Triangular lattice generator

Former-commit-id: b3b2bdafacb2cc91b1ebb28ed48b1549451e528a
This commit is contained in:
Marek Nečada 2018-08-23 11:38:58 +03:00
parent ca454669d1
commit e6217bd363
3 changed files with 324 additions and 48 deletions

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@ -2,23 +2,20 @@
#define LATTICES_H
#include <math.h>
#include <stdbool.h>
#include <assert.h>
#include <stddef.h>
#define M_SQRT3 1.7320508075688772935274463415058724
#define M_SQRT3_2 (M_SQRT3/2)
// This might be reduced to x, y only; not sure yet
typedef struct {
double key; // distance key in a given lattice
double x, y, r, phi;
} point2d;
// fuck, I already had had suitable type
#include "vectors.h"
typedef cart2_t point2d;
static inline point2d point2d_fromxy(const double x, const double y) {
point2d p;
p.x = x;
p.y = y;
p.r = sqrt(x*x+y*y);
p.phi = atan2(y, x);
return p;
}
/*
@ -32,14 +29,30 @@ static inline point2d point2d_fromxy(const double x, const double y) {
typedef struct {
size_t nrs; // number of different radii
double *rs; // the radii; of length nrs (largest contained radius == rs[nrs-1])
point2d **points_at_r; // of length nrs+1
point2d *base;
ptrdiff_t *r_offsets; // of length nrs+1 (using relative offsets due to possible realloc's)
// the jth point of i-th radius is base[r_offsets[i]+j] or using the inline below..
/* // redundand (therefore removed) members
* point2d *points; // redundant as it is the same as points_at_r[0]
* size_t npoints; // redundant as it is the same as points_at_r[nrs]-points_at_r[0]
*/
} points2d_rordered_t;
// returns a copy but scaled by a factor
points2d_rordered_t *points2d_rordered_scale(const points2d_rordered_t *orig, double factor);
void points2d_rordered_free(points2d_rordered_t *); // use only for result of points2d_rordered_scale
static inline point2d points2d_rordered_get_point(const points2d_rordered_t *ps, int r_order, int i) {
assert(i >= 0);
assert(r_order < ps->nrs);
assert(i < (ps->r_offsets[r_order+1] - ps->r_offsets[r_order]));
return ps->base[ps->r_offsets[r_order] + i];
}
static inline double points2d_rordered_get_r(const points2d_rordered_t *ps, int r_order) {
assert(r_order < ps->nrs);
return ps->rs[r_order];
}
/*
* EQUILATERAL TRIANGULAR LATTICE
@ -68,10 +81,10 @@ typedef struct {
} triangular_lattice_gen_t;
triangular_lattice_gen_t *triangular_lattice_gen_init(double a, TriangularLatticeOrientation ori, bool include_origin);
const points2d_reordered_t * triangular_lattice_gen_getpoints(const triangular lattice_generator_t *g);
int triangular_lattice_gen_extend_to_r(triangular_lattice_generator_t *g, double r);
int triangular_lattice_gen_extend_to_steps(triangular_lattice_generator_t *g, int maxsteps);
void triangular_lattice_gen_free(triangular_lattice_generator_t *g);
const points2d_rordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_gen_t *g);
int triangular_lattice_gen_extend_to_r(triangular_lattice_gen_t *g, double r);
int triangular_lattice_gen_extend_to_steps(triangular_lattice_gen_t *g, int maxsteps);
void triangular_lattice_gen_free(triangular_lattice_gen_t *g);
#if 0

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@ -1,5 +1,6 @@
#include "lattices.h"
#include <assert.h>
#include <stdlib.h>
typedef struct {
int i, j;
@ -8,6 +9,39 @@ typedef struct {
static inline int sqi(int 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];
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);
}
/*
* EQUILATERAL TRIANGULAR LATTICE
*/
@ -67,12 +101,27 @@ static inline int sqi(int x) { return x*x; }
* 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) lattice cells (FIXME pretty stupid but safe estimate).
* 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;
}
@ -81,12 +130,8 @@ static inline int trilat_r2_coord(const intcoord2_t c) {
return trilat_r2_ij(c.i, c.j);
}
static int trilat_cmp_intcoord2_by_r2(const void *p1, const void *p2) {
// CHECK the sign is right
return trilat_r2_coord(*(const intcoord2_t *)p1) - trilat_r2_coord(*(const intcoord2_t *)p2);
}
// Classify points into sextants (variant [a])
// 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;
@ -99,23 +144,155 @@ static int trilat_sextant_ij_a(const int i, const int j) {
assert(0); // other options should be impossible
}
typedef struct {
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_end;
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_t_privstuff_t;
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) {
// CHECK the sign is right
return trilat_r2_coord(*(const intcoord2_t *)p1) - trilat_r2_coord(*(const intcoord2_t *)p2);
}
static void trilatgen_sort_pointlist(triangular_lattice_gen_t *g) {
trilatgen_pointlist_linearise(g);
triangular_lattice_gen_privstuff_t *p = g->priv;
qsort(p->pointlist_base + p->pointlist_beg, p->pointlist_n, sizeof(intcoord2_t), trilat_cmp_intcoord2_by_r2);
}
triangular_lattice_gen_t * triangular_lattice_gen_init(double a, TriangularLatticeOrientation ori, bool include_origin)
{
triangular_lattice_gen_t *g = malloc(sizeof(triangular_latice_gen_t));
triangular_lattice_gen_t *g = malloc(sizeof(triangular_lattice_gen_t));
g->orientation = ori;
g->includes_origin = include_origin;
g->ps.nrs = 0;
@ -127,13 +304,13 @@ triangular_lattice_gen_t * triangular_lattice_gen_init(double a, TriangularLatti
g->priv->pointlist_capacity = 0;
g->priv->pointlist_base = NULL;
g->priv->pointlist_beg = 0;
g->priv->pointlist_end = 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_get_t *g) {
void triangular_lattice_gen_free(triangular_lattice_gen_t *g) {
free(g->ps.rs);
free(g->ps.base);
free(g->ps.r_offsets);
@ -142,11 +319,12 @@ void triangular_lattice_gen_free(triangular_lattice_get_t *g) {
free(g);
}
const points2d_reordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_generator_t *g) {
const points2d_rordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_gen_t *g) {
return &(g->ps);
}
int triangular_lattice_gen_extend_to_steps(triangular_lattice_generator_t * g, int maxsteps) {
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)
@ -159,23 +337,58 @@ int triangular_lattice_gen_extend_to_steps(triangular_lattice_generator_t * g, i
if(err) return err;
if(g->includes_origin && g->priv->maxs < 0) // Add origin if not there yet
trilatgen_append_ij(g, 0, 0);
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_append_ij(g,i,j);
for (i = 0, j = s; i + j > 0; --i) trilatgen_append_ij(g,i,j);
for (i = -s, j = s; j > 0; --j) trilatgen_append_ij(g,i,j);
for (i = -s, j = 0; i < 0; ++i, --j) trilatgen_append_ij(g,i,j);
for (i = 0, j = -s; i + j < 0; ++i) trilatgen_append_ij(g,i,j);
for (i = s, j = -s; j < 0; ++j) trilatgen_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);
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);
// TODO doma a ted je potřeba vytahat potřebný počet bodů z fronty a naflákat je do ps.
// 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;
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)
break;
g->ps.rs[g->ps.nrs] = sqrt(r2i_cur) * 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))
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->a);
break;
case TRIANGULAR_VERTICAL:
thepoint = point2d_fromxy((-M_SQRT3_2*coord.j)*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->priv->maxs = maxsteps;
return 0;
}

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@ -0,0 +1,50 @@
#include <qpms/lattices.h>
#include <stdio.h>
void dump_points2d_rordered(const points2d_rordered_t *ps, char *filename) {
FILE *f = fopen(filename, "w");
for (size_t i = 0; i < ps->nrs; ++i) {
fprintf(f, "# r = %.16g\n", ps->rs[i]);
for (ptrdiff_t j = ps->r_offsets[i]; j < ps->r_offsets[i+1]; ++j)
fprintf(f, "%.16g %.16g\n", ps->base[j].x, ps->base[j].y);
}
fclose(f);
}
int main() {
triangular_lattice_gen_t *g = triangular_lattice_gen_init(5, TRIANGULAR_HORIZONTAL, false);
dump_points2d_rordered(&(g->ps), "triang_h_empty.out");
points2d_rordered_t *p = points2d_rordered_scale(&(g->ps), 1.5464);
dump_points2d_rordered(p, "triang_h_empty_scaled.out");
points2d_rordered_free(p);
triangular_lattice_gen_free(g);
g = triangular_lattice_gen_init(5, TRIANGULAR_HORIZONTAL, false);
triangular_lattice_gen_extend_to_steps(g, 5);
dump_points2d_rordered(&(g->ps), "triang_h_s5.out");
triangular_lattice_gen_extend_to_steps(g, 20);
dump_points2d_rordered(&(g->ps), "triang_h_s20.out");
triangular_lattice_gen_extend_to_steps(g, 160);
dump_points2d_rordered(&(g->ps), "triang_h_s160.out");
triangular_lattice_gen_extend_to_steps(g, 20);
dump_points2d_rordered(&(g->ps), "triang_h_s160_20.out");
p = points2d_rordered_scale(&(g->ps), -.2);
dump_points2d_rordered(p, "triang_h_s160_20_scaled.out");
points2d_rordered_free(p);
triangular_lattice_gen_free(g);
g = triangular_lattice_gen_init(7, TRIANGULAR_HORIZONTAL, true);
triangular_lattice_gen_extend_to_steps(g, 7);
dump_points2d_rordered(&(g->ps), "triang_v_s7.out");
p = points2d_rordered_scale(&(g->ps), 1/7.);
triangular_lattice_gen_free(g);
dump_points2d_rordered(p, "triang_v_s7_scaled_out");
points2d_rordered_free(p);
return 0;
}