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35 /*! \page page_module_selection_insolidangle Selection method: insolidangle
37 * This method selects a subset of particles that are located in a solid
38 * angle defined by a center and a set of points.
39 * The solid angle is constructed as a union of small cones whose axis
40 * goes through the center and a point.
41 * So there's such a cone for each position, and a
42 * point is in the solid angle if it lies within any of these cones.
43 * The width of the cones can be adjusted.
47 * The method is implemented by partitioning the surface of the unit sphere
48 * into bins using the polar coordinates \f$(\theta, \phi)\f$.
49 * The partitioning is always uniform in the zenith angle \f$\theta\f$,
50 * while the partitioning in the azimuthal angle \f$\phi\f$ varies.
51 * For each reference point, the unit vector from the center to the point
52 * is constructed, and it is stored in all the bins that overlap with the
53 * cone defined by the point.
54 * Bins that are completely covered by a single cone are marked as such.
55 * Checking whether a point is in the solid angle is then straightforward
56 * with this data structure: one finds the bin that corresponds to the point,
57 * and checks whether the bin is completely covered. If it is not, one
58 * additionally needs to check whether it is within the specified cutoff of
59 * any of the stored points.
61 * The above construction gives quite a lot of flexibility for constructing
62 * the bins without modifying the rest of the code.
63 * The current (quite inefficient) implementation is discussed below, but
64 * it should be optimized to get the most out of the code.
66 * The current way of constructing the bins constructs the boundaries
67 * statically: the bin size in the zenith direction is set to approximately
68 * half the angle cutoff, and the bins in the azimuthal direction have
69 * sizes such that the shortest edge of the bin is approximately equal to
70 * half the angle cutoff (for the regions close to the poles, a single bin
72 * Each reference point is then added to the bins as follows:
73 * -# Find the zenith angle range that is spanned by the cone centered at the
74 * point (this is simple addition/subtraction).
75 * -# Calculate the maximal span of the cone in the azimuthal direction using
77 * \f[\sin \Delta \phi_{max} = \frac{\sin \alpha}{\sin \theta}\f]
78 * (a sine formula in spherical coordinates),
79 * where \f$\alpha\f$ is the width of the cone and \f$\theta\f$ is the
80 * zenith angle of the cone center.
81 * Similarly, the zenith angle at which this extent is achieved is
83 * \f[\cos \theta_{max} = \frac{\cos \theta}{\cos \alpha}\f]
84 * (Pythagoras's theorem in spherical coordinates).
85 * -# For each zenith angle bin that is at least partially covered by the
86 * cone, calculate the span of the cone at the edges using
87 * \f[\sin^2 \frac{\Delta \phi}{2} = \frac{\sin^2 \frac{\alpha}{2} - \sin^2 \frac{\theta - \theta'}{2}}{\sin \theta \sin \theta'}\f]
88 * (distance in spherical geometry),
89 * where \f$\theta'\f$ is the zenith angle of the bin edge.
90 * Treat zenith angle bins that are completely covered by the cone (in the
91 * 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
120 #include "gromacs/legacyheaders/macros.h"
121 #include "gromacs/legacyheaders/maths.h"
122 #include "gromacs/legacyheaders/pbc.h"
123 #include "gromacs/legacyheaders/physics.h"
124 #include "gromacs/legacyheaders/smalloc.h"
125 #include "gromacs/legacyheaders/vec.h"
127 #include "gromacs/selection/indexutil.h"
128 #include "gromacs/selection/position.h"
129 #include "gromacs/selection/selection.h"
130 #include "gromacs/selection/selmethod.h"
131 #include "gromacs/utility/exceptions.h"
139 * Internal data structure for the \p insolidangle selection method.
141 * \see \c t_partition
145 /** Left edge of the partition. */
147 /** Bin index corresponding to this partition. */
152 * Internal data structure for the \p insolidangle selection method.
154 * Describes the surface partitioning within one slice along the zenith angle.
155 * The slice from azimuthal angle \p p[i].left to \p p[i+1].left belongs to
160 /** Number of partition items (\p p contains \p n+1 items). */
162 /** Array of partition edges and corresponding bins. */
167 * Internal data structure for the \p insolidangle selection method.
169 * Contains the reference points that partially cover a certain region on the
170 * surface of the unit sphere.
171 * If \p n is -1, the whole region described by the bin is covered.
175 /** Number of points in the array \p x, -1 if whole bin covered. */
177 /** Number of elements allocated for \p x. */
179 /** Array of points that partially cover the bin. */
181 } t_spheresurfacebin;
184 * Data structure for the \p insolidangle selection method.
186 * All angle values are in the units of radians.
190 /** Center of the solid angle. */
191 gmx_ana_pos_t center;
192 /** Positions that span the solid angle. */
196 /** Estimate of the covered fraction. */
199 /** Cutoff for the cosine (equals cos(angcut)). */
201 /** Bin size to be used as the target bin size when constructing the bins. */
204 /** Number of bins in the \p tbin array. */
206 /** Size of one bin in the zenith angle direction. */
208 /** Array of zenith angle slices. */
210 /** Number of elements allocated for the \p bin array. */
212 /** Number of elements used in the \p bin array. */
214 /** Array of individual bins. */
215 t_spheresurfacebin *bin;
216 } t_methoddata_insolidangle;
218 /** Allocates data for the \p insolidangle selection method. */
220 init_data_insolidangle(int npar, gmx_ana_selparam_t *param);
221 /** Initializes the \p insolidangle selection method. */
223 init_insolidangle(t_topology *top, int npar, gmx_ana_selparam_t *param, void *data);
224 /** Frees the data allocated for the \p insolidangle selection method. */
226 free_data_insolidangle(void *data);
227 /** Initializes the evaluation of the \p insolidangle selection method for a frame. */
229 init_frame_insolidangle(t_topology *top, t_trxframe *fr, t_pbc *pbc, void *data);
230 /** Internal helper function for evaluate_insolidangle(). */
232 accept_insolidangle(rvec x, t_pbc *pbc, void *data);
233 /** Evaluates the \p insolidangle selection method. */
235 evaluate_insolidangle(t_topology *top, t_trxframe *fr, t_pbc *pbc,
236 gmx_ana_pos_t *pos, gmx_ana_selvalue_t *out, void *data);
238 /** Calculates the distance between unit vectors. */
240 sph_distc(rvec x1, rvec x2);
241 /** Does a binary search on a \p t_partition to find a bin for a value. */
243 find_partition_bin(t_partition *p, real value);
244 /** Finds a bin that corresponds to a location on the unit sphere surface. */
246 find_surface_bin(t_methoddata_insolidangle *surf, rvec x);
247 /** Clears/initializes the bins on the unit sphere surface. */
249 clear_surface_points(t_methoddata_insolidangle *surf);
250 /** Frees memory allocated for storing the reference points in the surface bins. */
252 free_surface_points(t_methoddata_insolidangle *surf);
253 /** Adds a reference point to a given bin. */
255 add_surface_point(t_methoddata_insolidangle *surf, int tbin, int pbin, rvec x);
256 /** Marks a bin as completely covered. */
258 mark_surface_covered(t_methoddata_insolidangle *surf, int tbin, int pbin);
259 /** Helper function for store_surface_point() to update a single zenith angle bin. */
261 update_surface_bin(t_methoddata_insolidangle *surf, int tbin,
262 real phi, real pdelta1, real pdelta2, real pdeltamax,
264 /** Adds a single reference point and updates the surface bins. */
266 store_surface_point(t_methoddata_insolidangle *surf, rvec x);
267 /** Optimizes the surface bins for faster searching. */
269 optimize_surface_points(t_methoddata_insolidangle *surf);
270 /** Estimates the area covered by the reference cones. */
272 estimate_covered_fraction(t_methoddata_insolidangle *surf);
273 /** Checks whether a point lies within a solid angle. */
275 is_surface_covered(t_methoddata_insolidangle *surf, rvec x);
277 /** Parameters for the \p insolidangle selection method. */
278 static gmx_ana_selparam_t smparams_insolidangle[] = {
279 {"center", {POS_VALUE, 1, {NULL}}, NULL, SPAR_DYNAMIC},
280 {"span", {POS_VALUE, -1, {NULL}}, NULL, SPAR_DYNAMIC | SPAR_VARNUM},
281 {"cutoff", {REAL_VALUE, 1, {NULL}}, NULL, SPAR_OPTIONAL},
284 /** Help text for the \p insolidangle selection method. */
285 static const char *help_insolidangle[] = {
286 "SELECTING ATOMS IN A SOLID ANGLE[PAR]",
288 "[TT]insolidangle center POS span POS_EXPR [cutoff REAL][tt][PAR]",
290 "This keyword selects atoms that are within [TT]REAL[tt] degrees",
291 "(default=5) of any position in [TT]POS_EXPR[tt] as seen from [TT]POS[tt]",
292 "a position expression that evaluates to a single position), i.e., atoms",
293 "in the solid angle spanned by the positions in [TT]POS_EXPR[tt] and",
294 "centered at [TT]POS[tt].[PAR]"
296 "Technically, the solid angle is constructed as a union of small cones",
297 "whose tip is at [TT]POS[tt] and the axis goes through a point in",
298 "[TT]POS_EXPR[tt]. There is such a cone for each position in",
299 "[TT]POS_EXPR[tt], and point is in the solid angle if it lies within any",
300 "of these cones. The cutoff determines the width of the cones.",
303 /** \internal Selection method data for the \p insolidangle method. */
304 gmx_ana_selmethod_t sm_insolidangle = {
305 "insolidangle", GROUP_VALUE, SMETH_DYNAMIC,
306 asize(smparams_insolidangle), smparams_insolidangle,
307 &init_data_insolidangle,
311 &free_data_insolidangle,
312 &init_frame_insolidangle,
314 &evaluate_insolidangle,
315 {"insolidangle center POS span POS_EXPR [cutoff REAL]",
316 asize(help_insolidangle), help_insolidangle},
320 * \param[in] npar Not used (should be 3).
321 * \param[in,out] param Method parameters (should point to
322 * \ref smparams_insolidangle).
323 * \returns Pointer to the allocated data (\ref t_methoddata_insolidangle).
325 * Allocates memory for a \ref t_methoddata_insolidangle structure and
326 * initializes the parameter as follows:
327 * - \p center defines the value for t_methoddata_insolidangle::center.
328 * - \p span defines the value for t_methoddata_insolidangle::span.
329 * - \p cutoff defines the value for t_methoddata_insolidangle::angcut.
332 init_data_insolidangle(int npar, gmx_ana_selparam_t *param)
334 t_methoddata_insolidangle *data;
338 param[0].val.u.p = &data->center;
339 param[1].val.u.p = &data->span;
340 param[2].val.u.r = &data->angcut;
345 * \param top Not used.
346 * \param npar Not used.
347 * \param param Not used.
348 * \param data Pointer to \ref t_methoddata_insolidangle to initialize.
349 * \returns 0 on success, -1 on failure.
351 * Converts t_methoddata_insolidangle::angcut to radians and allocates
352 * and allocates memory for the bins used during the evaluation.
355 init_insolidangle(t_topology *top, int npar, gmx_ana_selparam_t *param, void *data)
357 t_methoddata_insolidangle *surf = (t_methoddata_insolidangle *)data;
360 if (surf->angcut <= 0)
362 GMX_THROW(gmx::InvalidInputError("Angle cutoff should be > 0"));
365 surf->angcut *= DEG2RAD;
367 surf->distccut = -cos(surf->angcut);
368 surf->targetbinsize = surf->angcut / 2;
369 surf->ntbins = static_cast<int>(M_PI / surf->targetbinsize);
370 surf->tbinsize = (180.0 / surf->ntbins)*DEG2RAD;
372 snew(surf->tbin, static_cast<int>(M_PI / surf->tbinsize) + 1);
374 for (i = 0; i < surf->ntbins; ++i)
376 c = static_cast<int>(max(sin(surf->tbinsize*i),
377 sin(surf->tbinsize*(i+1)))
378 * M_2PI / surf->targetbinsize) + 1;
379 snew(surf->tbin[i].p, c+1);
383 snew(surf->bin, surf->maxbins);
387 * \param data Data to free (should point to a \ref t_methoddata_insolidangle).
389 * Frees the memory allocated for \c t_methoddata_insolidangle::center and
390 * \c t_methoddata_insolidangle::span, as well as the memory for the internal
394 free_data_insolidangle(void *data)
396 t_methoddata_insolidangle *d = (t_methoddata_insolidangle *)data;
401 for (i = 0; i < d->ntbins; ++i)
407 free_surface_points(d);
413 * \param[in] top Not used.
414 * \param[in] fr Current frame.
415 * \param[in] pbc PBC structure.
416 * \param data Should point to a \ref t_methoddata_insolidangle.
418 * Creates a lookup structure that enables fast queries of whether a point
419 * is within the solid angle or not.
422 init_frame_insolidangle(t_topology *top, t_trxframe *fr, t_pbc *pbc, void *data)
424 t_methoddata_insolidangle *d = (t_methoddata_insolidangle *)data;
428 free_surface_points(d);
429 clear_surface_points(d);
430 for (i = 0; i < d->span.nr; ++i)
434 pbc_dx(pbc, d->span.x[i], d->center.x[0], dx);
438 rvec_sub(d->span.x[i], d->center.x[0], dx);
441 store_surface_point(d, dx);
443 optimize_surface_points(d);
448 * \param[in] x Test point.
449 * \param[in] pbc PBC data (if NULL, no PBC are used).
450 * \param[in] data Pointer to a \c t_methoddata_insolidangle data structure.
451 * \returns true if \p x is within the solid angle, false otherwise.
454 accept_insolidangle(rvec x, t_pbc *pbc, void *data)
456 t_methoddata_insolidangle *d = (t_methoddata_insolidangle *)data;
461 pbc_dx(pbc, x, d->center.x[0], dx);
465 rvec_sub(x, d->center.x[0], dx);
468 return is_surface_covered(d, dx);
472 * See sel_updatefunc() for description of the parameters.
473 * \p data should point to a \c t_methoddata_insolidangle.
475 * Calculates which atoms in \p g are within the solid angle spanned by
476 * \c t_methoddata_insolidangle::span and centered at
477 * \c t_methoddata_insolidangle::center, and stores the result in \p out->u.g.
480 evaluate_insolidangle(t_topology *top, t_trxframe *fr, t_pbc *pbc,
481 gmx_ana_pos_t *pos, gmx_ana_selvalue_t *out, void *data)
486 for (b = 0; b < pos->nr; ++b)
488 if (accept_insolidangle(pos->x[b], pbc, data))
490 gmx_ana_pos_append(NULL, out->u.g, pos, b, 0);
496 * \param[in] sel Selection element to query.
497 * \returns true if the covered fraction can be estimated for \p sel with
498 * _gmx_selelem_estimate_coverfrac(), false otherwise.
501 _gmx_selelem_can_estimate_cover(const gmx::SelectionTreeElement &sel)
503 if (sel.type == SEL_BOOLEAN && sel.u.boolt == BOOL_OR)
508 bool bDynFound = false;
509 gmx::SelectionTreeElementPointer child = sel.child;
512 if (child->type == SEL_EXPRESSION)
514 if (child->u.expr.method->name == sm_insolidangle.name)
516 if (bFound || bDynFound)
522 else if (child->u.expr.method
523 && (child->u.expr.method->flags & SMETH_DYNAMIC))
532 else if (!_gmx_selelem_can_estimate_cover(*child))
542 * \param[in] sel Selection for which the fraction should be calculated.
543 * \returns Fraction of angles covered by the selection (between zero and one).
545 * The return value is undefined if _gmx_selelem_can_estimate_cover() returns
547 * Should be called after gmx_ana_evaluate_selections() has been called for the
551 _gmx_selelem_estimate_coverfrac(const gmx::SelectionTreeElement &sel)
555 if (sel.type == SEL_EXPRESSION && sel.u.expr.method->name == sm_insolidangle.name)
557 t_methoddata_insolidangle *d = (t_methoddata_insolidangle *)sel.u.expr.mdata;
560 d->cfrac = estimate_covered_fraction(d);
564 if (sel.type == SEL_BOOLEAN && sel.u.boolt == BOOL_NOT)
566 cfrac = _gmx_selelem_estimate_coverfrac(*sel.child);
574 /* Here, we assume that the selection is simple enough */
575 gmx::SelectionTreeElementPointer child = sel.child;
578 cfrac = _gmx_selelem_estimate_coverfrac(*child);
589 * \param[in] x1 Unit vector 1.
590 * \param[in] x2 Unit vector 2.
591 * \returns Minus the dot product of \p x1 and \p x2.
593 * This function is used internally to calculate the distance between the
594 * unit vectors \p x1 and \p x2 to find out whether \p x2 is within the
595 * cone centered at \p x1. Currently, the cosine of the angle is used
596 * for efficiency, and the minus is there to make it behave like a normal
597 * distance (larger values mean longer distances).
600 sph_distc(rvec x1, rvec x2)
602 return -iprod(x1, x2);
606 * \param[in] p Partition to search.
607 * \param[in] value Value to search for.
608 * \returns The partition index in \p p that contains \p value.
610 * If \p value is outside the range of \p p, the first/last index is returned.
611 * Otherwise, the return value \c i satisfies \c p->p[i].left<=value and
612 * \c p->p[i+1].left>value
615 find_partition_bin(t_partition *p, real value)
617 int pmin, pmax, pbin;
619 /* Binary search the partition */
620 pmin = 0; pmax = p->n;
621 while (pmax > pmin + 1)
623 pbin = pmin + (pmax - pmin) / 2;
624 if (p->p[pbin].left <= value)
638 * \param[in] surf Surface data structure to search.
639 * \param[in] x Unit vector to find.
640 * \returns The bin index that contains \p x.
642 * The return value is an index to the \p surf->bin array.
645 find_surface_bin(t_methoddata_insolidangle *surf, rvec x)
651 phi = atan2(x[YY], x[XX]);
652 tbin = static_cast<int>(floor(theta / surf->tbinsize));
653 if (tbin >= surf->ntbins)
655 tbin = surf->ntbins - 1;
657 pbin = find_partition_bin(&surf->tbin[tbin], phi);
658 return surf->tbin[tbin].p[pbin].bin;
662 * \param[in,out] surf Surface data structure.
664 * Clears the reference points from the bins and (re)initializes the edges
665 * of the azimuthal bins.
668 clear_surface_points(t_methoddata_insolidangle *surf)
673 for (i = 0; i < surf->ntbins; ++i)
675 c = static_cast<int>(min(sin(surf->tbinsize*i),
676 sin(surf->tbinsize*(i+1)))
677 * M_2PI / surf->targetbinsize) + 1;
683 for (j = 0; j < c; ++j)
685 surf->tbin[i].p[j].left = -M_PI + j*M_2PI/c - 0.0001;
686 surf->tbin[i].p[j].bin = surf->nbins;
687 surf->bin[surf->nbins].n = 0;
690 surf->tbin[i].p[c].left = M_PI + 0.0001;
691 surf->tbin[i].p[c].bin = -1;
696 * \param[in,out] surf Surface data structure.
699 free_surface_points(t_methoddata_insolidangle *surf)
703 for (i = 0; i < surf->nbins; ++i)
707 sfree(surf->bin[i].x);
709 surf->bin[i].n_alloc = 0;
710 surf->bin[i].x = NULL;
715 * \param[in,out] surf Surface data structure.
716 * \param[in] tbin Bin number in the zenith angle direction.
717 * \param[in] pbin Bin number in the azimuthal angle direction.
718 * \param[in] x Point to store.
721 add_surface_point(t_methoddata_insolidangle *surf, int tbin, int pbin, rvec x)
725 bin = surf->tbin[tbin].p[pbin].bin;
726 /* Return if bin is already completely covered */
727 if (surf->bin[bin].n == -1)
731 /* Allocate more space if necessary */
732 if (surf->bin[bin].n == surf->bin[bin].n_alloc)
734 surf->bin[bin].n_alloc += 10;
735 srenew(surf->bin[bin].x, surf->bin[bin].n_alloc);
737 /* Add the point to the bin */
738 copy_rvec(x, surf->bin[bin].x[surf->bin[bin].n]);
743 * \param[in,out] surf Surface data structure.
744 * \param[in] tbin Bin number in the zenith angle direction.
745 * \param[in] pbin Bin number in the azimuthal angle direction.
748 mark_surface_covered(t_methoddata_insolidangle *surf, int tbin, int pbin)
752 bin = surf->tbin[tbin].p[pbin].bin;
753 surf->bin[bin].n = -1;
757 * \param[in,out] surf Surface data structure.
758 * \param[in] tbin Bin number in the zenith angle direction.
759 * \param[in] phi Azimuthal angle of \p x.
760 * \param[in] pdelta1 Width of the cone at the lower edge of \p tbin.
761 * \param[in] pdelta2 Width of the cone at the uppper edge of \p tbin.
762 * \param[in] pdeltamax Max. width of the cone inside \p tbin.
763 * \param[in] x Point to store (should have unit length).
766 update_surface_bin(t_methoddata_insolidangle *surf, int tbin,
767 real phi, real pdelta1, real pdelta2, real pdeltamax,
770 real pdelta, phi1, phi2;
771 int pbin1, pbin2, pbiniter, pbin;
773 /* Find the edges of the bins affected */
774 pdelta = max(max(pdelta1, pdelta2), pdeltamax);
778 pbin = find_partition_bin(&surf->tbin[tbin], phi1);
783 pbin = find_partition_bin(&surf->tbin[tbin], phi1 + M_2PI);
784 pbin1 = pbin - surf->tbin[tbin].n;
789 pbin2 = find_partition_bin(&surf->tbin[tbin], phi2);
793 pbin2 = find_partition_bin(&surf->tbin[tbin], phi2 - M_2PI);
794 pbin2 += surf->tbin[tbin].n;
797 if (pbin2 - pbin1 > surf->tbin[tbin].n)
799 pbin2 = pbin1 + surf->tbin[tbin].n;
801 /* Find the edges of completely covered region */
802 pdelta = min(pdelta1, pdelta2);
809 /* Loop over all affected bins */
810 for (pbiniter = pbin1; pbiniter != pbin2; ++pbiniter, ++pbin)
812 /* Wrap bin around if end reached */
813 if (pbin == surf->tbin[tbin].n)
819 /* Check if bin is completely covered and update */
820 if (surf->tbin[tbin].p[pbin].left >= phi1
821 && surf->tbin[tbin].p[pbin+1].left <= phi2)
823 mark_surface_covered(surf, tbin, pbin);
827 add_surface_point(surf, tbin, pbin, x);
833 * \param[in,out] surf Surface data structure.
834 * \param[in] x Point to store (should have unit length).
836 * Finds all the bins covered by the cone centered at \p x and calls
837 * update_surface_bin() to update them.
840 store_surface_point(t_methoddata_insolidangle *surf, rvec x)
843 real pdeltamax, tmax;
844 real theta1, theta2, pdelta1, pdelta2;
848 phi = atan2(x[YY], x[XX]);
849 /* Find the maximum extent in the phi direction */
850 if (theta <= surf->angcut)
855 else if (theta >= M_PI - surf->angcut)
862 pdeltamax = asin(sin(surf->angcut) / sin(theta));
863 tmax = acos(cos(theta) / cos(surf->angcut));
865 /* Find the first affected bin */
866 tbin = max(static_cast<int>(floor((theta - surf->angcut) / surf->tbinsize)), 0);
867 theta1 = tbin * surf->tbinsize;
868 if (theta1 < theta - surf->angcut)
876 /* Loop through all affected bins */
877 while (tbin < ceil((theta + surf->angcut) / surf->tbinsize)
878 && tbin < surf->ntbins)
880 /* Calculate the next boundaries */
881 theta2 = (tbin+1) * surf->tbinsize;
882 if (theta2 > theta + surf->angcut)
884 /* The circle is completely outside the cone */
887 else if (theta2 <= -(theta - surf->angcut)
888 || theta2 >= M_2PI - (theta + surf->angcut)
889 || tbin == surf->ntbins - 1)
891 /* The circle is completely inside the cone, or we are in the
892 * 360 degree bin covering the pole. */
897 /* TODO: This formula is numerically unstable if theta is very
898 * close to the pole. In practice, it probably does not matter
899 * much, but it would be nicer to adjust the theta bin boundaries
900 * such that the case above catches this instead of falling through
902 pdelta2 = 2*asin(sqrt(
903 (sqr(sin(surf->angcut/2)) - sqr(sin((theta2-theta)/2))) /
904 (sin(theta) * sin(theta2))));
907 if (tmax >= theta1 && tmax <= theta2)
909 update_surface_bin(surf, tbin, phi, pdelta1, pdelta2, pdeltamax, x);
913 update_surface_bin(surf, tbin, phi, pdelta1, pdelta2, 0, x);
923 * \param[in,out] surf Surface data structure.
925 * Currently, this function does nothing.
928 optimize_surface_points(t_methoddata_insolidangle *surf)
930 /* TODO: Implement */
934 * \param[in] surf Surface data structure.
935 * \returns An estimate for the area covered by the reference points.
938 estimate_covered_fraction(t_methoddata_insolidangle *surf)
941 real cfrac, tfrac, pfrac;
944 for (t = 0; t < surf->ntbins; ++t)
946 tfrac = cos(t * surf->tbinsize) - cos((t+1) * surf->tbinsize);
947 for (p = 0; p < surf->tbin[t].n; ++p)
949 pfrac = surf->tbin[t].p[p+1].left - surf->tbin[t].p[p].left;
950 n = surf->bin[surf->tbin[t].p[p].bin].n;
951 if (n == -1) /* Bin completely covered */
953 cfrac += tfrac * pfrac;
955 else if (n > 0) /* Bin partially covered */
957 cfrac += tfrac * pfrac / 2; /* A rough estimate */
961 return cfrac / (4*M_PI);
965 * \param[in] surf Surface data structure to search.
966 * \param[in] x Unit vector to check.
967 * \returns true if \p x is within the solid angle, false otherwise.
970 is_surface_covered(t_methoddata_insolidangle *surf, rvec x)
974 bin = find_surface_bin(surf, x);
975 /* Check for completely covered bin */
976 if (surf->bin[bin].n == -1)
980 /* Check each point that partially covers the bin */
981 for (i = 0; i < surf->bin[bin].n; ++i)
983 if (sph_distc(x, surf->bin[bin].x[i]) < surf->distccut)