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Flight Planning
Published in Yasmina Bestaoui Sebbane, Multi-UAV Planning and Task Allocation, 2020
The Hermite spline is a special spline with the unique property that the curve generated from the spline passes through the control points that define the spline. Thus, a set of predetermined points can be smoothly interpolated by simply setting these points as control points for the Hermite spline.
Dose Coefficients
Published in Shaheen A. Dewji, Nolan E. Hertel, Advanced Radiation Protection Dosimetry, 2019
Nolan E. Hertel, Derek Jokisch
One such algorithm achieves a monotone interpolation using a piecewise cubic Hermite spline. This method was developed by Fritsch and Carlson (1980). This algorithm uses all known data points and will return multiple interpolants in single call.
Optimization of three-dimensional modeling for geometric precision and efficiency for healthy and diseased aortas
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2018
Christopher P. Cheng, Yufei D. Zhu, Ga-Young Suh
Geometric modeling was performed on the open-source software (SimVascular, Open Source Medical Software Corporation, San Diego, California) as shown in Figure 1 (Wang et al. 1999; Wilson et al. 2001; Choi et al. 2009; Suh et al. 2014). Modeling begins by loading images into the software framework and manually picking centroid points along the lengths of vessel lumens (Figure 1(a)) (Wilson et al. 2001). These points are then connected with an interpolated cubic hermite spline (Figure 1(b)), and 2D segmentations are performed orthogonally along the centerline to create perpendicular vessel cross-sections (Figure 1(c)). The cross-section contours are formed automatically using a level set segmentation technique, with manual adjustments when the automatic segmentation fails to capture the lumen contour (Wang et al. 1999).
Construction new rational cubic spline with application in shape preservations
Published in Cogent Engineering, 2018
Example 2. Table 3 shows the data used in Sarfraz et al. (2010) which demonstrates the volumeof NaOH taken in a beaker vs HCl as stated in the experiment procedures. Figure 3(a) shows the cubic Hermite spline interpolation. Figure 3(b) shows the positivity preserving interpolation by using the scheme of Hussain and Ali (2006). Figure 3(c,d) show the positivity preserving interpolation by using the schemes of Hussain and Sarfraz (2008) and PCHIP, respectively. Figure 3(e) shows the positivity preserving interpolation by using the proposed scheme when for and the parameter is calculated from Condition (19). Figure 3(f) shows the positive interpolating curve when for and . Finally, Figure 3(g) shows the interpolating curve when for and . From Figure 3(g), the smaller the value of (or increasing value) give loose curve while the bigger value of (or reducing value) produce tight curve as shown in Figure 3(e).
Simulation of Legionella concentration in domestic hot water: comparison of pipe and boiler models
Published in Journal of Building Performance Simulation, 2019
Elisa Van Kenhove, Lien De Backer, Arnold Janssens, Jelle Laverge
A third degree piece-wise polynomial fitting technique (cubic hermite spline) was chosen in Modelica for constructing a smooth curve through the defined points. In total, four different functions were developed: a separate function for the L. pneumophila growth and death, each of them for L. pneumophila in water and for L. pneumophila in biofilm. Several approaches have been tested, the current approach seems to have the fewest drawbacks. The flexible use of the models is the reason to choose the current approach. The advantage of using this approach is that the user can easily adapt each curve based on his own measurement points or new findings or for another type of bacteria.