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The Convex Hull of Two Closed Implicit Surfaces
Published in Wasim Ahmed Khan, Ghulam Abbas, Khalid Rahman, Ghulam Hussain, Cedric Aimal Edwin, Functional Reverse Engineering of Machine Tools, 2019
Now let us consider the case of implicit surface, i.e., surface S is defined by implicit form f(x, y, z) = 0. Here the developable surface T is characterized by the following independent equation system: {[C(t)−P(t)]⋅∇f=0C′(t)⋅∇f=0f(P(t))=0.
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Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017
isosurface a technique used in three-dimensional data visualization where a surface is drawn around points in three-dimensional space that represent the same data value. For example, the set of points { (x, y, z) : f(x, y,z) = c } where c is a given constant. See implicit surface.
Implicit modelling and dynamic update of tunnel unfavourable geology based on multi-source data fusion using support vector machine
Published in Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2023
Binru Yang, Yulin Ding, Qing Zhu, Liguo Zhang, Haoyu Wu, Yongxin Guo, Mingwei Liu, Wei Wang
The implicit surface has an important application in graphics because of its topological independence. It first constructs the implicit function through scattered data points and then extracts the zero isosurfaces of the implicit function to establish a closed 3D model (Smolik, Skala, and Majdisova 2018). Implicit surface reconstruction algorithms include the moving least squares method (Alexa et al. 2001; Manchuk and Deutsch 2019; Phan et al. 2008; Renaudeau et al. 2019), Shepard method (Franke 1982), and radial basis function method (Cuomo et al. 2017; Liu, Wang, and Qiang 2007). The radial basis function (RBF) is used to stably and accurately build 3D models of discrete point cloud data, and it is widely used in civil engineering, medicine, film, and gaming fields. RBF methods are divided into two categories: GS-RBF and compactly supported RBF method (CS-RBF) (Zhong, Wang, and Bi 2020). The former takes each discrete point as the centre, establishes a distance function from the remaining points to the centre, and sums all functions to obtain the fitting function for all discrete points. It is suitable for the case of missing data and has good interpolation and extension abilities (Škala 2016). The CS-RBF establishes a local radial basis function by selecting the appropriate supporting radius, making the solution faster and more suitable for uniformly distributed point cloud data (Zhong, Wang, and Bi 2020).