Medical Imaging Interaction Toolkit  2018.4.99-6a3ea89d Medical Imaging Interaction Toolkit
mitkFresnel.h
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1 /*============================================================================
2
3 The Medical Imaging Interaction Toolkit (MITK)
4
5 Copyright (c) German Cancer Research Center (DKFZ)
7
8 Use of this source code is governed by a 3-clause BSD license that can be
9 found in the LICENSE file.
10
11 ============================================================================*/
12
13 /****************************************************************************
14  * fresnel.h -
15  * Calculation of Fresnel integrals by expansion to Chebyshev series
16  * Expansions are taken from the book
17  * Y.L. Luke. Mathematical functions and their approximations.
18  * Ìoscow, "Mir", 1980. PP. 145-149 (Russian edition)
19  ****************************************************************************
20  */
21
22 #ifndef MITKFRESNEL_H_
23 #define MITKFRESNEL_H_
24
25 namespace mitk
26 {
27
28  /* fresnel_c(x) - Fresnel Cosine Integral
29  * C(x)=fresnel_c(x)=\dint\limits_{0}^{x}\cos (\frac{\pi}{2}t^{2})dt
30  */
31  double fresnel_c(double x);
32
33  /* fresnel_s(x) - Fresnel Sine Integral
34  * S(x)=fresnel_s(x)=\dint\limits_{0}^{x}\sin (\frac{\pi}{2}t^{2})dt
35  */
36  double fresnel_s(double x);
37
39  /* fresnel_c2(x)
40  * fresnel_c2(x)=fresnel_c(x*sqrt(2/pi))=
41  * = \sqrt{\frac{2}{\pi }}\dint\limits_{0}^{x}\cos (t^{2})dt
42  */
43  double fresnel_c2(double x);
44
45  /* fresnel_s2(x)
46  * fresnel_s2(x)=fresnel_s(x*sqrt(2/pi))=
47  * = \sqrt{\frac{2}{\pi }}\dint\limits_{0}^{x}\sin (t^{2})dt
48  */
49  double fresnel_s2(double x);
50 }
51
52 #endif /* FRESNEL_H_ */
53