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38 * \page page_module_selection_insolidangle Selection method: insolidangle
40 * This method selects a subset of particles that are located in a solid
41 * angle defined by a center and a set of points.
42 * The solid angle is constructed as a union of small cones whose axis
43 * goes through the center and a point.
44 * So there's such a cone for each position, and a
45 * point is in the solid angle if it lies within any of these cones.
46 * The width of the cones can be adjusted.
48 * The method is implemented by partitioning the surface of the unit sphere
49 * into bins using the polar coordinates \f$(\theta, \phi)\f$.
50 * The partitioning is always uniform in the zenith angle \f$\theta\f$,
51 * while the partitioning in the azimuthal angle \f$\phi\f$ varies.
52 * For each reference point, the unit vector from the center to the point
53 * is constructed, and it is stored in all the bins that overlap with the
54 * cone defined by the point.
55 * Bins that are completely covered by a single cone are marked as such.
56 * Checking whether a point is in the solid angle is then straightforward
57 * with this data structure: one finds the bin that corresponds to the point,
58 * and checks whether the bin is completely covered. If it is not, one
59 * additionally needs to check whether it is within the specified cutoff of
60 * any of the stored points.
62 * The above construction gives quite a lot of flexibility for constructing
63 * the bins without modifying the rest of the code.
64 * The current (quite inefficient) implementation is discussed below, but
65 * it should be optimized to get the most out of the code.
67 * The current way of constructing the bins constructs the boundaries
68 * statically: the bin size in the zenith direction is set to approximately
69 * half the angle cutoff, and the bins in the azimuthal direction have
70 * sizes such that the shortest edge of the bin is approximately equal to
71 * half the angle cutoff (for the regions close to the poles, a single bin
73 * Each reference point is then added to the bins as follows:
74 * -# Find the zenith angle range that is spanned by the cone centered at the
75 * point (this is simple addition/subtraction).
76 * -# Calculate the maximal span of the cone in the azimuthal direction using
78 * \f[\sin \Delta \phi_{max} = \frac{\sin \alpha}{\sin \theta}\f]
79 * (a sine formula in spherical coordinates),
80 * where \f$\alpha\f$ is the width of the cone and \f$\theta\f$ is the
81 * zenith angle of the cone center.
82 * Similarly, the zenith angle at which this extent is achieved is
84 * \f[\cos \theta_{max} = \frac{\cos \theta}{\cos \alpha}\f]
85 * (Pythagoras's theorem in spherical coordinates).
86 * -# For each zenith angle bin that is at least partially covered by the
87 * cone, calculate the span of the cone at the edges using
88 * \f[\sin^2 \frac{\Delta \phi}{2} = \frac{\sin^2 \frac{\alpha}{2} - \sin^2 \frac{\theta -
89 * \theta'}{2}}{\sin \theta \sin \theta'}\f] (distance in spherical geometry), where \f$\theta'\f$
90 * is the zenith angle of the bin edge. Treat zenith angle bins that are completely covered by the
91 * cone (in the case that the cone is centered close to the pole) as a special case.
92 * -# Using the values calculated above, loop through the azimuthal bins that
93 * are partially or completely covered by the cone and update them.
95 * The total solid angle (for covered fraction calculations) is estimated by
96 * taking the total area of completely covered bins plus
97 * half the area of partially covered bins.
98 * The second one is an approximation, but should give reasonable estimates
99 * for the averages as well as in cases where the bin size is small.
103 * Implements the \ref sm_insolidangle "insolidangle" selection method.
106 * The implementation could be optimized quite a bit.
109 * Move the covered fraction stuff somewhere else and make it more generic
110 * (along the lines it is handled in selection.h and trajana.h in the old C
113 * \author Teemu Murtola <teemu.murtola@gmail.com>
114 * \ingroup module_selection
122 #include "gromacs/math/functions.h"
123 #include "gromacs/math/units.h"
124 #include "gromacs/math/utilities.h"
125 #include "gromacs/math/vec.h"
126 #include "gromacs/pbcutil/pbc.h"
127 #include "gromacs/selection/indexutil.h"
128 #include "gromacs/selection/selection.h"
129 #include "gromacs/utility/arraysize.h"
130 #include "gromacs/utility/exceptions.h"
131 #include "gromacs/utility/smalloc.h"
133 #include "position.h"
135 #include "selmethod.h"
136 #include "selmethod_impl.h"
143 * Internal data structure for the \p insolidangle selection method.
145 * \see \c t_partition
147 * \ingroup module_selection
151 /** Left edge of the partition. */
153 /** Bin index corresponding to this partition. */
159 * Internal data structure for the \p insolidangle selection method.
161 * Describes the surface partitioning within one slice along the zenith angle.
162 * The slice from azimuthal angle \p p[i].left to \p p[i+1].left belongs to
165 * \ingroup module_selection
169 /** Number of partition items (\p p contains \p n+1 items). */
171 /** Array of partition edges and corresponding bins. */
177 * Internal data structure for the \p insolidangle selection method.
179 * Contains the reference points that partially cover a certain region on the
180 * surface of the unit sphere.
181 * If \p n is -1, the whole region described by the bin is covered.
183 * \ingroup module_selection
187 /** Number of points in the array \p x, -1 if whole bin covered. */
189 /** Number of elements allocated for \p x. */
191 /** Array of points that partially cover the bin. */
193 } t_spheresurfacebin
;
197 * Data structure for the \p insolidangle selection method.
199 * All angle values are in the units of radians.
201 * \ingroup module_selection
205 /** Center of the solid angle. */
206 gmx_ana_pos_t center
;
207 /** Positions that span the solid angle. */
211 /** Estimate of the covered fraction. */
214 /** Cutoff for the cosine (equals cos(angcut)). */
216 /** Bin size to be used as the target bin size when constructing the bins. */
219 /** Number of bins in the \p tbin array. */
221 /** Size of one bin in the zenith angle direction. */
223 /** Array of zenith angle slices. */
225 /** Number of elements allocated for the \p bin array. */
227 /** Number of elements used in the \p bin array. */
229 /** Array of individual bins. */
230 t_spheresurfacebin
* bin
;
231 } t_methoddata_insolidangle
;
234 * Allocates data for the \p insolidangle selection method.
236 * \param[in] npar Not used (should be 3).
237 * \param[in,out] param Method parameters (should point to
238 * \ref smparams_insolidangle).
239 * \returns Pointer to the allocated data (\ref t_methoddata_insolidangle).
241 * Allocates memory for a \ref t_methoddata_insolidangle structure and
242 * initializes the parameter as follows:
243 * - \p center defines the value for t_methoddata_insolidangle::center.
244 * - \p span defines the value for t_methoddata_insolidangle::span.
245 * - \p cutoff defines the value for t_methoddata_insolidangle::angcut.
247 static void* init_data_insolidangle(int npar
, gmx_ana_selparam_t
* param
);
249 * Initializes the \p insolidangle selection method.
251 * \param top Not used.
252 * \param npar Not used.
253 * \param param Not used.
254 * \param data Pointer to \ref t_methoddata_insolidangle to initialize.
255 * \returns 0 on success, -1 on failure.
257 * Converts t_methoddata_insolidangle::angcut to radians and allocates
258 * and allocates memory for the bins used during the evaluation.
260 static void init_insolidangle(const gmx_mtop_t
* top
, int npar
, gmx_ana_selparam_t
* param
, void* data
);
261 /** Frees the data allocated for the \p insolidangle selection method. */
262 static void free_data_insolidangle(void* data
);
264 * Initializes the evaluation of the \p insolidangle selection method for a frame.
266 * \param[in] context Evaluation context.
267 * \param data Should point to a \ref t_methoddata_insolidangle.
269 * Creates a lookup structure that enables fast queries of whether a point
270 * is within the solid angle or not.
272 static void init_frame_insolidangle(const gmx::SelMethodEvalContext
& context
, void* data
);
273 /** Internal helper function for evaluate_insolidangle(). */
274 static bool accept_insolidangle(rvec x
, const t_pbc
* pbc
, void* data
);
275 /** Evaluates the \p insolidangle selection method. */
276 static void evaluate_insolidangle(const gmx::SelMethodEvalContext
& context
,
278 gmx_ana_selvalue_t
* out
,
281 /** Calculates the distance between unit vectors. */
282 static real
sph_distc(rvec x1
, rvec x2
);
283 /** Does a binary search on a \p t_partition to find a bin for a value. */
284 static int find_partition_bin(t_partition
* p
, real value
);
285 /** Finds a bin that corresponds to a location on the unit sphere surface. */
286 static int find_surface_bin(t_methoddata_insolidangle
* surf
, rvec x
);
287 /** Clears/initializes the bins on the unit sphere surface. */
288 static void clear_surface_points(t_methoddata_insolidangle
* surf
);
289 /** Frees memory allocated for storing the reference points in the surface bins. */
290 static void free_surface_points(t_methoddata_insolidangle
* surf
);
291 /** Adds a reference point to a given bin. */
292 static void add_surface_point(t_methoddata_insolidangle
* surf
, int tbin
, int pbin
, rvec x
);
293 /** Marks a bin as completely covered. */
294 static void mark_surface_covered(t_methoddata_insolidangle
* surf
, int tbin
, int pbin
);
295 /** Helper function for store_surface_point() to update a single zenith angle bin. */
296 static void update_surface_bin(t_methoddata_insolidangle
* surf
,
303 /** Adds a single reference point and updates the surface bins. */
304 static void store_surface_point(t_methoddata_insolidangle
* surf
, rvec x
);
306 * Optimizes the surface bins for faster searching.
308 * \param[in,out] surf Surface data structure.
310 * Currently, this function does nothing.
312 static void optimize_surface_points(t_methoddata_insolidangle
* surf
);
313 /** Estimates the area covered by the reference cones. */
314 static real
estimate_covered_fraction(t_methoddata_insolidangle
* surf
);
315 /** Checks whether a point lies within a solid angle. */
316 static bool is_surface_covered(t_methoddata_insolidangle
* surf
, rvec x
);
318 /** Parameters for the \p insolidangle selection method. */
319 static gmx_ana_selparam_t smparams_insolidangle
[] = {
320 { "center", { POS_VALUE
, 1, { nullptr } }, nullptr, SPAR_DYNAMIC
},
321 { "span", { POS_VALUE
, -1, { nullptr } }, nullptr, SPAR_DYNAMIC
| SPAR_VARNUM
},
322 { "cutoff", { REAL_VALUE
, 1, { nullptr } }, nullptr, SPAR_OPTIONAL
},
325 /** Help text for the \p insolidangle selection method. */
326 static const char* const help_insolidangle
[] = {
329 " insolidangle center POS span POS_EXPR [cutoff REAL]",
331 "This keyword selects atoms that are within [TT]REAL[tt] degrees",
332 "(default=5) of any position in [TT]POS_EXPR[tt] as seen from [TT]POS[tt]",
333 "a position expression that evaluates to a single position), i.e., atoms",
334 "in the solid angle spanned by the positions in [TT]POS_EXPR[tt] and",
335 "centered at [TT]POS[tt].[PAR]",
337 "Technically, the solid angle is constructed as a union of small cones",
338 "whose tip is at [TT]POS[tt] and the axis goes through a point in",
339 "[TT]POS_EXPR[tt]. There is such a cone for each position in",
340 "[TT]POS_EXPR[tt], and point is in the solid angle if it lies within any",
341 "of these cones. The cutoff determines the width of the cones.",
344 /** Selection method data for the \p insolidangle method. */
345 gmx_ana_selmethod_t sm_insolidangle
= {
349 asize(smparams_insolidangle
),
350 smparams_insolidangle
,
351 &init_data_insolidangle
,
355 &free_data_insolidangle
,
356 &init_frame_insolidangle
,
358 &evaluate_insolidangle
,
359 { "insolidangle center POS span POS_EXPR [cutoff REAL]", "Selecting atoms in a solid angle",
360 asize(help_insolidangle
), help_insolidangle
},
363 static void* init_data_insolidangle(int /* npar */, gmx_ana_selparam_t
* param
)
365 t_methoddata_insolidangle
* data
= new t_methoddata_insolidangle();
369 data
->distccut
= 0.0;
370 data
->targetbinsize
= 0.0;
373 data
->tbinsize
= 0.0;
374 data
->tbin
= nullptr;
379 param
[0].val
.u
.p
= &data
->center
;
380 param
[1].val
.u
.p
= &data
->span
;
381 param
[2].val
.u
.r
= &data
->angcut
;
385 static void init_insolidangle(const gmx_mtop_t
* /* top */,
387 gmx_ana_selparam_t
* /* param */,
390 t_methoddata_insolidangle
* surf
= static_cast<t_methoddata_insolidangle
*>(data
);
393 if (surf
->angcut
<= 0)
395 GMX_THROW(gmx::InvalidInputError("Angle cutoff should be > 0"));
398 surf
->angcut
*= DEG2RAD
;
400 surf
->distccut
= -std::cos(surf
->angcut
);
401 surf
->targetbinsize
= surf
->angcut
/ 2;
402 surf
->ntbins
= static_cast<int>(M_PI
/ surf
->targetbinsize
);
403 surf
->tbinsize
= (180.0 / surf
->ntbins
) * DEG2RAD
;
405 snew(surf
->tbin
, static_cast<int>(M_PI
/ surf
->tbinsize
) + 1);
407 for (i
= 0; i
< surf
->ntbins
; ++i
)
409 c
= static_cast<int>(std::max(std::sin(surf
->tbinsize
* i
), std::sin(surf
->tbinsize
* (i
+ 1)))
410 * M_2PI
/ surf
->targetbinsize
)
412 snew(surf
->tbin
[i
].p
, c
+ 1);
416 snew(surf
->bin
, surf
->maxbins
);
420 * \param data Data to free (should point to a \ref t_methoddata_insolidangle).
422 * Frees the memory allocated for \c t_methoddata_insolidangle::center and
423 * \c t_methoddata_insolidangle::span, as well as the memory for the internal
426 static void free_data_insolidangle(void* data
)
428 t_methoddata_insolidangle
* d
= static_cast<t_methoddata_insolidangle
*>(data
);
433 for (i
= 0; i
< d
->ntbins
; ++i
)
439 free_surface_points(d
);
444 static void init_frame_insolidangle(const gmx::SelMethodEvalContext
& context
, void* data
)
446 t_methoddata_insolidangle
* d
= static_cast<t_methoddata_insolidangle
*>(data
);
450 free_surface_points(d
);
451 clear_surface_points(d
);
452 for (i
= 0; i
< d
->span
.count(); ++i
)
456 pbc_dx(context
.pbc
, d
->span
.x
[i
], d
->center
.x
[0], dx
);
460 rvec_sub(d
->span
.x
[i
], d
->center
.x
[0], dx
);
463 store_surface_point(d
, dx
);
465 optimize_surface_points(d
);
470 * \param[in] x Test point.
471 * \param[in] pbc PBC data (if NULL, no PBC are used).
472 * \param[in] data Pointer to a \c t_methoddata_insolidangle data structure.
473 * \returns true if \p x is within the solid angle, false otherwise.
475 static bool accept_insolidangle(rvec x
, const t_pbc
* pbc
, void* data
)
477 t_methoddata_insolidangle
* d
= static_cast<t_methoddata_insolidangle
*>(data
);
482 pbc_dx(pbc
, x
, d
->center
.x
[0], dx
);
486 rvec_sub(x
, d
->center
.x
[0], dx
);
489 return is_surface_covered(d
, dx
);
493 * See sel_updatefunc() for description of the parameters.
494 * \p data should point to a \c t_methoddata_insolidangle.
496 * Calculates which atoms in \p g are within the solid angle spanned by
497 * \c t_methoddata_insolidangle::span and centered at
498 * \c t_methoddata_insolidangle::center, and stores the result in \p out->u.g.
500 static void evaluate_insolidangle(const gmx::SelMethodEvalContext
& context
,
502 gmx_ana_selvalue_t
* out
,
506 for (int b
= 0; b
< pos
->count(); ++b
)
508 if (accept_insolidangle(pos
->x
[b
], context
.pbc
, data
))
510 gmx_ana_pos_add_to_group(out
->u
.g
, pos
, b
);
516 * \param[in] sel Selection element to query.
517 * \returns true if the covered fraction can be estimated for \p sel with
518 * _gmx_selelem_estimate_coverfrac(), false otherwise.
520 bool _gmx_selelem_can_estimate_cover(const gmx::SelectionTreeElement
& sel
)
522 if (sel
.type
== SEL_BOOLEAN
&& sel
.u
.boolt
== BOOL_OR
)
527 bool bDynFound
= false;
528 gmx::SelectionTreeElementPointer child
= sel
.child
;
531 if (child
->type
== SEL_EXPRESSION
)
533 if (child
->u
.expr
.method
->name
== sm_insolidangle
.name
)
535 if (bFound
|| bDynFound
)
541 else if (child
->u
.expr
.method
&& (child
->u
.expr
.method
->flags
& SMETH_DYNAMIC
))
550 else if (!_gmx_selelem_can_estimate_cover(*child
))
560 * \param[in] sel Selection for which the fraction should be calculated.
561 * \returns Fraction of angles covered by the selection (between zero and one).
563 * The return value is undefined if _gmx_selelem_can_estimate_cover() returns
565 * Should be called after gmx_ana_evaluate_selections() has been called for the
568 real
_gmx_selelem_estimate_coverfrac(const gmx::SelectionTreeElement
& sel
)
572 if (sel
.type
== SEL_EXPRESSION
&& sel
.u
.expr
.method
->name
== sm_insolidangle
.name
)
574 t_methoddata_insolidangle
* d
= static_cast<t_methoddata_insolidangle
*>(sel
.u
.expr
.mdata
);
577 d
->cfrac
= estimate_covered_fraction(d
);
581 if (sel
.type
== SEL_BOOLEAN
&& sel
.u
.boolt
== BOOL_NOT
)
583 cfrac
= _gmx_selelem_estimate_coverfrac(*sel
.child
);
591 /* Here, we assume that the selection is simple enough */
592 gmx::SelectionTreeElementPointer child
= sel
.child
;
595 cfrac
= _gmx_selelem_estimate_coverfrac(*child
);
606 * \param[in] x1 Unit vector 1.
607 * \param[in] x2 Unit vector 2.
608 * \returns Minus the dot product of \p x1 and \p x2.
610 * This function is used internally to calculate the distance between the
611 * unit vectors \p x1 and \p x2 to find out whether \p x2 is within the
612 * cone centered at \p x1. Currently, the cosine of the angle is used
613 * for efficiency, and the minus is there to make it behave like a normal
614 * distance (larger values mean longer distances).
616 static real
sph_distc(rvec x1
, rvec x2
)
618 return -iprod(x1
, x2
);
622 * \param[in] p Partition to search.
623 * \param[in] value Value to search for.
624 * \returns The partition index in \p p that contains \p value.
626 * If \p value is outside the range of \p p, the first/last index is returned.
627 * Otherwise, the return value \c i satisfies \c p->p[i].left<=value and
628 * \c p->p[i+1].left>value
630 static int find_partition_bin(t_partition
* p
, real value
)
632 int pmin
, pmax
, pbin
;
634 /* Binary search the partition */
637 while (pmax
> pmin
+ 1)
639 pbin
= pmin
+ (pmax
- pmin
) / 2;
640 if (p
->p
[pbin
].left
<= value
)
654 * \param[in] surf Surface data structure to search.
655 * \param[in] x Unit vector to find.
656 * \returns The bin index that contains \p x.
658 * The return value is an index to the \p surf->bin array.
660 static int find_surface_bin(t_methoddata_insolidangle
* surf
, rvec x
)
666 phi
= atan2(x
[YY
], x
[XX
]);
667 tbin
= static_cast<int>(std::floor(theta
/ surf
->tbinsize
));
668 if (tbin
>= surf
->ntbins
)
670 tbin
= surf
->ntbins
- 1;
672 pbin
= find_partition_bin(&surf
->tbin
[tbin
], phi
);
673 return surf
->tbin
[tbin
].p
[pbin
].bin
;
677 * \param[in,out] surf Surface data structure.
679 * Clears the reference points from the bins and (re)initializes the edges
680 * of the azimuthal bins.
682 static void clear_surface_points(t_methoddata_insolidangle
* surf
)
687 for (i
= 0; i
< surf
->ntbins
; ++i
)
689 c
= static_cast<int>(std::min(std::sin(surf
->tbinsize
* i
), std::sin(surf
->tbinsize
* (i
+ 1)))
690 * M_2PI
/ surf
->targetbinsize
)
697 for (j
= 0; j
< c
; ++j
)
699 surf
->tbin
[i
].p
[j
].left
= -M_PI
+ j
* M_2PI
/ c
- 0.0001;
700 surf
->tbin
[i
].p
[j
].bin
= surf
->nbins
;
701 surf
->bin
[surf
->nbins
].n
= 0;
704 surf
->tbin
[i
].p
[c
].left
= M_PI
+ 0.0001;
705 surf
->tbin
[i
].p
[c
].bin
= -1;
710 * \param[in,out] surf Surface data structure.
712 static void free_surface_points(t_methoddata_insolidangle
* surf
)
716 for (i
= 0; i
< surf
->nbins
; ++i
)
720 sfree(surf
->bin
[i
].x
);
722 surf
->bin
[i
].n_alloc
= 0;
723 surf
->bin
[i
].x
= nullptr;
728 * \param[in,out] surf Surface data structure.
729 * \param[in] tbin Bin number in the zenith angle direction.
730 * \param[in] pbin Bin number in the azimuthal angle direction.
731 * \param[in] x Point to store.
733 static void add_surface_point(t_methoddata_insolidangle
* surf
, int tbin
, int pbin
, rvec x
)
737 bin
= surf
->tbin
[tbin
].p
[pbin
].bin
;
738 /* Return if bin is already completely covered */
739 if (surf
->bin
[bin
].n
== -1)
743 /* Allocate more space if necessary */
744 if (surf
->bin
[bin
].n
== surf
->bin
[bin
].n_alloc
)
746 surf
->bin
[bin
].n_alloc
+= 10;
747 srenew(surf
->bin
[bin
].x
, surf
->bin
[bin
].n_alloc
);
749 /* Add the point to the bin */
750 copy_rvec(x
, surf
->bin
[bin
].x
[surf
->bin
[bin
].n
]);
755 * \param[in,out] surf Surface data structure.
756 * \param[in] tbin Bin number in the zenith angle direction.
757 * \param[in] pbin Bin number in the azimuthal angle direction.
759 static void mark_surface_covered(t_methoddata_insolidangle
* surf
, int tbin
, int pbin
)
763 bin
= surf
->tbin
[tbin
].p
[pbin
].bin
;
764 surf
->bin
[bin
].n
= -1;
768 * \param[in,out] surf Surface data structure.
769 * \param[in] tbin Bin number in the zenith angle direction.
770 * \param[in] phi Azimuthal angle of \p x.
771 * \param[in] pdelta1 Width of the cone at the lower edge of \p tbin.
772 * \param[in] pdelta2 Width of the cone at the uppper edge of \p tbin.
773 * \param[in] pdeltamax Max. width of the cone inside \p tbin.
774 * \param[in] x Point to store (should have unit length).
776 static void update_surface_bin(t_methoddata_insolidangle
* surf
,
784 real pdelta
, phi1
, phi2
;
785 int pbin1
, pbin2
, pbiniter
, pbin
;
787 /* Find the edges of the bins affected */
788 pdelta
= max(max(pdelta1
, pdelta2
), pdeltamax
);
792 pbin
= find_partition_bin(&surf
->tbin
[tbin
], phi1
);
797 pbin
= find_partition_bin(&surf
->tbin
[tbin
], phi1
+ M_2PI
);
798 pbin1
= pbin
- surf
->tbin
[tbin
].n
;
803 pbin2
= find_partition_bin(&surf
->tbin
[tbin
], phi2
);
807 pbin2
= find_partition_bin(&surf
->tbin
[tbin
], phi2
- M_2PI
);
808 pbin2
+= surf
->tbin
[tbin
].n
;
811 if (pbin2
- pbin1
> surf
->tbin
[tbin
].n
)
813 pbin2
= pbin1
+ surf
->tbin
[tbin
].n
;
815 /* Find the edges of completely covered region */
816 pdelta
= min(pdelta1
, pdelta2
);
823 /* Loop over all affected bins */
824 for (pbiniter
= pbin1
; pbiniter
!= pbin2
; ++pbiniter
, ++pbin
)
826 /* Wrap bin around if end reached */
827 if (pbin
== surf
->tbin
[tbin
].n
)
833 /* Check if bin is completely covered and update */
834 if (surf
->tbin
[tbin
].p
[pbin
].left
>= phi1
&& surf
->tbin
[tbin
].p
[pbin
+ 1].left
<= phi2
)
836 mark_surface_covered(surf
, tbin
, pbin
);
840 add_surface_point(surf
, tbin
, pbin
, x
);
846 * \param[in,out] surf Surface data structure.
847 * \param[in] x Point to store (should have unit length).
849 * Finds all the bins covered by the cone centered at \p x and calls
850 * update_surface_bin() to update them.
852 static void store_surface_point(t_methoddata_insolidangle
* surf
, rvec x
)
855 real pdeltamax
, tmax
;
856 real theta1
, theta2
, pdelta1
, pdelta2
;
860 phi
= atan2(x
[YY
], x
[XX
]);
861 /* Find the maximum extent in the phi direction */
862 if (theta
<= surf
->angcut
)
867 else if (theta
>= M_PI
- surf
->angcut
)
874 pdeltamax
= std::asin(sin(surf
->angcut
) / sin(theta
));
875 tmax
= std::acos(cos(theta
) / cos(surf
->angcut
));
877 /* Find the first affected bin */
878 tbin
= max(static_cast<int>(std::floor((theta
- surf
->angcut
) / surf
->tbinsize
)), 0);
879 theta1
= tbin
* surf
->tbinsize
;
880 if (theta1
< theta
- surf
->angcut
)
888 /* Loop through all affected bins */
889 while (tbin
< std::ceil((theta
+ surf
->angcut
) / surf
->tbinsize
) && tbin
< surf
->ntbins
)
891 /* Calculate the next boundaries */
892 theta2
= (tbin
+ 1) * surf
->tbinsize
;
893 if (theta2
> theta
+ surf
->angcut
)
895 /* The circle is completely outside the cone */
898 else if (theta2
<= -(theta
- surf
->angcut
) || theta2
>= M_2PI
- (theta
+ surf
->angcut
)
899 || tbin
== surf
->ntbins
- 1)
901 /* The circle is completely inside the cone, or we are in the
902 * 360 degree bin covering the pole. */
907 /* TODO: This formula is numerically unstable if theta is very
908 * close to the pole. In practice, it probably does not matter
909 * much, but it would be nicer to adjust the theta bin boundaries
910 * such that the case above catches this instead of falling through
913 * asin(std::sqrt((gmx::square(std::sin(surf
->angcut
/ 2))
914 - gmx::square(std::sin((theta2
- theta
) / 2)))
915 / (sin(theta
) * sin(theta2
))));
918 if (tmax
>= theta1
&& tmax
<= theta2
)
920 update_surface_bin(surf
, tbin
, phi
, pdelta1
, pdelta2
, pdeltamax
, x
);
924 update_surface_bin(surf
, tbin
, phi
, pdelta1
, pdelta2
, 0, x
);
933 static void optimize_surface_points(t_methoddata_insolidangle
* /* surf */)
935 /* TODO: Implement */
939 * \param[in] surf Surface data structure.
940 * \returns An estimate for the area covered by the reference points.
942 static real
estimate_covered_fraction(t_methoddata_insolidangle
* surf
)
945 real cfrac
, tfrac
, pfrac
;
948 for (t
= 0; t
< surf
->ntbins
; ++t
)
950 tfrac
= std::cos(t
* surf
->tbinsize
) - std::cos((t
+ 1) * surf
->tbinsize
);
951 for (p
= 0; p
< surf
->tbin
[t
].n
; ++p
)
953 pfrac
= surf
->tbin
[t
].p
[p
+ 1].left
- surf
->tbin
[t
].p
[p
].left
;
954 n
= surf
->bin
[surf
->tbin
[t
].p
[p
].bin
].n
;
955 if (n
== -1) /* Bin completely covered */
957 cfrac
+= tfrac
* pfrac
;
959 else if (n
> 0) /* Bin partially covered */
961 cfrac
+= tfrac
* pfrac
/ 2; /* A rough estimate */
965 return cfrac
/ (4 * M_PI
);
969 * \param[in] surf Surface data structure to search.
970 * \param[in] x Unit vector to check.
971 * \returns true if \p x is within the solid angle, false otherwise.
973 static bool is_surface_covered(t_methoddata_insolidangle
* surf
, rvec x
)
977 bin
= find_surface_bin(surf
, x
);
978 /* Check for completely covered bin */
979 if (surf
->bin
[bin
].n
== -1)
983 /* Check each point that partially covers the bin */
984 for (i
= 0; i
< surf
->bin
[bin
].n
; ++i
)
986 if (sph_distc(x
, surf
->bin
[bin
].x
[i
]) < surf
->distccut
)