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Dimensioning
Published in Ken Morling, Stéphane Danjou, Geometric and Engineering Drawing, 2022
A chamfer is a bevelled edge, usually added to two adjacent faces to avoid sharp edges. They are used, for example, to ensure the function of two mating parts, to avoid injuries and to prevent damage to the part. As a rule, a chamfer is created at an angle of 45°. However, other angles might be necessary for specific applications. When dimensioning a chamfer, the length of the offset and the angle shall be provided. As long as the angle is 45°, the presentation can be simplified according Figure 7.19 (a). When drawing space is limited or the value for the offset is very small, the dimension can be given with a leader line as shown in Figure 7.19 (b). Whenever the angle is unequal 45°, the chamfer shall be conventionally dimensioned, i.e. indicating the angle and separately the offset or alternatively the chamfer diameter (compare Figure 7.19 (c)).
The Basic Principle of Urban True Orthophotomap Generation
Published in Guoqing Zhou, Urban High-Resolution Remote Sensing, 2020
Spatial objects are abstractly understood as the following four types of geometric objects (Zhou et al. 2000; Grün and Wang 1998):Point objects. Described by x and y planimetric coordinates, like benchmarks.Line objects. One-dimensional objects, length being the only measurable one-dimensional spatial extension.Surface objects. Two-dimensional or two and half-dimensional objects with area and perimeter as measurable spatial extensions.Body objects. Three-dimensional objects with volume and surface area as measurable spatial extensions, which are bordered by facets.Of the above four types of objects, point is the basic geometric element. For example, a point can present a point object, or the starting or ending point of an edge. An edge is a line segment, which is an ordered connection between two points: beginning point and ending point. A facet is completely described by the ordered edges that define the border of the facet. A polyhedron is described by the ordered facets. Image data and thematic data can be attached to a facet. Each facet is related to an image patch through a corresponding link (Figure 11.5). In the proposed data model, each object is identified by a defined attribute data, such as Type Identifier (TI), and thus the four types of objects are referred to as PI (point identifier), LI (line identifier), FI (facet identifier), and PHI (polyhedron identifier), respectively. The other attribute data (e.g., thematic data and geometric data) can be attached to each type of object. The geometric data of 3D objects contain the information of position, shape, size, structure definition, and image identification.
Investigation of cooling hole blockage in the plasma spraying of thermal barrier coatings on super-alloy
Published in Transactions of the IMF, 2023
Zhuang Liu, Changshui Gao, Zhongyu Wang, Xiaoyu Yu
Figure 3 exhibits the geometric definition of the blockage morphology caused by TBC. Plane A-A is the smallest cross-sectional area selected from the reconstructed 3D model resulting from the CT measurement, where d is the hole diameter before coating, S1 is the cross-sectional area before coating and S2 is the cross-sectional area after coating. The hole blockage ratio is defined as a percentage of B = ((S1−S2)/S1)×100%. As illustrated in the figure, the left wall, where the angle between the side wall and top surface is acute, is defined as the leading edge. In contrast, the right wall is defined as the trailing edge. h and l, H and L represent the coating deposition height and length for the leading edge and the trailing edge, respectively. For the vertical holes, the deposition height and length will be averaged on the sum of left and right walls.
Development and performance evaluation of a web-based feature extraction and recognition system for sheet metal bending process planning operations
Published in International Journal of Computer Integrated Manufacturing, 2021
Eriyeti Murena, Khumbulani Mpofu, Alfred T Ncube, Olasumbo Makinde, John A Trimble, Xi Vincent Wang
The length of the edge is obtained by computing the distance between two points (e.g. V5 and V6) in 3D space, Figure 7. In this case, the distance between two vertices is required to calculate the length of a bend. The distance between points is calculated by considering vertices to at a point with (X, Y, Z) coordinates. The bend length was obtained by calculating the distance between vertices and or vertices and . The thickness defining faces defined by vertices , and , or , and .
Exploring the Relative Effects of Body Position and Spatial Cognition on Presence When Playing Virtual Reality Games
Published in International Journal of Human–Computer Interaction, 2020
Aelee Kim, Min Woo Kim, Hayoung Bae, Kyoung-Min Lee
In graph theory, a graph is a collection of points called vertices (V), connected by lines called edges (E). The degree of a vertex (d(V)) is the number of edges incident to the vertex. In this research, it should be noted that we use the term route instead of edge when describing the formulas. In Appendix A, we explain the foundational concepts of the formulas. According to the formulas, when playing Bomb Hero, the number of routes that a player can select from a place (i.e., vertex) is no more than four, thus the DFN is finite. In contrast, for Moss, the number of routes a player can choose from a place (i.e., vertex) is not limited, meaning that the DFN is infinite. Through the formulas, we clearly understand that the DFN is much higher for Moss than Bomb Hero. Based on the more detailed explanation given in Appendix A, we constructed the two mathematical formulas presented in Table 1.