Medical Imaging Interaction Toolkit  2024.06.00
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)
6 All rights reserved.
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 #ifndef mitkFresnel_h
14 #define mitkFresnel_h
15 
16 /****************************************************************************
17  * fresnel.h -
18  * Calculation of Fresnel integrals by expansion to Chebyshev series
19  * Expansions are taken from the book
20  * Y.L. Luke. Mathematical functions and their approximations.
21  * Ìoscow, "Mir", 1980. PP. 145-149 (Russian edition)
22  ****************************************************************************
23  */
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 
38  /* Additional functions*/
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
mitk::fresnel_c
double fresnel_c(double x)
mitk
Find image slices visible on a given plane.
Definition: RenderingTests.dox:1
mitk::fresnel_s2
double fresnel_s2(double x)
mitk::fresnel_c2
double fresnel_c2(double x)
mitk::fresnel_s
double fresnel_s(double x)