395 lines
12 KiB
C
395 lines
12 KiB
C
#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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} intcoord2_t;
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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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/*
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* N. B. the possible radii (distances from origin) of the lattice points can be described as
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*
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* r**2 / a**2 == i**2 + j**2 + i*j ,
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*
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* where i, j are integer indices describing steps along two basis vectors (which have
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* 60 degree angle between them).
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*
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* The plane can be divided into six sextants, characterized as:
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*
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* 0) i >= 0 && j >= 0,
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* [a] i > 0,
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* [b] j > 0,
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* 1) i <= 0 && {j >= 0} && i + j >= 0,
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* [a] i + j > 0,
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* [b] i < 0,
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* 2) {i <= 0} && j >= 0 && i + j <= 0,
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* [a] j > 0,
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* [b] i + j < 0,
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* 3) i <= 0 && j <= 0,
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* [a] i < 0,
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* [b] j < 0,
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* 4) i >= 0 && {j <= 0} && i + j <= 0,
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* [a] i + j < 0,
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* [b] i > 0,
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* 5) {i >= 0} && j <= 0 && i + j >= 0,
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* [a] j < 0,
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* [b] i + j > 0.
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*
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* The [a], [b] are two variants that uniquely assign the points at the sextant boundaries.
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* The {conditions} in braces are actually redundant.
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*
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* In each sextant, the "minimum steps from the origin" value is calculated as:
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* 0) i + j,
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* 1) j
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* 2) -i
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* 3) -i - j,
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* 4) -j,
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* 5) i.
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*
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* The "spider web" generation for s steps from the origin (s-th layer) goes as following (variant [a]):
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* 0) for (i = s, j = 0; i > 0; --i, ++j)
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* 1) for (i = 0, j = s; i + j > 0; --i)
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* 2) for (i = -s, j = s; j > 0; --j)
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* 3) for (i = -s, j = 0; i < 0; ++i, --j)
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* 4) for (i = 0, j = -s; i + j < 0; ++i)
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* 5) for (i = s, j = -s; j < 0; ++j)
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*
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*
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* Length of the s-th layer is 6*s for s >= 1. Size (number of lattice points) of the whole s-layer "spider web"
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* is therefore 3*s*(s+1), excluding origin.
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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) + 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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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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// 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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if (i <= 0 && w > 0) return 1;
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if (w <= 0 && j > 0) return 2;
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if (i < 0 && j <= 0) return 3;
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if (i >= 0 && w < 0) return 4;
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if (w >= 0 && j < 0) return 5;
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if (i == 0 && j == 0) return -1; // origin
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assert(0); // other options should be impossible
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}
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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_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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g->ps.rs = NULL;
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g->ps.base = NULL;
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g->ps.r_offsets = NULL;
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g->priv = malloc(sizeof(triangular_lattice_gen_privstuff_t));
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g->priv->maxs = -1;
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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_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_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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free(g->priv->pointlist_base);
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free(g->priv);
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free(g);
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}
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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_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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int err;
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err = trilatgen_ensure_pointlist_capacity(g, maxsteps);
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if(err) return err;
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err = trilatgen_ensure_ps_rs_capacity(g, maxsteps);
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if(err) return err;
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err = trilatgen_ensure_ps_points_capacity(g, maxsteps);
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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_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_pointlist_append_ij(g,i,j);
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for (i = 0, j = s; i + j > 0; --i) trilatgen_pointlist_append_ij(g,i,j);
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for (i = -s, j = s; j > 0; --j) trilatgen_pointlist_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);
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for (i = 0, j = -s; i + j < 0; ++i) trilatgen_pointlist_append_ij(g,i,j);
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for (i = s, j = -s; j < 0; ++j) trilatgen_pointlist_append_ij(g,i,j);
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}
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trilatgen_sort_pointlist(g);
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// initialise first r_offset if needed
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if (0 == g->ps.nrs)
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g->ps.r_offsets[0] = 0;
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//ted je potřeba vytahat potřebný počet bodů z fronty a naflákat je do ps.
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// FIXME pohlídat si kapacitu datových typů
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int maxr2i = sqi(maxsteps) * 3 / 4;
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while (g->priv->pointlist_n > 0) { // This condition should probably be always true anyways.
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intcoord2_t coord = trilatgen_pointlist_first(g);
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int r2i_cur = trilat_r2_coord(coord);
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if(r2i_cur > maxr2i)
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break;
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g->ps.rs[g->ps.nrs] = sqrt(r2i_cur) * g->a;
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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
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while(1) {
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coord = trilatgen_pointlist_first(g);
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if(r2i_cur != trilat_r2_coord(coord))
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break;
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else {
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trilatgen_pointlist_deletefirst(g);
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point2d thepoint;
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switch (g->orientation) {
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case TRIANGULAR_HORIZONTAL:
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thepoint = point2d_fromxy((coord.i+.5*coord.j)*g->a, (M_SQRT3_2*coord.j)*g->a);
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break;
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case TRIANGULAR_VERTICAL:
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thepoint = point2d_fromxy((-M_SQRT3_2*coord.j)*g->a, (coord.i+.5*coord.j)*g->a);
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break;
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default:
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abort();
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}
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g->ps.base[g->ps.r_offsets[g->ps.nrs+1]] = thepoint;
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++(g->ps.r_offsets[g->ps.nrs+1]);
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}
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}
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}
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g->priv->maxs = maxsteps;
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return 0;
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}
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