Along with a picture of each shape, the number of faces, edges and vertices are also given. Common properties of the 3D shapes are also given. Please note that there is some disagreement over the definitions and properties of 3d shapes. ...
First, geometric information, including position and section shape, is obtained from the acquired point cloud using domain-specific contextual knowledge and supervised classification. Then, structural members’ function and section family type is inferred from geometric information. Finally, a BIM is ...
Several branches of mathematics: statistics, information theory, set theory and linear algebra are combined in this one consistent crate, based on the abstraction that they all operate on the same data objects (here Rust Vecs). The only difference being that an ordering of their components is so...
To us today these names of ratios might appear to be abstract terminology, but the important point is that each of these terms describes a shape, independent of the lengths that define it. The shape of the sesquialtera is unchanged, regardless of whether its sides are 3:2, 6:4 or 99:...
outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The ...
The data structure implemented is based on the OpenCascade [27,28] platform and it resembles a B-Rep data structure. Figure 7 shows the implemented data structure. Figure 7. Original geometry-topology data structure, using OpenCascadeTM data names (which differ but are mathematically equivalent to...
Table 1 provides the code, names, and acronyms, as well as the description and equations for each first and second-order geometric attribute integrating the feature space (X). Table 1. Geometric features description: acronyms, names, and equations. As recommended (Section 1.2), this unique ...
Suppose that a binary operation $$\circ $$ on a finite set X is injective in each variable separately and also associative. It is easy to prove that $$(X,\