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Fractional factorial experiments
Published in Adedeji B. Badiru, Ibidapo-Obe Oye, Babatunde J. Ayeni, Manufacturing and Enterprise, 2018
Adedeji B. Badiru, Ibidapo-Obe Oye, Babatunde J. Ayeni
A three-factor central composite design (Table 11.7) is a member of the most popular class of designs used for estimating the coefficients in the second order model. This design consists of 8 vertices of a 3-dimensional cube. The values of the coded factors in this factorial portion of the design are (B, G, H) = (+1, +1, +1). In addition, this design consists of 6 vertices (+1.63, 0, 0), (0, +1.63, 0), (0, 0, +1.63) of a 3-dimensional octahedron or star and six center points. If properly set up, a central composite design has the ability to possess the constant variance property of a rotatable design or may be an orthogonal design thereby allowing an independent assessment of the three factors under study. For the illustrative study, a second order response surface experiment was conducted for the three factors B, G, and H previously declared statistically significant from the above screening experiment. The design set up is provided in Table 11.10.
Visual 3D Form in the Context of Additive Manufacturing
Published in Steinar Killi, Additive Manufacturing, 2017
Nina Bjørnstad, Andrew Morrison
In his book Principles of Form and Design Wucius Wong [20] developed a visual form of grammar and defined constructional elements. Vertex, edge, and faces are examples and can help in defining volumes. According to Wong, for example, a cube has 8 vertices, 12 edges, and 6 faces. In terms of design processes and development, we are able to discuss these properties in detail since they are captured in the clay models without user function as in products.
Matrices
Published in James R. Kirkwood, Bessie H. Kirkwood, Elementary Linear Algebra, 2017
James R. Kirkwood, Bessie H. Kirkwood
A graph is a set of vertexes and a set of edges between some of the vertices. If the graph is simple, then there is no edge from a vertex to itself. If the graph is not directed, then an edge from vertex i to vertex j is also an edge from j to vertex i. Figure 1.2 shows a simple graph that is not directed.
When a tree model meets texture baking: an approach for quality-preserving lightweight visualization in virtual 3D scene construction
Published in International Journal of Digital Earth, 2023
Chen Zhang, Biao He, Renzhong Guo, Ding Ma
We compare the model attributes and visualization effect between the high-poly mesh and the low-poly mesh with the baked textures. The model attributes encompass the following metrics of geometry and texture. Vertices: The number of vertices. Each triangle has three vertices, and each vertex can be shared by multiple triangles. A lower value is better for the loading mesh.Indices: The number of indices for constructing triangles. Each index corresponds to a vertex in space, and stores a texture coordinate, a normal and other information. A lower value is better for the loading mesh.Triangles: The number of triangles. The number of indices is triple the number of triangles.Mesh size: The data size of the geometry loaded in real time. A lower value is better for the loading mesh.Texture size: The data size of textures loaded in real-time. In our work, the high-poly mesh only uses the diffuse map, and the low-poly mesh uses three baked textures.
Evolutionary multiplayer game analysis of accounts receivable financing based on supply chain financing
Published in International Journal of Production Research, 2021
Bo Yan, Zhuo Chen, Chang Yan, Zhenyu Zhang, Hanwen Kang
We can obtain 10 candidate equilibrium points (Ji, Ma, and Li 2015), the equilibrium point must satisfy F(x) = 0, F(y) = 0, F(z) = 0. As , , , (x*, y*, z*) can be deduced, namely, E1 = (0,0,0), E2 = (0,0,1), E3=(0,1,0), E4 = (0,1,1), E5 = (1,0,0), E6 = (1,0,1), E7 = (1,1,0), E8 = (1,1,1), E9 = ((P + T)/(P + M(L + rL)), 1 – (M(L – L1)(r – r0))/(P – C2 + LM + rLM), 0), E10 = ((P + T)/(P + M(L + rL – 1)), 1 – (M(L – L1)(r – r0))/(P – M – C2 + LM + rLM),1). E1–E8 constitutes 8 vertices of a unit cube. And E9 and E10 are inside this unit cube.
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.