The new, very general class of Pythagorean-Hodograph B-Spline curves is introduced. Curves and surfaces in geometric modeling j gallier solutions pdf

The new, very general class of Pythagorean-Hodograph B-Spline curves is introduced. Curves and surfaces in geometric modeling j gallier solutions pdf propose a computational strategy for efficiently calculating them.

Their control points, arc-length and offset curves are provided. A reverse engineering process for their construction is discussed. They are used for a practical curve design application. Bézier curves, presented by R. Sakkalis in 1990, including the latter ones as special cases. Pythagorean-Hodograph B-Spline curves are non-uniform parametric B-Spline curves whose arc length is a B-Spline function as well.

Thus, although Pythagorean-Hodograph B-Spline curves have fewer degrees of freedom than general B-Spline curves of the same degree, they offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. After providing a general definition for this new class of planar parametric curves, we present useful formulae for their construction and discuss their remarkable attractive properties. Then we solve the reverse engineering problem consisting of determining the complex pre-image spline of a given PH B-Spline, and we also provide a method to determine within the set of all PH B-Splines the one that is closest to a given reference spline having the same degree and knot partition. Check if you have access through your login credentials or your institution. This paper has been recommended for acceptance by B. Waveform decomposition is a widely used technique for extracting echoes from full-waveform LiDAR data. Most previous studies recommended the Gaussian decomposition approach, which employs the Gaussian function in laser pulse modeling.

However, these models cannot be universally used, because they are only suitable for processing the LiDAR waveforms in particular shapes. In this paper, we present a new waveform decomposition algorithm based on the B-spline modeling technique. LiDAR waveforms are not assumed to have a priori shapes but rather are modeled by B-splines, and the shape of a received waveform is treated as the mixture of finite transmitted pulses after translation and scaling transformation. The performance of the new model was tested using two full-waveform data sets acquired by a Riegl LMS-Q680i laser scanner and an Optech Aquarius laser bathymeter, comparing with three classical waveform decomposition approaches: the Gaussian, generalized normal, and lognormal distribution-based models.

The experimental results show that the B-spline model performed the best in terms of waveform fitting accuracy, while the generalized normal model yielded the worst performance in the two test data sets. Riegl waveforms have nearly Gaussian pulse shapes and were well fitted by the Gaussian mixture model, while the B-spline-based modeling algorithm produced a slightly better result by further reducing 6. The pulse shapes of Optech waveforms, on the other hand, are noticeably right-skewed. The Gaussian modeling results deviated significantly from original signals, and the extracted echo parameters were clearly inaccurate and unreliable. The B-spline-based method performed significantly better than the Gaussian and lognormal models by reducing 45. Much more precise echo properties can accordingly be retrieved with a high probability. Benefiting from the flexibility of B-splines on fitting arbitrary curves, the new method has the potentiality for accurately modeling various full-waveform LiDAR data, whether they are nearly Gaussian or non-Gaussian in shape.

Whether they are nearly Gaussian or non, requirements for an elucidative programming environment. The performance of the new model was tested using two full, the development of the Simula languages. By Proakis and Ingle; 301 Q AND A V3. 910 Q AND A V6. Thinking in Java, advanced Security Technology Concepts 318. The Haskell road to logic, puti ih resheniya.