Triangular lattice generator
Former-commit-id: b3b2bdafacb2cc91b1ebb28ed48b1549451e528a
This commit is contained in:
Marek Nečada
parent
ca454669d1
commit
e6217bd363
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@ -2,23 +2,20 @@
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#define LATTICES_H
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#include <math.h>
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#include <stdbool.h>
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#include <assert.h>
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#include <stddef.h>
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#define M_SQRT3 1.7320508075688772935274463415058724
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#define M_SQRT3_2 (M_SQRT3/2)
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// This might be reduced to x, y only; not sure yet
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typedef struct {
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double key; // distance key in a given lattice
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double x, y, r, phi;
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} point2d;
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// fuck, I already had had suitable type
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#include "vectors.h"
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typedef cart2_t point2d;
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static inline point2d point2d_fromxy(const double x, const double y) {
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point2d p;
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p.x = x;
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p.y = y;
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p.r = sqrt(x*x+y*y);
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p.phi = atan2(y, x);
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return p;
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}
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/*
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@ -32,14 +29,30 @@ static inline point2d point2d_fromxy(const double x, const double y) {
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typedef struct {
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size_t nrs; // number of different radii
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double *rs; // the radii; of length nrs (largest contained radius == rs[nrs-1])
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point2d **points_at_r; // of length nrs+1
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point2d *base;
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ptrdiff_t *r_offsets; // of length nrs+1 (using relative offsets due to possible realloc's)
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// the jth point of i-th radius is base[r_offsets[i]+j] or using the inline below..
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/* // redundand (therefore removed) members
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* point2d *points; // redundant as it is the same as points_at_r[0]
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* size_t npoints; // redundant as it is the same as points_at_r[nrs]-points_at_r[0]
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*/
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} points2d_rordered_t;
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// returns a copy but scaled by a factor
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points2d_rordered_t *points2d_rordered_scale(const points2d_rordered_t *orig, double factor);
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void points2d_rordered_free(points2d_rordered_t *); // use only for result of points2d_rordered_scale
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static inline point2d points2d_rordered_get_point(const points2d_rordered_t *ps, int r_order, int i) {
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assert(i >= 0);
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assert(r_order < ps->nrs);
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assert(i < (ps->r_offsets[r_order+1] - ps->r_offsets[r_order]));
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return ps->base[ps->r_offsets[r_order] + i];
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}
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static inline double points2d_rordered_get_r(const points2d_rordered_t *ps, int r_order) {
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assert(r_order < ps->nrs);
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return ps->rs[r_order];
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}
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/*
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* EQUILATERAL TRIANGULAR LATTICE
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@ -68,10 +81,10 @@ typedef struct {
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} triangular_lattice_gen_t;
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triangular_lattice_gen_t *triangular_lattice_gen_init(double a, TriangularLatticeOrientation ori, bool include_origin);
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const points2d_reordered_t * triangular_lattice_gen_getpoints(const triangular lattice_generator_t *g);
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int triangular_lattice_gen_extend_to_r(triangular_lattice_generator_t *g, double r);
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int triangular_lattice_gen_extend_to_steps(triangular_lattice_generator_t *g, int maxsteps);
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void triangular_lattice_gen_free(triangular_lattice_generator_t *g);
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const points2d_rordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_gen_t *g);
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int triangular_lattice_gen_extend_to_r(triangular_lattice_gen_t *g, double r);
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int triangular_lattice_gen_extend_to_steps(triangular_lattice_gen_t *g, int maxsteps);
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void triangular_lattice_gen_free(triangular_lattice_gen_t *g);
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#if 0
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@ -1,5 +1,6 @@
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#include "lattices.h"
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#include <assert.h>
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#include <stdlib.h>
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typedef struct {
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int i, j;
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@ -8,6 +9,39 @@ typedef struct {
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static inline int sqi(int x) { return x*x; }
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void points2d_rordered_free(points2d_rordered_t *p) {
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free(p->rs);
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free(p->base);
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free(p->r_offsets);
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free(p);
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}
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points2d_rordered_t *points2d_rordered_scale(const points2d_rordered_t *orig, const double f)
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{
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points2d_rordered_t *p = malloc(sizeof(points2d_rordered_t));
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if(0 == orig->nrs) { // orig is empty
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p->nrs = 0;
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p->rs = NULL;
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p->base = NULL;
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p->r_offsets = NULL;
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return p;
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}
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p->nrs = orig->nrs;
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p->rs = malloc(p->nrs*sizeof(double));
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p->r_offsets = malloc((p->nrs+1)*sizeof(ptrdiff_t));
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const double af = fabs(f);
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for(size_t i = 0; i < p->nrs; ++i) {
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p->rs[i] = orig->rs[i] * af;
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p->r_offsets[i] = orig->r_offsets[i];
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}
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p->r_offsets[p->nrs] = orig->r_offsets[p->nrs];
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for(size_t i = 0; i < p->r_offsets[p->nrs]; ++i)
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p->base[i] = point2d_fromxy(orig->base[i].x * f, orig->base[i].y * f);
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}
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/*
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* EQUILATERAL TRIANGULAR LATTICE
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*/
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@ -67,12 +101,27 @@ static inline int sqi(int x) { return x*x; }
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* The real area inside the web is (a*s)**2 * 3 * sqrt(3) / 2.
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* Area of a unit cell is a**2 * sqrt(3)/2.
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* Inside the web, but excluding the circumscribed circle, there is no more
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* than 3/4.*s*(s+1) lattice cells (FIXME pretty stupid but safe estimate).
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* than 3/4.*s*(s+1) + 6*s lattice cells (FIXME pretty stupid but safe estimate).
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*
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* s-th layer circumscribes a circle of radius a * s * sqrt(3)/2.
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*
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*/
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typedef struct triangular_lattice_gen_privstuff_t {
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intcoord2_t *pointlist_base; // allocated memory for the point "buffer"
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size_t pointlist_capacity;
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// beginning and end of the point "buffer"
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// not 100% sure what type should I use here
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// (these are both relative to pointlist_base, due to possible realloc's)
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ptrdiff_t pointlist_beg, pointlist_n; // end of queue is at [(pointlist_beg+pointlist_n)%pointlist_capacity]
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int maxs; // the highest layer of the spider web generated (-1 by init, 0 is only origin (if applicable))
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// capacities of the arrays in ps
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size_t ps_rs_capacity;
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size_t ps_points_capacity; // this is the "base" array
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// TODO anything else?
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} triangular_lattice_gen_privstuff_t;
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static inline int trilat_r2_ij(const int i, const int j) {
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return sqi(i) + sqi(j) + i*j;
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}
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@ -81,12 +130,8 @@ static inline int trilat_r2_coord(const intcoord2_t c) {
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return trilat_r2_ij(c.i, c.j);
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}
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static int trilat_cmp_intcoord2_by_r2(const void *p1, const void *p2) {
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// CHECK the sign is right
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return trilat_r2_coord(*(const intcoord2_t *)p1) - trilat_r2_coord(*(const intcoord2_t *)p2);
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}
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// Classify points into sextants (variant [a])
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// Classify points into sextants (variant [a] above)
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static int trilat_sextant_ij_a(const int i, const int j) {
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const int w = i + j;
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if (i > 0 && j >= 0) return 0;
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@ -99,23 +144,155 @@ static int trilat_sextant_ij_a(const int i, const int j) {
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assert(0); // other options should be impossible
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}
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typedef struct {
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intcoord2_t *pointlist_base; // allocated memory for the point "buffer"
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size_t pointlist_capacity;
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// beginning and end of the point "buffer"
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// not 100% sure what type should I use here
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// (these are both relative to pointlist_base, due to possible realloc's)
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ptrdiff_t pointlist_beg, pointlist_end;
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int maxs; // the highest layer of the spider web generated (-1 by init, 0 is only origin (if applicable))
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// capacities of the arrays in ps
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size_t ps_rs_capacity;
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size_t ps_points_capacity; // this is the "base" array
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// TODO anything else?
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} triangular_lattice_gen_t_privstuff_t;
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static inline size_t tlgp_pl_end(const triangular_lattice_gen_privstuff_t *p) {
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return (p->pointlist_beg + p->pointlist_n) % p->pointlist_capacity;
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}
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#if 0
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static inline void tlgpl_end_inc(triangular_lattice_gen_privstuff_t *p) {
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p->p_pointlist_n += 1;
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}
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#endif
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// Puts a point to the end of the point queue
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static inline void trilatgen_pointlist_append_ij(triangular_lattice_gen_t *g, int i, int j) {
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intcoord2_t thepoint = {i, j};
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triangular_lattice_gen_privstuff_t *p = g->priv;
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assert(p->pointlist_n < p->pointlist_capacity);
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// the actual addition
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p->pointlist_base[tlgp_pl_end(p)] = thepoint;
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p->pointlist_n += 1;
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}
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// Arange the pointlist queue into a continuous chunk of memory, so that we can qsort() it
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static void trilatgen_pointlist_linearise(triangular_lattice_gen_t *g) {
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triangular_lattice_gen_privstuff_t *p = g->priv;
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assert(p->pointlist_n <= p->pointlist_capacity);
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if (p->pointlist_beg + p->pointlist_n <= p->pointlist_capacity)
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return; // already linear, do nothing
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else if (p->pointlist_n == p->pointlist_capacity) { // full, therefore linear
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p->pointlist_beg = 0;
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return;
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} else { // non-linear; move "to the right"
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while (p->pointlist_beg < p->pointlist_capacity) {
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p->pointlist_base[tlgp_pl_end(p)] = p->pointlist_base[p->pointlist_beg];
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++(p->pointlist_beg);
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}
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p->pointlist_beg = 0;
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return;
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}
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}
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static inline intcoord2_t trilatgen_pointlist_first(const triangular_lattice_gen_t *g) {
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return g->priv->pointlist_base[g->priv->pointlist_beg];
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}
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static inline void trilatgen_pointlist_deletefirst(triangular_lattice_gen_t *g) {
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triangular_lattice_gen_privstuff_t *p = g->priv;
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assert(p->pointlist_n > 0);
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++p->pointlist_beg;
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if(p->pointlist_beg == p->pointlist_capacity)
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p->pointlist_beg = 0;
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--(p->pointlist_n);
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}
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// TODO abort() and void or errorchecks and int?
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static int trilatgen_pointlist_extend_capacity(triangular_lattice_gen_t *g, size_t newcapacity) {
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triangular_lattice_gen_privstuff_t *p = g->priv;
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if (newcapacity <= p->pointlist_capacity)
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return 0;
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trilatgen_pointlist_linearise(g);
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intcoord2_t *newmem = realloc(p->pointlist_base, newcapacity * sizeof(intcoord2_t));
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if (newmem != NULL) {
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p->pointlist_base = newmem;
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p->pointlist_capacity = newcapacity;
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return 0;
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} else
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abort();
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}
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// lower estimate for the number of lattice points inside the circumscribed hexagon, but outside the circle
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static inline size_t tlg_circumscribe_reserve(int maxs) {
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if (maxs <= 0)
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return 0;
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return 3*maxs*(maxs+1)/4 + 6*maxs;
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}
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static inline size_t tlg_websize(int maxs) {
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if (maxs <= 0)
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return 0;
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else
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return 3*maxs*(maxs+1); // does not include origin point!
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}
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static int trilatgen_ensure_pointlist_capacity(triangular_lattice_gen_t *g, int newmaxs) {
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return trilatgen_pointlist_extend_capacity(g,
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tlg_circumscribe_reserve(g->priv->maxs) // Space for those which are already in
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+ tlg_websize(newmaxs) - tlg_websize(g->priv->maxs) // space for the new web layers
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+ 1 // reserve for the origin
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);
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}
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static int trilatgen_ensure_ps_rs_capacity(triangular_lattice_gen_t *g, int maxs) {
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if (maxs < 0)
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return 0;
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size_t needed_capacity = 1 // reserve for origin
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+ maxs*(maxs+1)/2; // stupid but safe estimate: number of points in a sextant of maxs-layered spider web
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if (needed_capacity <= g->priv->ps_rs_capacity)
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return 0; // probably does not happen, but fuck it
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double *newmem = realloc(g->ps.rs, needed_capacity * sizeof(double));
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if (newmem != NULL)
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g->ps.rs = newmem;
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else
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abort();
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ptrdiff_t *newmem2 = realloc(g->ps.r_offsets, (needed_capacity + 1) * sizeof(ptrdiff_t));
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if (newmem2 != NULL)
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g->ps.r_offsets = newmem2;
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else
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abort();
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g->priv->ps_rs_capacity = needed_capacity;
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return 0;
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}
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static int trilatgen_ensure_ps_points_capacity(triangular_lattice_gen_t *g, int maxs) {
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if (maxs < 0)
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return 0;
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size_t needed_capacity = 1 /*res. for origin */ + tlg_websize(maxs) /* stupid but safe */;
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if(needed_capacity <= g->priv->ps_points_capacity)
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return 0;
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point2d *newmem = realloc(g->ps.base, needed_capacity * sizeof(point2d));
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if (newmem != NULL)
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g->ps.base = newmem;
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else
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abort();
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g->priv->ps_points_capacity = needed_capacity;
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return 0;
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}
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static int trilat_cmp_intcoord2_by_r2(const void *p1, const void *p2) {
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// CHECK the sign is right
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return trilat_r2_coord(*(const intcoord2_t *)p1) - trilat_r2_coord(*(const intcoord2_t *)p2);
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}
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static void trilatgen_sort_pointlist(triangular_lattice_gen_t *g) {
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trilatgen_pointlist_linearise(g);
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triangular_lattice_gen_privstuff_t *p = g->priv;
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qsort(p->pointlist_base + p->pointlist_beg, p->pointlist_n, sizeof(intcoord2_t), trilat_cmp_intcoord2_by_r2);
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}
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triangular_lattice_gen_t * triangular_lattice_gen_init(double a, TriangularLatticeOrientation ori, bool include_origin)
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{
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triangular_lattice_gen_t *g = malloc(sizeof(triangular_latice_gen_t));
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triangular_lattice_gen_t *g = malloc(sizeof(triangular_lattice_gen_t));
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g->orientation = ori;
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g->includes_origin = include_origin;
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g->ps.nrs = 0;
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@ -127,13 +304,13 @@ triangular_lattice_gen_t * triangular_lattice_gen_init(double a, TriangularLatti
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g->priv->pointlist_capacity = 0;
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g->priv->pointlist_base = NULL;
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g->priv->pointlist_beg = 0;
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g->priv->pointlist_end = 0;
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g->priv->pointlist_n = 0;
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g->priv->ps_rs_capacity = 0;
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g->priv->ps_points_capacity = 0;
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return g;
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}
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void triangular_lattice_gen_free(triangular_lattice_get_t *g) {
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void triangular_lattice_gen_free(triangular_lattice_gen_t *g) {
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free(g->ps.rs);
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free(g->ps.base);
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free(g->ps.r_offsets);
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@ -142,11 +319,12 @@ void triangular_lattice_gen_free(triangular_lattice_get_t *g) {
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free(g);
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}
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const points2d_reordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_generator_t *g) {
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const points2d_rordered_t * triangular_lattice_gen_getpoints(const triangular_lattice_gen_t *g) {
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return &(g->ps);
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}
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int triangular_lattice_gen_extend_to_steps(triangular_lattice_generator_t * g, int maxsteps) {
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int triangular_lattice_gen_extend_to_steps(triangular_lattice_gen_t * g, int maxsteps)
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{
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if (maxsteps <= g->priv->maxs) // nothing needed
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return 0;
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// TODO FIXME: check for maximum possible maxsteps (not sure what it is)
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@ -159,23 +337,58 @@ int triangular_lattice_gen_extend_to_steps(triangular_lattice_generator_t * g, i
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if(err) return err;
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if(g->includes_origin && g->priv->maxs < 0) // Add origin if not there yet
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trilatgen_append_ij(g, 0, 0);
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trilatgen_pointlist_append_ij(g, 0, 0);
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for (int s = g->priv->maxs + 1; s <= maxsteps; ++s) {
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int i, j;
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// now go along the spider web layer as indicated in the lenghthy comment above
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for (i = s, j = 0; i > 0; --i; ++j) trilatgen_append_ij(g,i,j);
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for (i = 0, j = s; i + j > 0; --i) trilatgen_append_ij(g,i,j);
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for (i = -s, j = s; j > 0; --j) trilatgen_append_ij(g,i,j);
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for (i = -s, j = 0; i < 0; ++i, --j) trilatgen_append_ij(g,i,j);
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for (i = 0, j = -s; i + j < 0; ++i) trilatgen_append_ij(g,i,j);
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for (i = s, j = -s; j < 0; ++j) trilatgen_append_ij(g,i,j);
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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;
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -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;
|
||||
}
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue