A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Robust Modeling of Polyhedral Space Partitions
https://orcid.org/http://orcid.org/0000-0002-4643-1004
https://orcid.org/http://orcid.org/0000-0002-1732-5982
This paper introduces polyhedral space partition as a representation of geometric objects in digital building models. Operators to modify such a partition model are presented and strategies to guaranty robustness are explained. The topology of a polyhedral space partition can be stored explicitly by pointers in a digital environment. However, coordinates are mapped to numbers which are unavoidably imprecise in a digital environment. The partition model is called consistent, if its imprecise geometric attributes do not contradict its exact topological attributes. The platform is called robust if the imprecision in typical applications does not make the model inconsistent. This paper presents two novel concepts that enhance robust modeling: focused model construction and topologically controlled work steps. Conventionally, each object is constructed individually and added to the existing set of objects. Geometric imprecision leads to collisions of and gaps between objects. The algorithms that detect collisions or gaps are not focused on a subset; and they are expensive because they must consider all existing objects. Focused transformations affect only a small number of domains. A work step is topologically controlled, if modifications on boundary elements of the domain must be performed in preceding work steps. Errors are reported and corrected before the construction proceeds. Topological checks are performed on the manifolds based on a rank concept. It is tested geometrically that all domains that are added to a domain lie inside the existing domain using the novel concept of anchors and their clients for robustness. Truncation and round-off errors are treated with a single value subjected to the machine epsilon.
Robust Modeling of Polyhedral Space Partitions
https://orcid.org/http://orcid.org/0000-0002-4643-1004
https://orcid.org/http://orcid.org/0000-0002-1732-5982
This paper introduces polyhedral space partition as a representation of geometric objects in digital building models. Operators to modify such a partition model are presented and strategies to guaranty robustness are explained. The topology of a polyhedral space partition can be stored explicitly by pointers in a digital environment. However, coordinates are mapped to numbers which are unavoidably imprecise in a digital environment. The partition model is called consistent, if its imprecise geometric attributes do not contradict its exact topological attributes. The platform is called robust if the imprecision in typical applications does not make the model inconsistent. This paper presents two novel concepts that enhance robust modeling: focused model construction and topologically controlled work steps. Conventionally, each object is constructed individually and added to the existing set of objects. Geometric imprecision leads to collisions of and gaps between objects. The algorithms that detect collisions or gaps are not focused on a subset; and they are expensive because they must consider all existing objects. Focused transformations affect only a small number of domains. A work step is topologically controlled, if modifications on boundary elements of the domain must be performed in preceding work steps. Errors are reported and corrected before the construction proceeds. Topological checks are performed on the manifolds based on a rank concept. It is tested geometrically that all domains that are added to a domain lie inside the existing domain using the novel concept of anchors and their clients for robustness. Truncation and round-off errors are treated with a single value subjected to the machine epsilon.
Robust Modeling of Polyhedral Space Partitions
https://orcid.org/http://orcid.org/0000-0002-4643-1004
https://orcid.org/http://orcid.org/0000-0002-1732-5982
This paper introduces polyhedral space partition as a representation of geometric objects in digital building models. Operators to modify such a partition model are presented and strategies to guaranty robustness are explained. The topology of a polyhedral space partition can be stored explicitly by pointers in a digital environment. However, coordinates are mapped to numbers which are unavoidably imprecise in a digital environment. The partition model is called consistent, if its imprecise geometric attributes do not contradict its exact topological attributes. The platform is called robust if the imprecision in typical applications does not make the model inconsistent. This paper presents two novel concepts that enhance robust modeling: focused model construction and topologically controlled work steps. Conventionally, each object is constructed individually and added to the existing set of objects. Geometric imprecision leads to collisions of and gaps between objects. The algorithms that detect collisions or gaps are not focused on a subset; and they are expensive because they must consider all existing objects. Focused transformations affect only a small number of domains. A work step is topologically controlled, if modifications on boundary elements of the domain must be performed in preceding work steps. Errors are reported and corrected before the construction proceeds. Topological checks are performed on the manifolds based on a rank concept. It is tested geometrically that all domains that are added to a domain lie inside the existing domain using the novel concept of anchors and their clients for robustness. Truncation and round-off errors are treated with a single value subjected to the machine epsilon.
Robust Modeling of Polyhedral Space Partitions
Lecture Notes in Civil Engineering
Skatulla, Sebastian (editor) / Beushausen, Hans (editor) / Sternal, Maximilian (author) / Huhnt, Wolfgang (author)
International Conference on Computing in Civil and Building Engineering ; 2022 ; Cape Town, South Africa
Advances in Information Technology in Civil and Building Engineering ; Chapter: 30 ; 427-442
2023-08-30
16 pages
Article/Chapter (Book)
Electronic Resource
English
Norm induced polyhedral uncertainty sets for robust linear optimization
| Springer Verlag | 2022
| Engineering Index Backfile | 1967