qpms/qpms/lattices2d.c

838 lines
26 KiB
C

#include "lattices.h"
#include <assert.h>
#include <stdlib.h>
#include <string.h>
typedef struct {
int i, j;
} intcoord2_t;
static inline int sqi(int x) { return x*x; }
static inline double sqf(double x) { return x*x; }
void points2d_rordered_free(points2d_rordered_t *p) {
free(p->rs);
free(p->base);
free(p->r_offsets);
free(p);
}
points2d_rordered_t *points2d_rordered_scale(const points2d_rordered_t *orig, const double f)
{
points2d_rordered_t *p = malloc(sizeof(points2d_rordered_t));
if(0 == orig->nrs) { // orig is empty
p->nrs = 0;
p->rs = NULL;
p->base = NULL;
p->r_offsets = NULL;
return p;
}
p->nrs = orig->nrs;
p->rs = malloc(p->nrs*sizeof(double));
p->r_offsets = malloc((p->nrs+1)*sizeof(ptrdiff_t));
const double af = fabs(f);
for(size_t i = 0; i < p->nrs; ++i) {
p->rs[i] = orig->rs[i] * af;
p->r_offsets[i] = orig->r_offsets[i];
}
p->r_offsets[p->nrs] = orig->r_offsets[p->nrs];
p->base = malloc(sizeof(point2d) * p->r_offsets[p->nrs]);
for(size_t i = 0; i < p->r_offsets[p->nrs]; ++i)
p->base[i] = point2d_fromxy(orig->base[i].x * f, orig->base[i].y * f);
return p;
}
ptrdiff_t points2d_rordered_locate_r(const points2d_rordered_t *p, const double r) {
//if(p->r_rs[0] > r)
// return -1;
//if(p->r_rs[p->nrs-1] < r)
// return p->nrs;
ptrdiff_t lo = 0, hi = p->nrs-1, piv;
while(lo < hi) {
piv = (lo + hi + 1) / 2;
if(p->rs[piv] > r) // the result will be less or equal
hi = piv - 1;
else
lo = piv;
}
return lo;
}
points2d_rordered_t points2d_rordered_annulus(const points2d_rordered_t *orig,
double minr, bool inc_minr, double maxr, bool inc_maxr) {
points2d_rordered_t p;
ptrdiff_t imin, imax;
imin = points2d_rordered_locate_r(orig, minr);
imax = points2d_rordered_locate_r(orig, maxr);
// TODO check
if(imax >= orig->nrs) --imax;
if(imax < 0) goto nothing;
// END TODO
if (!inc_minr && (orig->rs[imin] <= minr)) ++imin;
if (!inc_maxr && (orig->rs[imax] >= maxr)) --imax;
if (imax < imin) { // it's empty
nothing:
p.nrs = 0;
p.base = NULL;
p.rs = NULL;
p.r_offsets = NULL;
} else {
p.base = orig->base;
p.nrs = imax - imin + 1;
p.rs = orig->rs + imin;
p.r_offsets = orig->r_offsets + imin;
}
return p;
}
static inline double pr2(const point2d p) {
return sqf(p.x) + sqf(p.y);
}
static inline double prn(const point2d p) {
return sqrt(pr2(p));
}
static int point2d_cmp_by_r2(const void *p1, const void *p2) {
const point2d *z1 = (point2d *) p1, *z2 = (point2d *) p2;
double dif = pr2(*z1) - pr2(*z2);
if(dif > 0) return 1;
else if(dif < 0) return -1;
else return 0;
}
static points2d_rordered_t *points2d_rordered_frompoints_c(point2d *orig_base, const size_t nmemb,
const double rtol, const double atol, bool copybase)
{
// TODO should the rtol and atol relate to |r| or r**2? (Currently: |r|)
assert(rtol >= 0);
assert(atol >= 0);
points2d_rordered_t *p = malloc(sizeof(points2d_rordered_t));
if(nmemb == 0) {
p->nrs = 0;
p->rs = NULL;
p->base = NULL;
p->r_offsets = NULL;
return p;
}
if (copybase) {
p->base = malloc(nmemb * sizeof(point2d));
memcpy(p->base, orig_base, nmemb * sizeof(point2d));
} else
p->base = orig_base;
qsort(p->base, nmemb, sizeof(point2d), point2d_cmp_by_r2);
// first pass: determine the number of "different" r's.
size_t rcount = 0;
double rcur = -INFINITY;
double rcurmax = -INFINITY;
for (size_t i = 0; i < nmemb; ++i)
if ((rcur = prn(p->base[i])) > rcurmax) {
++rcount;
rcurmax = rcur * (1 + rtol) + atol;
}
p->nrs = rcount;
// TODO check malloc return values
p->rs = malloc(rcount * sizeof(double));
p->r_offsets = malloc((rcount+1) * sizeof(ptrdiff_t));
// second pass: fill teh rs;
size_t ri = 0;
size_t rcurcount = 0;
rcur = prn(p->base[0]);
rcurmax = rcur * (1 + rtol) + atol;
double rcursum = 0;
p->r_offsets[0] = 0;
for (size_t i = 0; i < nmemb; ++i) {
rcur = prn(p->base[i]);
if (rcur > rcurmax) {
p->rs[ri] = rcursum / (double) rcurcount; // average of the accrued r's within tolerance
++ri;
p->r_offsets[ri] = i; //r_offsets[ri-1] + rcurcount (is the same)
rcurcount = 0;
rcursum = 0;
rcurmax = rcur * (1 + rtol) + atol;
}
rcursum += rcur;
++rcurcount;
}
p->rs[ri] = rcursum / (double) rcurcount;
p->r_offsets[rcount] = nmemb;
return p;
}
points2d_rordered_t *points2d_rordered_frompoints(const point2d *orig_base, const size_t nmemb,
const double rtol, const double atol)
{
return points2d_rordered_frompoints_c((point2d *)orig_base, nmemb, rtol, atol, true);
}
points2d_rordered_t *points2d_rordered_shift(const points2d_rordered_t *orig, const point2d shift,
double rtol, double atol)
{
size_t n = (orig->nrs > 0) ?
orig->r_offsets[orig->nrs] - orig->r_offsets[0] : 0;
point2d * shifted = malloc(n * sizeof(point2d));
for(size_t i = 0; i < n; ++i)
shifted[i] = cart2_add(orig->base[i+orig->r_offsets[0]], shift);
return points2d_rordered_frompoints_c(shifted, n,rtol, atol, false);
}
/*
* EQUILATERAL TRIANGULAR LATTICE
*/
/*
* N. B. the possible radii (distances from origin) of the lattice points can be described as
*
* r**2 / a**2 == i**2 + j**2 + i*j ,
*
* where i, j are integer indices describing steps along two basis vectors (which have
* 60 degree angle between them).
*
* The plane can be divided into six sextants, characterized as:
*
* 0) i >= 0 && j >= 0,
* [a] i > 0,
* [b] j > 0,
* 1) i <= 0 && {j >= 0} && i + j >= 0,
* [a] i + j > 0,
* [b] i < 0,
* 2) {i <= 0} && j >= 0 && i + j <= 0,
* [a] j > 0,
* [b] i + j < 0,
* 3) i <= 0 && j <= 0,
* [a] i < 0,
* [b] j < 0,
* 4) i >= 0 && {j <= 0} && i + j <= 0,
* [a] i + j < 0,
* [b] i > 0,
* 5) {i >= 0} && j <= 0 && i + j >= 0,
* [a] j < 0,
* [b] i + j > 0.
*
* The [a], [b] are two variants that uniquely assign the points at the sextant boundaries.
* The {conditions} in braces are actually redundant.
*
* In each sextant, the "minimum steps from the origin" value is calculated as:
* 0) i + j,
* 1) j
* 2) -i
* 3) -i - j,
* 4) -j,
* 5) i.
*
* The "spider web" generation for s steps from the origin (s-th layer) goes as following (variant [a]):
* 0) for (i = s, j = 0; i > 0; --i, ++j)
* 1) for (i = 0, j = s; i + j > 0; --i)
* 2) for (i = -s, j = s; j > 0; --j)
* 3) for (i = -s, j = 0; i < 0; ++i, --j)
* 4) for (i = 0, j = -s; i + j < 0; ++i)
* 5) for (i = s, j = -s; j < 0; ++j)
*
*
* Length of the s-th layer is 6*s for s >= 1. Size (number of lattice points) of the whole s-layer "spider web"
* is therefore 3*s*(s+1), excluding origin.
* The real area inside the web is (a*s)**2 * 3 * sqrt(3) / 2.
* Area of a unit cell is a**2 * sqrt(3)/2.
* Inside the web, but excluding the circumscribed circle, there is no more
* than 3/4.*s*(s+1) + 6*s lattice cells (FIXME pretty stupid but safe estimate).
*
* s-th layer circumscribes a circle of radius a * s * sqrt(3)/2.
*
*/
typedef struct triangular_lattice_gen_privstuff_t {
intcoord2_t *pointlist_base; // allocated memory for the point "buffer"
size_t pointlist_capacity;
// beginning and end of the point "buffer"
// not 100% sure what type should I use here
// (these are both relative to pointlist_base, due to possible realloc's)
ptrdiff_t pointlist_beg, pointlist_n; // end of queue is at [(pointlist_beg+pointlist_n)%pointlist_capacity]
int maxs; // the highest layer of the spider web generated (-1 by init, 0 is only origin (if applicable))
// capacities of the arrays in ps
size_t ps_rs_capacity;
size_t ps_points_capacity; // this is the "base" array
// TODO anything else?
} triangular_lattice_gen_privstuff_t;
static inline int trilat_r2_ij(const int i, const int j) {
return sqi(i) + sqi(j) + i*j;
}
static inline int trilat_r2_coord(const intcoord2_t c) {
return trilat_r2_ij(c.i, c.j);
}
// version with offset (n.b. this is includes a factor of 3)
static inline int trilat_3r2_ijs(const int i, const int j, const int s) {
return 3*(sqi(i) + sqi(j) + i*j + j*s) + sqi(s);
}
static inline int trilat_3r2_coord_s(const intcoord2_t c, const int s) {
return trilat_3r2_ijs(c.i, c.j, s);
}
// Classify points into sextants (variant [a] above)
static int trilat_sextant_ij_a(const int i, const int j) {
const int w = i + j;
if (i > 0 && j >= 0) return 0;
if (i <= 0 && w > 0) return 1;
if (w <= 0 && j > 0) return 2;
if (i < 0 && j <= 0) return 3;
if (i >= 0 && w < 0) return 4;
if (w >= 0 && j < 0) return 5;
if (i == 0 && j == 0) return -1; // origin
assert(0); // other options should be impossible
}
static inline size_t tlgp_pl_end(const triangular_lattice_gen_privstuff_t *p) {
return (p->pointlist_beg + p->pointlist_n) % p->pointlist_capacity;
}
#if 0
static inline void tlgpl_end_inc(triangular_lattice_gen_privstuff_t *p) {
p->p_pointlist_n += 1;
}
#endif
// Puts a point to the end of the point queue
static inline void trilatgen_pointlist_append_ij(triangular_lattice_gen_t *g, int i, int j) {
intcoord2_t thepoint = {i, j};
triangular_lattice_gen_privstuff_t *p = g->priv;
assert(p->pointlist_n < p->pointlist_capacity);
// the actual addition
p->pointlist_base[tlgp_pl_end(p)] = thepoint;
p->pointlist_n += 1;
}
// Arange the pointlist queue into a continuous chunk of memory, so that we can qsort() it
static void trilatgen_pointlist_linearise(triangular_lattice_gen_t *g) {
triangular_lattice_gen_privstuff_t *p = g->priv;
assert(p->pointlist_n <= p->pointlist_capacity);
if (p->pointlist_beg + p->pointlist_n <= p->pointlist_capacity)
return; // already linear, do nothing
else if (p->pointlist_n == p->pointlist_capacity) { // full, therefore linear
p->pointlist_beg = 0;
return;
} else { // non-linear; move "to the right"
while (p->pointlist_beg < p->pointlist_capacity) {
p->pointlist_base[tlgp_pl_end(p)] = p->pointlist_base[p->pointlist_beg];
++(p->pointlist_beg);
}
p->pointlist_beg = 0;
return;
}
}
static inline intcoord2_t trilatgen_pointlist_first(const triangular_lattice_gen_t *g) {
return g->priv->pointlist_base[g->priv->pointlist_beg];
}
static inline void trilatgen_pointlist_deletefirst(triangular_lattice_gen_t *g) {
triangular_lattice_gen_privstuff_t *p = g->priv;
assert(p->pointlist_n > 0);
++p->pointlist_beg;
if(p->pointlist_beg == p->pointlist_capacity)
p->pointlist_beg = 0;
--(p->pointlist_n);
}
// TODO abort() and void or errorchecks and int?
static int trilatgen_pointlist_extend_capacity(triangular_lattice_gen_t *g, size_t newcapacity) {
triangular_lattice_gen_privstuff_t *p = g->priv;
if (newcapacity <= p->pointlist_capacity)
return 0;
trilatgen_pointlist_linearise(g);
intcoord2_t *newmem = realloc(p->pointlist_base, newcapacity * sizeof(intcoord2_t));
if (newmem != NULL) {
p->pointlist_base = newmem;
p->pointlist_capacity = newcapacity;
return 0;
} else
abort();
}
// lower estimate for the number of lattice points inside the circumscribed hexagon, but outside the circle
static inline size_t tlg_circumscribe_reserve(int maxs) {
if (maxs <= 0)
return 0;
return 3*maxs*(maxs+1)/4 + 6*maxs;
}
static inline size_t tlg_websize(int maxs) {
if (maxs <= 0)
return 0;
else
return 3*maxs*(maxs+1); // does not include origin point!
}
static int trilatgen_ensure_pointlist_capacity(triangular_lattice_gen_t *g, int newmaxs) {
return trilatgen_pointlist_extend_capacity(g,
tlg_circumscribe_reserve(g->priv->maxs) // Space for those which are already in
+ tlg_websize(newmaxs) - tlg_websize(g->priv->maxs) // space for the new web layers
+ 1 // reserve for the origin
);
}
static int trilatgen_ensure_ps_rs_capacity(triangular_lattice_gen_t *g, int maxs) {
if (maxs < 0)
return 0;
size_t needed_capacity = 1 // reserve for origin
+ maxs*(maxs+1)/2; // stupid but safe estimate: number of points in a sextant of maxs-layered spider web
if (needed_capacity <= g->priv->ps_rs_capacity)
return 0; // probably does not happen, but fuck it
double *newmem = realloc(g->ps.rs, needed_capacity * sizeof(double));
if (newmem != NULL)
g->ps.rs = newmem;
else
abort();
ptrdiff_t *newmem2 = realloc(g->ps.r_offsets, (needed_capacity + 1) * sizeof(ptrdiff_t));
if (newmem2 != NULL)
g->ps.r_offsets = newmem2;
else
abort();
g->priv->ps_rs_capacity = needed_capacity;
return 0;
}
static int trilatgen_ensure_ps_points_capacity(triangular_lattice_gen_t *g, int maxs) {
if (maxs < 0)
return 0;
size_t needed_capacity = 1 /*res. for origin */ + tlg_websize(maxs) /* stupid but safe */;
if(needed_capacity <= g->priv->ps_points_capacity)
return 0;
point2d *newmem = realloc(g->ps.base, needed_capacity * sizeof(point2d));
if (newmem != NULL)
g->ps.base = newmem;
else
abort();
g->priv->ps_points_capacity = needed_capacity;
return 0;
}
static int trilat_cmp_intcoord2_by_r2(const void *p1, const void *p2) {
return trilat_r2_coord(*(const intcoord2_t *)p1) - trilat_r2_coord(*(const intcoord2_t *)p2);
}
static int trilat_cmp_intcoord2_by_3r2_plus1s(const void *p1, const void *p2) {
return trilat_3r2_coord_s(*(const intcoord2_t *)p1, +1) - trilat_3r2_coord_s(*(const intcoord2_t *)p2, +1);
}
static int trilat_cmp_intcoord2_by_3r2_minus1s(const void *p1, const void *p2) {
return trilat_3r2_coord_s(*(const intcoord2_t *)p1, -1) - trilat_3r2_coord_s(*(const intcoord2_t *)p2, -1);
}
static int trilat_cmp_intcoord2_by_3r2(const void *p1, const void *p2, void *sarg) {
return trilat_3r2_coord_s(*(const intcoord2_t *)p1, *(int *)sarg) - trilat_3r2_coord_s(*(const intcoord2_t *)p2, *(int *)sarg);
}
static void trilatgen_sort_pointlist(triangular_lattice_gen_t *g) {
trilatgen_pointlist_linearise(g);
triangular_lattice_gen_privstuff_t *p = g->priv;
int (*compar)(const void *, const void *);
switch (g->hexshift) {
case 0:
compar = trilat_cmp_intcoord2_by_r2;
break;
case -1:
compar = trilat_cmp_intcoord2_by_3r2_minus1s;
break;
case 1:
compar = trilat_cmp_intcoord2_by_3r2_plus1s;
break;
default:
abort();
}
qsort(p->pointlist_base + p->pointlist_beg, p->pointlist_n, sizeof(intcoord2_t), compar);
}
triangular_lattice_gen_t * triangular_lattice_gen_init(double a, TriangularLatticeOrientation ori, bool include_origin,
int hexshift)
{
triangular_lattice_gen_t *g = malloc(sizeof(triangular_lattice_gen_t));
g->a = a;
g->hexshift = ((hexshift % 3)+3)%3; // reduce to the set {-1, 0, 1}
if (2 == g->hexshift)
g->hexshift = -1;
g->orientation = ori;
g->includes_origin = include_origin;
g->ps.nrs = 0;
g->ps.rs = NULL;
g->ps.base = NULL;
g->ps.r_offsets = NULL;
g->priv = malloc(sizeof(triangular_lattice_gen_privstuff_t));
g->priv->maxs = -1;
g->priv->pointlist_capacity = 0;
g->priv->pointlist_base = NULL;
g->priv->pointlist_beg = 0;
g->priv->pointlist_n = 0;
g->priv->ps_rs_capacity = 0;
g->priv->ps_points_capacity = 0;
return g;
}
void triangular_lattice_gen_free(triangular_lattice_gen_t *g) {
free(g->ps.rs);
free(g->ps.base);
free(g->ps.r_offsets);
free(g->priv->pointlist_base);
free(g->priv);
free(g);
}
const points2d_rordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_gen_t *g) {
return &(g->ps);
}
int triangular_lattice_gen_extend_to_r(triangular_lattice_gen_t * g, const double maxr) {
return triangular_lattice_gen_extend_to_steps(g, maxr/g->a);
}
int triangular_lattice_gen_extend_to_steps(triangular_lattice_gen_t * g, int maxsteps)
{
if (maxsteps <= g->priv->maxs) // nothing needed
return 0;
// TODO FIXME: check for maximum possible maxsteps (not sure what it is)
int err;
err = trilatgen_ensure_pointlist_capacity(g, maxsteps
+ abs(g->hexshift) /*FIXME this is quite brainless addition, probably not even needed.*/);
if(err) return err;
err = trilatgen_ensure_ps_rs_capacity(g, maxsteps
+ abs(g->hexshift) /*FIXME this is quite brainless addition, probably not even needed.*/);
if(err) return err;
err = trilatgen_ensure_ps_points_capacity(g, maxsteps
+ abs(g->hexshift) /*FIXME this is quite brainless addition, probably not even needed.*/);
if(err) return err;
if(g->includes_origin && g->priv->maxs < 0) // Add origin if not there yet
trilatgen_pointlist_append_ij(g, 0, 0);
for (int s = g->priv->maxs + 1; s <= maxsteps; ++s) {
int i, j;
// now go along the spider web layer as indicated in the lenghthy comment above
for (i = s, j = 0; i > 0; --i, ++j) trilatgen_pointlist_append_ij(g,i,j);
for (i = 0, j = s; i + j > 0; --i) trilatgen_pointlist_append_ij(g,i,j);
for (i = -s, j = s; j > 0; --j) trilatgen_pointlist_append_ij(g,i,j);
for (i = -s, j = 0; i < 0; ++i, --j) trilatgen_pointlist_append_ij(g,i,j);
for (i = 0, j = -s; i + j < 0; ++i) trilatgen_pointlist_append_ij(g,i,j);
for (i = s, j = -s; j < 0; ++j) trilatgen_pointlist_append_ij(g,i,j);
}
trilatgen_sort_pointlist(g);
// initialise first r_offset if needed
if (0 == g->ps.nrs)
g->ps.r_offsets[0] = 0;
//ted je potřeba vytahat potřebný počet bodů z fronty a naflákat je do ps.
// FIXME pohlídat si kapacitu datových typů
//int maxr2i = sqi(maxsteps) * 3 / 4;
int maxr2i3 = sqi(maxsteps) * 9 / 4 + sqi(g->hexshift) - abs(3*maxsteps*g->hexshift);
while (g->priv->pointlist_n > 0) { // This condition should probably be always true anyways.
intcoord2_t coord = trilatgen_pointlist_first(g);
//int r2i_cur = trilat_r2_coord(coord);
//if(r2i_cur > maxr2i)
int r2i3_cur = trilat_3r2_coord_s(coord, g->hexshift);
if(r2i3_cur > maxr2i3)
break;
g->ps.rs[g->ps.nrs] = sqrt(/*r2i_cur*/ r2i3_cur/3.) * g->a;
g->ps.r_offsets[g->ps.nrs+1] = g->ps.r_offsets[g->ps.nrs]; // the difference is the number of points on the circle
while(1) {
coord = trilatgen_pointlist_first(g);
//if(r2i_cur != trilat_r2_coord(coord))
if (r2i3_cur != trilat_3r2_coord_s(coord, g->hexshift))
break;
else {
trilatgen_pointlist_deletefirst(g);
point2d thepoint;
switch (g->orientation) {
case TRIANGULAR_HORIZONTAL:
thepoint = point2d_fromxy((coord.i+.5*coord.j)*g->a, (M_SQRT3_2*coord.j + g->hexshift*M_1_SQRT3)*g->a);
break;
case TRIANGULAR_VERTICAL:
thepoint = point2d_fromxy(-(M_SQRT3_2*coord.j + g->hexshift*M_1_SQRT3)*g->a, (coord.i+.5*coord.j)*g->a);
break;
default:
abort();
}
g->ps.base[g->ps.r_offsets[g->ps.nrs+1]] = thepoint;
++(g->ps.r_offsets[g->ps.nrs+1]);
}
}
++(g->ps.nrs);
}
g->priv->maxs = maxsteps;
return 0;
}
honeycomb_lattice_gen_t *honeycomb_lattice_gen_init_h(double h, TriangularLatticeOrientation ori) {
double a = M_SQRT3 * h;
honeycomb_lattice_gen_t *g = honeycomb_lattice_gen_init_a(a, ori);
g->h = h; // maybe it's not necessary as sqrt is "exact"
return g;
}
honeycomb_lattice_gen_t *honeycomb_lattice_gen_init_a(double a, TriangularLatticeOrientation ori) {
honeycomb_lattice_gen_t *g = calloc(1, sizeof(honeycomb_lattice_gen_t)); // this already inits g->ps to zeros
g->a = a;
g->h = a * M_1_SQRT3;
g->tg = triangular_lattice_gen_init(a, ori, true, 1);
return g;
}
void honeycomb_lattice_gen_free(honeycomb_lattice_gen_t *g) {
free(g->ps.rs);
free(g->ps.base);
free(g->ps.r_offsets);
triangular_lattice_gen_free(g->tg);
free(g);
}
int honeycomb_lattice_gen_extend_to_r(honeycomb_lattice_gen_t *g, double maxr) {
return honeycomb_lattice_gen_extend_to_steps(g, maxr/g->a); /*CHECKME whether g->a is the correct denom.*/
}
int honeycomb_lattice_gen_extend_to_steps(honeycomb_lattice_gen_t *g, const int maxsteps) {
if (maxsteps <= g->tg->priv->maxs) // nothing needed
return 0;
triangular_lattice_gen_extend_to_steps(g->tg, maxsteps);
double *newmem = realloc(g->ps.rs, g->tg->ps.nrs * sizeof(double));
if (NULL != newmem)
g->ps.rs = newmem;
else abort();
ptrdiff_t *newmem2 = realloc(g->ps.r_offsets, (g->tg->ps.nrs+1) * sizeof(ptrdiff_t));
if (NULL != newmem2)
g->ps.r_offsets = newmem2;
else abort();
point2d *newmem3 = realloc(g->ps.base, 2 * (g->tg->ps.r_offsets[g->tg->ps.nrs]) * sizeof(point2d));
if (NULL != newmem3)
g->ps.base = newmem3;
else abort();
// Now copy (new) contents of g->tg->ps into g->ps, but with inverse copy of each point
for (size_t ri = g->ps.nrs; ri <= g->tg->ps.nrs; ++ri)
g->ps.r_offsets[ri] = g->tg->ps.r_offsets[ri] * 2;
for (ptrdiff_t i_orig = g->tg->ps.r_offsets[g->ps.nrs]; i_orig < g->tg->ps.r_offsets[g->tg->ps.nrs]; ++i_orig) {
point2d p = g->tg->ps.base[i_orig];
g->ps.base[2*i_orig] = p;
p.x *= -1; p.y *= -1;
g->ps.base[2*i_orig + 1] = p;
}
g->ps.nrs = g->tg->ps.nrs;
return 0;
}
// THE NICE PART
/*
* Lagrange-Gauss reduction of a 2D basis.
* The output shall satisfy |out1| <= |out2| <= |out2 - out1|
*/
void l2d_reduceBasis(cart2_t b1, cart2_t b2, cart2_t *out1, cart2_t *out2){
double B1 = cart2_dot(b1, b1);
double mu = cart2_dot(b1, b2) / B1;
b2 = cart2_substract(b2, cart2_scale(round(mu), b1));
double B2 = cart2_dot(b2, b2);
while(B2 < B1) {
cart2_t b2t = b1;
b1 = b2;
b2 = b2t;
B1 = B2;
mu = cart2_dot(b1, b2) / B1;
b2 = cart2_substract(b2, cart2_scale(round(mu), b1));
B2 = cart2_dot(b2, b2);
}
*out1 = b1;
*out2 = b2;
}
/*
* This gives the "ordered shortest triple" of base vectors (each pair from the triple
* is a base) and there may not be obtuse angle between o1, o2 and between o2, o3
*/
void l2d_shortestBase3(cart2_t b1, cart2_t b2, cart2_t *o1, cart2_t *o2, cart2_t *o3){
l2d_reduceBasis(b1, b2, &b1, &b2);
*o1 = b1;
if (l2d_is_obtuse_r(b1, b2, 0)) {
*o3 = b2;
*o2 = cart2_add(b2, b1);
} else {
*o2 = b2;
*o3 = cart2_substract(b2, b1);
}
}
// Determines whether angle between inputs is obtuse
bool l2d_is_obtuse_r(cart2_t b1, cart2_t b2, double rtol) {
const double B1 = cart2_normsq(b1);
const double B2 = cart2_normsq(b2);
const cart2_t b3 = cart2_substract(b2, b1);
const double B3 = cart2_normsq(b3);
const double eps = rtol * (B1 + B2); // TODO check what kind of quantity this should be. Maybe rtol should relate to lengths, not lengths**2
return (B3 - B2 - B1 > eps);
}
/*
* TODO doc
* return value is 4 or 6.
*/
int l2d_shortestBase46(const cart2_t i1, const cart2_t i2, cart2_t *o1, cart2_t *o2, cart2_t *o3, cart2_t *o4, cart2_t *o5, cart2_t *o6, double rtol){
cart2_t b1, b2, b3;
l2d_reduceBasis(i1, i2, &b1, &b2);
const double b1s = cart2_normsq(b1);
const double b2s = cart2_normsq(b2);
b3 = cart2_substract(b2, b1);
const double b3s = cart2_normsq(b3);
const double eps = rtol * (b1s + b2s); // TODO check the same as in l2d_is_obtuse_r
if(fabs(b3s-b2s-b1s) < eps) {
*o1 = b1; *o2 = b2; *o3 = cart2_scale(-1, b1); *o4 = cart2_scale(-1, b2);
return 4;
}
else {
if (b3s-b2s-b1s > eps) { //obtuse
b3 = b2;
b2 = cart2_add(b2, b1);
}
*o1 = b1; *o2 = b2; *o3 = b3;
*o4 = cart2_scale(-1, b1);
*o5 = cart2_scale(-1, b2);
*o6 = cart2_scale(-1, b3);
return 6;
}
}
/*
* Given two basis vectors, returns 2D Bravais lattice type.
*/
LatticeType2 l2d_classifyLattice(cart2_t b1, cart2_t b2, double rtol)
{
l2d_reduceBasis(b1, b2, &b1, &b2);
cart2_t b3 = cart2_substract(b2, b1);
double b1s = cart2_normsq(b1), b2s = cart2_normsq(b2), b3s = cart2_normsq(b3);
double eps = rtol * (b2s + b1s); //FIXME what should eps be?
// avoid obtuse angle between b1 and b2. TODO this should be yet tested
// TODO use is_obtuse here?
if (b3s - b2s - b1s > eps) {
b3 = b2;
b2 = cart2_add(b2, b1);
// N.B. now the assumption |b3| >= |b2| is no longer valid
// b3 = cart2_substract(b2, b1)
b2s = cart2_normsq(b2);
b3s = cart2_normsq(b3);
}
if (fabs(b2s-b1s) < eps || fabs(b2s - b3s) < eps) { // isoscele
if (fabs(b3s-b1s) < eps)
return EQUILATERAL_TRIANGULAR;
else if (fabs(b3s - 2*b1s))
return SQUARE;
else
return RHOMBIC;
} else if (fabs(b3s-b2s-b1s) < eps)
return RECTANGULAR;
else
return OBLIQUE;
}
# if 0
// variant
int l2d_shortestBase46_arr(cart2_t i1, cart2_t i2, cart2_t *oarr, double rtol);
// Determines whether angle between inputs is obtuse
bool l2d_is_obtuse_r(cart2_t i1, cart2_t i2, double rtol);
// Other functions in lattices2d.py: TODO?
// range2D()
// generateLattice()
// generateLatticeDisk()
// cutWS()
// filledWS()
// change_basis()
/*
* Given basis vectors, returns the corners of the Wigner-Seits unit cell (W1, W2, -W1, W2)
* for rectangular and square lattice or (w1, w2, w3, -w1, -w2, -w3) otherwise.
*/
int l2d_cellCornersWS(cart2_t i1, cart2_t i2, cart2_t *o1, cart2_t *o2, cart2_t *o3, cart2_t *o4, cart2_t *o5, cart2_t *o6, double rtol);
// variant
int l2d_cellCornersWS_arr(cart2_t i1, cart2_t i2, cart2_t *oarr, double rtol);
#endif
// Reciprocal bases; returns 0 on success, TODO non-zero if b1 and b2 are parallel
int l2d_reciprocalBasis1(cart2_t b1, cart2_t b2, cart2_t *rb1, cart2_t *rb2) {
l2d_reduceBasis(b1, b2, &b1, &b2);
const double det = b1.x * b2.y - b1.y * b2.x;
if (!det) {
rb1->x = rb1->y = rb2->x = rb2->y = NAN;
return QPMS_ERROR; // TODO more specific error code
} else {
rb1->x = b2.y / det;
rb1->y = -b2.x / det;
rb2->x = -b1.y / det;
rb2->y = b1.x / det;
return QPMS_SUCCESS;
}
}
int l2d_reciprocalBasis2pi(cart2_t b1, cart2_t b2, cart2_t *rb1, cart2_t *rb2) {
int retval = l2d_reciprocalBasis1(b1, b2, rb1, rb2);
if (retval == QPMS_SUCCESS) {
*rb1 = cart2_scale(2 * M_PI, *rb1);
*rb2 = cart2_scale(2 * M_PI, *rb2);
}
return retval;
};
// returns the radius of inscribed circle of a hexagon (or rectangle/square if applicable) created by the shortest base triple
double l2d_hexWebInCircleRadius(cart2_t i1, cart2_t i2) {
cart2_t b1, b2, b3;
l2d_shortestBase3(i1, i2, &b1, &b2, &b3);
const double r1 = cart2norm(b1), r2 = cart2norm(b2), r3 = cart2norm(b3);
const double p = (r1+r2+r3)*0.5;
return 2*sqrt(p*(p-r1)*(p-r2)*(p-r3))/r3; // CHECK is r3 guaranteed to be longest?
}
double l2d_unitcell_area(cart2_t b1, cart2_t b2) {
l2d_reduceBasis(b1, b2, &b1, &b2);
const double det = b1.x * b2.y - b1.y * b2.x;
return fabs(det);
}