obstacle space | ||

Volume opacity | A continuous loss of visibility throughout the 3D global volume (fog, optical effects ...) | |

Surfaces | Surfaces with a certain degree of opacity | Set of triangles, modelling the surfaces. |

### Primitive Functions

Concept |
Counter-domain |
Denotation |

Distance | set of real-numbers | Distance from any point of the viewing space to any point of the viewed space |

Visibility | set of real-numbers from 0 to 1 | The degree of visibility of each point in the Viewing Space to any point in the Viewed Space through the Obstacle Space |

Depth (although depth is a derived concept from visibility, it is offered as a primitive to the users) | set of integers | Minimum number of straight lines in a Path of the Viewing space that need to be traversed from any point in the Viewing Space to see any point in the Viewed Space |

### Operational Model

### Applicability

3D analysis seems to bring better results in rough topography of the urban spaces; dynamic volumetric geometry: size, configuration, elevation and interpenetration; joint analysis of the interior of each building and its urban environment, in particular when there are high-rise buildings.

Due to operational constraints (time and memory) the use of DepthSpace3D should not be extended to large scale case studies.

Some case studies are presented in the figure – interior and exterior spaces, small-scale urban spaces, commercial and complex buildings, landscape studies.