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qpms/qpms/latticegens.c

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#include "lattices.h"
#include <limits.h>
#include <math.h>
// generic converting extractors
PGenPolReturnData PGen_next_pol_from_cart2(PGen *g) {
const PGenCart2ReturnData c = PGen_next_cart2(g);
if (c.flags & PGEN_DONE)
return PGenPolDoneVal;
else {
PGenPolReturnData p;
p.flags = c.flags;
p.point_pol = cart2pol(c.point_cart2);
return p;
}
}
PGenCart2ReturnData PGen_next_cart2_from_pol(PGen *g) {
const PGenPolReturnData p = PGen_next_pol(g);
if (p.flags & PGEN_DONE)
return PGenCart2DoneVal;
else {
PGenCart2ReturnData c;
c.flags = p.flags;
c.point_cart2 = pol2cart(p.point_pol);
return c;
}
}
PGenSphReturnData PGen_next_sph_from_cart3(PGen *g) {
const PGenCart3ReturnData c = PGen_next_cart3(g);
if (c.flags & PGEN_DONE)
return PGenSphDoneVal;
else {
PGenSphReturnData s;
s.flags = c.flags;
s.point_sph = cart2sph(c.point_cart3);
return s;
}
}
PGenCart3ReturnData PGen_next_cart3_from_cart2xy(PGen *g) {
const PGenCart2ReturnData c2 = PGen_next_cart2(g);
if (c2.flags & PGEN_DONE)
return PGenCart3DoneVal;
else {
PGenCart3ReturnData c3;
c3.flags = c2.flags;
c3.point_cart3 = cart22cart3xy(c2.point_cart2);
return c3;
}
}
PGenSphReturnData PGen_next_sph_from_cart2(PGen *g) {
const PGenCart2ReturnData c = PGen_next_cart2(g);
if (c.flags & PGEN_DONE)
return PGenSphDoneVal;
else {
PGenSphReturnData s;
s.flags = c.flags;
s.point_sph = cart22sph(c.point_cart2);
return s;
}
}
PGenCart3ReturnData PGen_next_cart3_from_sph(PGen *g) {
const PGenSphReturnData s = PGen_next_sph(g);
if (s.flags & PGEN_DONE)
return PGenCart3DoneVal;
else {
PGenCart3ReturnData c;
c.flags = s.flags;
c.point_cart3 = sph2cart(s.point_sph);
return c;
}
}
// here, various "classes" of the PGenSph point generators are implemented.
// const PGenSphReturnData PGenSphDoneVal = {PGEN_DONE, {0,0,0}}; // defined already in lattices.h
// const PGenCart3ReturnData PGenCart3DoneVal = {PGEN_DONE, {0,0,0}}; // defined already in lattices.h
// General structure of a generator implementation looks like this:
#if 0
//==== PGen_NAME ====
extern const PGenClassInfo PGen_NAME; // forward declaration needed by constructor (may be placed in header file instead)
// Internal state structure
typedef struct PGen_NAME_StateData {
...
} PGen_NAME_StateData;
// Constructor
PGenSph PGen_NAME_new(...) {
g->stateData = malloc(sizeof(PGen_NAME_StateData));
...
PGenSph g = {&PGen_NAME, (void *) stateData};
return g;
}
// Dectructor
void PGen_NAME_dectructor(PGen *g) {
...
free(g->stateData);
g->stateData = NULL;
}
// Extractor, spherical coordinate output
PGenSphReturnData PGen_NAME_next_sph(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenSphDoneVal;
else {
PGen_NAME_StateData *s = (PGen_NAME_StateData *) g->stateData;
if (... /* there are still points to be generated */) {
...
PGenSphReturnData retval = {.../*flags*/, .../*thePoint*/};
return retval;
} else {
PGen_destroy(g);
return PGenSphDoneVal;
}
}
}
// Extractor, 3D cartesian coordinate output
PGenCart3ReturnData PGen_NAME_next_cart3(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart3DoneVal;
else {
PGen_NAME_StateData *s = (PGen_NAME_StateData *) g->stateData;
if (... /* there are still points to be generated */) {
...
PGenCart3ReturnData retval = {.../*flags*/, .../*thePoint*/};
return retval;
} else {
PGen_destroy(g);
return PGenCart3DoneVal;
}
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_NAME = {
"PGen_NAME",
?, //dimensionality
PGEN_COORDS_????, // native coordinate system
// some of the _next_... fun pointers can be NULL
PGen_NAME_next,
PGen_NAME_next_z,
PGen_NAME_next_pol,
PGen_NAME_next_sph,
PGen_NAME_next_cart2,
PGen_NAME_next_cart3,
PGen_NAME_destructor
};
#endif // 0
//==== PGenSph_FromPoint2DArray ====
// Internal state structure
typedef struct PGen_FromPoint2DArray_StateData {
const point2d *base;
size_t len;
size_t currentIndex;
}PGen_FromPoint2DArray_StateData;
// Constructor
PGen PGen_FromPoint2DArray_new(const point2d *points, size_t len) {
PGen_FromPoint2DArray_StateData *stateData = malloc(sizeof(PGen_FromPoint2DArray_StateData));
stateData->base = points;
stateData->len = len;
stateData->currentIndex = 0;
PGen g = {&PGen_FromPoint2DArray, (void *) stateData};
return g;
}
// Destructor
void PGen_FromPoint2DArray_destructor(PGen *g) {
free(g->stateData);
g->stateData = NULL;
}
// Extractor, 2D cartesian (native)
PGenCart2ReturnData PGen_FromPoint2DArray_next_cart2(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart2DoneVal;
else {
PGen_FromPoint2DArray_StateData *s = (PGen_FromPoint2DArray_StateData *) g->stateData;
if (s->currentIndex < s->len) {
cart2_t thePoint = s->base[s->currentIndex];
++(s->currentIndex);
PGenCart2ReturnData retval = {(PGEN_NOTDONE | PGEN_AT_XY | PGEN_NEWR | PGEN_COORDS_CART2), thePoint};
return retval;
} else {
PGen_destroy(g);
return PGenCart2DoneVal;
}
}
}
// Extractor, spherical
PGenSphReturnData PGen_FromPoint2DArray_next_sph(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenSphDoneVal;
else {
PGen_FromPoint2DArray_StateData *s = (PGen_FromPoint2DArray_StateData *) g->stateData;
if (s->currentIndex < s->len) {
sph_t thePoint = cart22sph(s->base[s->currentIndex]);
++(s->currentIndex);
PGenSphReturnData retval = {(PGEN_AT_XY | PGEN_NEWR | PGEN_COORDS_SPH), thePoint};
return retval;
} else {
PGen_destroy(g);
return PGenSphDoneVal;
}
}
}
const PGenClassInfo PGen_FromPoint2DArray = {
"PGen_FromPoint2DArray",
2, // dimensionality
PGEN_COORDS_CART2,
NULL,//PGen_FromPoint2DArray_next,
NULL,
NULL,//PGen_FromPoint2DArray_next_pol,
PGen_FromPoint2DArray_next_sph,
PGen_FromPoint2DArray_next_cart2,
NULL,//PGen_FromPoint2DArray_next_cart3,
PGen_FromPoint2DArray_destructor,
};
//==== PGen_1D ====
//equidistant points along the z-axis;
extern const PGenClassInfo PGen_1D; // forward declaration needed by constructor (may be placed in header file instead)
/* // This had to go to the header file:
enum PGen_1D_incrementDirection{
//PGEN1D_POSITIVE_INC, // not implemented
//PGEN1D_NEGATIVE_INC, // not implemented
PGEN1D_INC_FROM_ORIGIN,
PGEN1D_INC_TOWARDS_ORIGIN
};
*/
// Internal state structure
typedef struct PGen_1D_StateData {
long ptindex;
//long stopindex;
double minR, maxR;
bool inc_minR, inc_maxR;
double a; // lattice period
double offset; // offset of the zeroth lattice point from origin (will be normalised to interval [-a/2,a/2]
enum PGen_1D_incrementDirection incdir;
//bool skip_origin;
} PGen_1D_StateData;
static inline long ptindex_inc(long i) {
if (i > 0)
return -i;
else
return -i + 1;
}
static inline long ptindex_dec(long i) {
if (i > 0)
return -i + 1;
else
return -i;
}
// Constructor, specified by maximum and maximum absolute value
PGen PGen_1D_new_minMaxR(double period, double offset, double minR, bool inc_minR, double maxR, bool inc_maxR,
PGen_1D_incrementDirection incdir) {
PGen_1D_StateData *s = malloc(sizeof(PGen_1D_StateData));
s->minR = minR;
s->maxR = maxR;
s->inc_minR = inc_minR;
s->inc_maxR = inc_maxR;
s->incdir = incdir;
period = fabs(period);
double offset_normalised = offset - period * floor(offset / period); // shift to interval [0, period]
if (offset_normalised > period / 2) offset_normalised -= period; // and to interval [-period/2, period/2]
s->offset = offset_normalised;
if (offset_normalised > 0) // reverse the direction so that the conditions in _next() are hit in correct order
period *= -1;
switch(s->incdir) {
double curR;
case PGEN_1D_INC_FROM_ORIGIN:
s->ptindex = floor(minR / fabs(period));
while ( (curR = fabs(s->offset + s->ptindex * period)) < minR || (!inc_minR && curR <= minR))
s->ptindex = ptindex_inc(s->ptindex);
break;
case PGEN_1D_INC_TOWARDS_ORIGIN:
s->ptindex = - ceil(maxR / fabs(period));
while ( (curR = fabs(s->offset + s->ptindex * period)) > maxR || (!inc_minR && curR >= maxR))
s->ptindex = ptindex_dec(s->ptindex);
break;
default:
abort(); // invalid argument / not implemented
}
s->a = period;
PGen g = {&PGen_1D, (void *) s};
return g;
}
// Dectructor
void PGen_1D_destructor(PGen *g) {
free(g->stateData);
g->stateData = NULL;
}
// Extractor 1D number
PGenZReturnData PGen_1D_next_z(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenZDoneVal;
PGen_1D_StateData *s = (PGen_1D_StateData *) g->stateData;
const double zval = s->ptindex * s->a + s->offset;
const double r = fabs(zval);
bool theEnd = false;
switch (s->incdir) {
case PGEN_1D_INC_FROM_ORIGIN:
if (r < s->maxR || (s->inc_maxR && r == s->maxR))
s->ptindex = ptindex_inc(s->ptindex);
else theEnd = true;
break;
case PGEN_1D_INC_TOWARDS_ORIGIN:
if (r > s->minR || (s->inc_minR && r == s->minR)) {
if (s->ptindex == 0) // handle "underflow"
s->minR = INFINITY;
else
s->ptindex = ptindex_dec(s->ptindex);
} else theEnd = true;
break;
default:
abort(); // invalid value
}
if (!theEnd) {
const PGenZReturnData retval = {PGEN_NOTDONE | PGEN_NEWR | PGEN_AT_Z,
zval};
return retval;
} else {
PGen_destroy(g);
return PGenZDoneVal;
}
}
// Extractor spherical coordinates // TODO remove/simplify
PGenSphReturnData PGen_1D_next_sph(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenSphDoneVal;
PGen_1D_StateData *s = (PGen_1D_StateData *) g->stateData;
const double zval = s->ptindex * s->a + s->offset;
const double r = fabs(zval);
bool theEnd = false;
switch (s->incdir) {
case PGEN_1D_INC_FROM_ORIGIN:
if (r < s->maxR || (s->inc_maxR && r == s->maxR))
s->ptindex = ptindex_inc(s->ptindex);
else theEnd = true;
break;
case PGEN_1D_INC_TOWARDS_ORIGIN:
if (r > s->minR || (s->inc_minR && r == s->minR)) {
if (s->ptindex == 0) // handle "underflow"
s->minR = INFINITY;
else
s->ptindex = ptindex_dec(s->ptindex);
} else theEnd = true;
break;
default:
abort(); // invalid value
}
if (!theEnd) {
const PGenSphReturnData retval = {PGEN_NOTDONE | PGEN_NEWR | PGEN_AT_Z | PGEN_COORDS_SPH,
{r, zval >= 0 ? 0 : M_PI, 0}};
return retval;
} else {
PGen_destroy(g);
return PGenSphDoneVal;
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_1D = {
"PGen_1D",
1, // dimensionality
PGEN_COORDS_CART1,
NULL, //PGen_1D_next,
PGen_1D_next_z,
NULL,//PGen_1D_next_pol,
PGen_1D_next_sph,
NULL,//PGen_1D_next_cart2,
NULL,//PGen_1D_next_cart3,
PGen_1D_destructor
};
//==== PGen_xyWeb ====
// 2D lattice generator in the "spiderweb" style, generated in the "perimetre" order,
// not strictly ordered (or limited) by distance from origin.
// The minR and maxR here refer to the TODO WWHAT
extern const PGenClassInfo PGen_xyWeb; // forward declaration needed by constructor (may be placed in header file instead)
// Internal state structure
typedef struct PGen_xyWeb_StateData {
long i, j;
unsigned short phase; // 0 to 5
long layer;
long last_layer; // generation stops when layer > last_layer
double layer_min_height; // this * layer is what minR and maxR are compared to
double minR, maxR;
bool inc_minR, inc_maxR;
cart2_t b1, b2; // lattice vectors
cart2_t offset; // offset of the zeroth lattice point from origin (TODO will be normalised to the WS cell)
// TODO type rectangular vs. triangular
LatticeType2 lt;
} PGen_xyWeb_StateData;
// Constructor
PGen PGen_xyWeb_new(cart2_t b1, cart2_t b2, double rtol, cart2_t offset, double minR, bool inc_minR, double maxR, bool inc_maxR) {
PGen_xyWeb_StateData *s = malloc(sizeof(PGen_xyWeb_StateData));
s->minR = minR; s->maxR = maxR;
s->inc_minR = inc_minR;
s->inc_maxR = inc_maxR;
l2d_reduceBasis(b1, b2, &(s->b1), &(s->b2));
s->offset = offset; // TODO shorten into the WS cell ?
s->lt = l2d_classifyLattice(s->b1, s->b2, rtol);
s->layer_min_height = l2d_hexWebInCircleRadius(s->b1, s->b2);
s->layer = ceil(s->minR/s->layer_min_height);
if(!inc_minR && (s->layer * s->layer_min_height) <= minR)
++(s->layer);
s->i = s->layer; s->j = 0; s->phase = 0; // init indices
s->last_layer = floor(s->maxR/s->layer_min_height);
if(!inc_maxR && (s->last_layer * s->layer_min_height) >= maxR)
--(s->last_layer);
PGen g = {&PGen_xyWeb, (void *) s};
return g;
}
// Destructor
void PGen_xyWeb_destructor(PGen *g) {
free(g->stateData);
g->stateData = NULL;
}
// Extractor (2D cartesian, native)
PGenCart2ReturnData PGen_xyWeb_next_cart2(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart2DoneVal;
else {
PGen_xyWeb_StateData * const s = (PGen_xyWeb_StateData *) g->stateData;
assert(s->layer >= 0);
if (s->layer <= s->last_layer) {
const cart2_t thePoint = cart2_add(s->offset,
cart2_add(cart2_scale(s->i, s->b1), cart2_scale(s->j, s->b2)));
if(s->layer == 0) { // origin is unique, proceed with next layer
++s->layer;
s->phase = 0;
s->i = s->layer;
s->j = 0;
}
else if(s->lt & (SQUARE | RECTANGULAR)) {
// rectangular or square lattice, four perimeters
switch(s->phase) {
case 0: // initial i = l, j = 0
--s->i;
++s->j;
if(s->i <= 0) ++s->phase;
break;
case 1: // initial i = 0, j = l
--s->i;
--s->j;
if(s->j <= 0) ++s->phase;
break;
case 2: // initial i = -l, j = 0
++s->i;
--s->j;
if(s->i >= 0) ++s->phase;
break;
case 3: // initial i = 0, j = -l
++s->i;
++s->j;
if(s->j >= 0) ++s->phase;
break;
default:
abort();
}
if(s->phase == 4) { // phase overflow, start new layer
++s->layer;
s->phase = 0;
s->i = s->layer;
s->j = 0;
}
} else { // non-rectangular lattice, six perimeters
switch(s->phase) {
case 0:
--s->i;
++s->j;
if(s->i <= 0) ++s->phase;
break;
case 1:
--s->i;
if(s->i + s->j <= 0) ++s->phase;
break;
case 2:
--s->j;
if(s->j <= 0) ++s->phase;
break;
case 3:
++s->i;
--s->j;
if(s->i >= 0) ++s->phase;
break;
case 4:
++s->i;
if(s->i + s->j >= 0) ++s->phase;
break;
case 5:
++s->j;
if(s->j >= 0) ++s->phase;
break;
default:
abort();
}
if(s->phase == 6) { // phase overflow, start next layer
++s->layer;
s->phase = 0;
s->i = s->layer;
s->j = 0;
}
}
PGenCart2ReturnData retval = {(PGEN_NOTDONE | PGEN_AT_XY | PGEN_NEWR | PGEN_COORDS_CART2), thePoint};
return retval;
} else {
PGen_destroy(g);
return PGenCart2DoneVal;
}
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_xyWeb = {
"PGen_xyWeb",
2,
PGEN_COORDS_CART2,
NULL,//PGen_xyWeb_next,
NULL,//PGen_xyWeb_next_z,
PGen_next_pol_from_cart2, //NULL,//PGen_xyWeb_next_pol,
PGen_next_sph_from_cart2, //NULL,//PGen_xyWeb_next_sph,
PGen_xyWeb_next_cart2, // native
PGen_next_cart3_from_cart2xy, //NULL,//PGen_xyWeb_next_cart3,
PGen_xyWeb_destructor
};
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