# source:sasmodels/sasmodels/models/capped_cylinder.c@becded3

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since becded3 was becded3, checked in by Paul Kienzle <pkienzle@…>, 7 years ago

update oriented models to new interface (which will be in the next commit)

• Property mode set to `100644`
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2
3// Integral over a convex lens kernel for t in [h/R,1].  See the docs for
4// the definition of the function being integrated.
5//   q is the magnitude of the q vector.
6//   h is the length of the lens "inside" the cylinder.  This negative wrt the
7//       definition of h in the docs.
8//   radius_cap is the radius of the lens
9//   length is the cylinder length, or the separation between the lens halves
10//   theta is the angle of the cylinder wrt q.
11static double
12_cap_kernel(double qab, double qc, double h, double radius_cap,
13    double half_length)
14{
15    // translate a point in [-1,1] to a point in [lower,upper]
16    const double upper = 1.0;
17    const double lower = h/radius_cap; // integral lower bound
18    const double zm = 0.5*(upper-lower);
19    const double zb = 0.5*(upper+lower);
20
21    // cos term in integral is:
22    //    cos (q (R t - h + L/2) cos(theta))
23    // so turn it into:
24    //    cos (m t + b)
25    // where:
26    //    m = q R cos(theta)
27    //    b = q(L/2-h) cos(theta)
28    const double m = radius_cap*qc; // cos argument slope
29    const double b = (half_length-h)*qc; // cos argument intercept
30    const double qab_r = radius_cap*qab; // Q*R*sin(theta)
31    double total = 0.0;
32    for (int i=0; i<76 ;i++) {
33        const double t = Gauss76Z[i]*zm + zb;
34        const double radical = 1.0 - t*t;
35        const double bj = sas_2J1x_x(qab_r*sqrt(radical));
36        const double Fq = cos(m*t + b) * radical * bj;
37        total += Gauss76Wt[i] * Fq;
38    }
39    // translate dx in [-1,1] to dx in [lower,upper]
40    const double integral = total*zm;
41    const double cap_Fq = 2.0*M_PI*cube(radius_cap)*integral;
42    return cap_Fq;
43}
44
45static double
46_fq(double qab, double qc, double h, double radius_cap, double radius, double half_length)
47{
48    const double cap_Fq = _cap_kernel(qab, qc, h, radius_cap, half_length);
49    const double bj = sas_2J1x_x(radius*qab);
50    const double si = sas_sinx_x(half_length*qc);
52    const double Aq = cap_Fq + cyl_Fq;
53    return Aq;
54}
55
56static double
58{
59    // cap radius should never be less than radius when this is called
60
61    // Note: volume V = 2*V_cap + V_cyl
62    //
63    // V_cyl = pi r_cyl^2 L
64    // V_cap = 1/6 pi h_c (3 r_cyl^2 + h_c^2) = 1/3 pi h_c^2 (3 r_cap - h_c)
65    //
66    // The docs for capped cylinder give the volume as:
67    //    V = pi r^2 L + 2/3 pi (R-h)^2 (2R + h)
68    // where r_cap=R and h = R - h_c.
69    //
70    // The first part is clearly V_cyl.  The second part requires some work:
71    //    (R-h)^2 => h_c^2
72    //    (2R+h) => 2R+ h_c-h_c + h => 2R + (R-h)-h_c + h => 3R-h_c
73    // And so:
74    //    2/3 pi (R-h)^2 (2R + h) => 2/3 pi h_c^2 (3 r_cap - h_c)
75    // which is 2 V_cap, using the second form above.
76    //
77    // In this function we are going to use the first form of V_cap
78    //
79    //      V = V_cyl + 2 V_cap
80    //        = pi r^2 L + pi hc (r^2 + hc^2/3)
81    //        = pi (r^2 (L+hc) + hc^3/3)
84}
85
86static double
87Iq(double q, double sld, double solvent_sld,
88    double radius, double radius_cap, double length)
89{
91    const double half_length = 0.5*length;
92
93    // translate a point in [-1,1] to a point in [0, pi/2]
94    const double zm = M_PI_4;
95    const double zb = M_PI_4;
96    double total = 0.0;
97    for (int i=0; i<76 ;i++) {
98        const double theta = Gauss76Z[i]*zm + zb;
99        double sin_theta, cos_theta; // slots to hold sincos function output
100        SINCOS(theta, sin_theta, cos_theta);
101        const double qab = q*sin_theta;
102        const double qc = q*cos_theta;
103        const double Aq = _fq(qab, qc, h, radius_cap, radius, half_length);
104        // scale by sin_theta for spherical coord integration
105        total += Gauss76Wt[i] * Aq * Aq * sin_theta;
106    }
107    // translate dx in [-1,1] to dx in [lower,upper]
108    const double form = total * zm;
109
110    // Contrast
111    const double s = (sld - solvent_sld);
112    return 1.0e-4 * s * s * form;
113}
114
115
116static double
117Iqxy(double qab, double qc,
118    double sld, double solvent_sld, double radius,
119    double radius_cap, double length)
120{