476 lines
16 KiB
C
476 lines
16 KiB
C
#ifndef LATTICES_H
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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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#include <stdlib.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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#define M_1_SQRT3 0.57735026918962576450914878050195746
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/* IMPORTANT TODO
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* ==============
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*
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* The current content of this part (and the implementation) is extremely ugly.
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* When I have some time, I have to rewrite this in the style of lattices2d.py
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*
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*/
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typedef enum LatticeDimensionality {
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LAT1D = 1,
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LAT2D = 2,
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LAT3D = 4,
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SPACE1D = 8,
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SPACE2D = 16,
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SPACE3D = 32,
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LAT_1D_IN_3D = 33,
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LAT_2D_IN_3D = 34,
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LAT_3D_IN_3D = 40,
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// special coordinate arrangements (indicating possible optimisations)
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LAT_ZONLY = 64,
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LAT_XYONLY = 128,
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LAT_1D_IN_3D_ZONLY = 97, // LAT1D | SPACE3D | 64
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LAT_2D_IN_3D_XYONLY = 162 // LAT2D | SPACE3D | 128
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} LatticeDimensionality;
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inline static bool LatticeDimensionality_checkflags(
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LatticeDimensionality a, LatticeDimensionality flags_a_has_to_contain) {
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return ((a & flags_a_has_to_contain) == flags_a_has_to_contain);
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}
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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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return p;
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}
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/*
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* GENERIC LATTICE POINT GENERATOR TYPE PGen
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* ============================================
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*
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* A bit of OOP-in-C brainfuck here.
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*
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* The basic principle of operation is following:
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* Instead of a list (array) of points, an initialized PGen object
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* is passed to a function that does something over a set of points.
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* Each time PGen-type object is "called", it returns PGenReturnData,
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* which contains a point in spherical coordinates (sph_t) and some metadata.
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*
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* After the last generated point, the generator frees all internal memory
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* and returns PGenSphReturnData with PGEN_NOTDONE flag unset (the rest
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* shall be considered invalid data).
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* The caller can also decide not to use the rest and end getting the points
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* even when the PGEN_NOTDONE was set in the last returned data.
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* In such case, the caller shall call PGen_destroy() manually.
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*
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* MEMORY MANAGEMENT POLICY
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* ------------------------
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* The basic PGen structure shall be allocated on stack (it's only two pointers),
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* everything internal goes on heap.
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*/
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struct PGen; // full definition below
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typedef enum PGenPointFlags {
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PGEN_NOTDONE = 2, // The most important flag: when this is not set, the interation ended – other data returned should be considered nonsense and at this point, the generator should have de-allocated all internal memory.
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PGEN_NEWR = 1, // The r-coordinate is different than in the previous generated point (so radial parts of the calculation have to be redone);
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PGEN_AT_Z = 4, // This is set if we are at the z-axis (theta is either 0 or M_PI)
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PGEN_AT_XY = 8, // This is set if we are at the xy-plane (theta is M_PI2)
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PGEN_DONE = 0, // convenience value, not an actual flag
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PGEN_COORDS_CART1 = QPMS_COORDS_CART1,
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PGEN_COORDS_CART2 = QPMS_COORDS_CART2,
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PGEN_COORDS_CART3 = QPMS_COORDS_CART3,
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PGEN_COORDS_POL = QPMS_COORDS_POL,
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PGEN_COORDS_SPH = QPMS_COORDS_SPH,
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PGEN_COORDS_BITRANGE = PGEN_COORDS_CART1 |
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PGEN_COORDS_CART2 | PGEN_COORDS_CART3 | PGEN_COORDS_POL | PGEN_COORDS_SPH
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} PGenPointFlags;
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typedef struct PGenReturnData { // Generic return type that might contain point represented in any of the supported coordinate systems
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PGenPointFlags flags; // metadata; must contain info about the coordinate system
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anycoord_point_t point;
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} PGenReturnData;
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typedef struct PGenZReturnData {
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PGenPointFlags flags; // metadata
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double point_z;
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} PGenZReturnData;
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typedef struct PGenPolReturnData {
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PGenPointFlags flags; // metadata
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pol_t point_pol;
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} PGenPolReturnData;
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typedef struct PGenSphReturnData {
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PGenPointFlags flags; // metadata
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sph_t point_sph; // the actual point data
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} PGenSphReturnData;
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typedef struct PGenCart2ReturnData {
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PGenPointFlags flags; // metadata
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cart2_t point_cart2; // the actual point data
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} PGenCart2ReturnData;
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typedef struct PGenCart3ReturnData {
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PGenPointFlags flags; // metadata
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cart3_t point_cart3; // the actual point data
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} PGenCart3ReturnData;
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// convenience constants for use in the extractor implementations
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static const PGenZReturnData PGenZDoneVal = {PGEN_DONE, 0};
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static const PGenPolReturnData PGenPolDoneVal = {PGEN_DONE, {0,0}};
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static const PGenSphReturnData PGenSphDoneVal = {PGEN_DONE, {0,0,0}};
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static const PGenCart2ReturnData PGenCart2DoneVal = {PGEN_DONE, {0,0}};
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static const PGenCart3ReturnData PGenCart3DoneVal = {PGEN_DONE, {0,0,0}};
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typedef struct PGenClassInfo { // static PGenSph info
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char * const name; // mainly for debugging purposes
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int dimensionality; // lower-dimensional can be converted to higher-D, not vice versa; bit redundant with the following, whatever.
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PGenPointFlags native_point_flags; // info about native coordinate system
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PGenReturnData (*next)(struct PGen *);
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PGenZReturnData (*next_z)(struct PGen *);
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PGenPolReturnData (*next_pol)(struct PGen *); // This contains the actual generator procedure (TODO shouldn't I rather point to stateData?)
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PGenSphReturnData (*next_sph)(struct PGen *);
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PGenCart2ReturnData (*next_cart2)(struct PGen *);
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PGenCart3ReturnData (*next_cart3)(struct PGen *);
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void (*destructor)(struct PGen *); // Destructor to be called by next() at iteration end, or by the caller if ending the generation prematurely
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} PGenClassInfo;
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// TOP DATA STRUCTURE DEFINITION HERE
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typedef struct PGen {
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const PGenClassInfo * /*const*/ c;
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void *stateData; // shall be NULL if invalid (destroyed)
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} PGen;
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static inline void PGen_destroy(PGen *g) {
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g->c->destructor(g);
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assert(g->stateData == NULL); // this should be done by the destructor
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}
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static inline PGenZReturnData PGen_next_z(PGen *g) {
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if (g->c->next_z)
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return g->c->next_z(g);
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else abort();
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}
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static inline PGenSphReturnData PGen_next_sph(PGen *g) {
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// TODO maybe some asserts around here
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if (g->c->next_sph)
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return g->c->next_sph(g);
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else abort(); // the current point generator does not support this type of output
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}
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static inline PGenPolReturnData PGen_next_pol(PGen *g) {
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// TODO maybe some asserts around here
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if (g->c->next_pol)
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return g->c->next_pol(g);
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else abort(); // the current point generator does not support this type of output
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}
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static inline PGenCart3ReturnData PGen_next_cart3(PGen *g) {
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// TODO maybe some asserts around here
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if (g->c->next_cart3)
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return g->c->next_cart3(g);
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else abort(); // the current point generator does not support this type of output
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}
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static inline PGenCart2ReturnData PGen_next_cart2(PGen *g) {
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// TODO maybe some asserts around here
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if (g->c->next_cart2)
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return g->c->next_cart2(g);
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else abort(); // the current point generator does not support this type of output
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}
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static inline bool PGenSph_notDone(PGenSphReturnData data) {
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return data.flags & PGEN_NOTDONE ? true : false;
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}
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static inline bool PGenCart3_notDone(PGenCart3ReturnData data) {
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return data.flags & PGEN_NOTDONE ? true : false;
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}
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static inline PGenCart3ReturnData PGenReturnDataConv_sph_cart3(PGenSphReturnData sphdata){
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PGenCart3ReturnData c3data;
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c3data.flags = sphdata.flags;
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c3data.point_cart3 = sph2cart(sphdata.point_sph);
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return c3data;
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}
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static inline PGenSphReturnData PGenReturnDataConv_cart3_sph(PGenCart3ReturnData c){
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PGenSphReturnData s;
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s.flags = c.flags;
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s.point_sph = cart2sph(c.point_cart3);
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return s;
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}
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/*
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* Some basic lattice generators implementing the abstract interface above (implemented in latticegens.c).
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*/
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// This one simply iterates over an existing array of Point2d
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extern const PGenClassInfo PGen_FromPoint2DArray; // TODO Do I even need this to be declared here?
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PGen PGen_FromPoints2DArray_new(const point2d *points, size_t len);
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extern const PGenClassInfo PGen_1D;
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typedef enum PGen_1D_incrementDirection{
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//PGEN_1D_POSITIVE_INC, // not implemented
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//PGEN_1D_NEGATIVE_INC, // not implemented
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PGEN_1D_INC_FROM_ORIGIN,
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PGEN_1D_INC_TOWARDS_ORIGIN
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} PGen_1D_incrementDirection;
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PGen PGen_1D_new_minMaxR(double period, double offset, double minR, bool inc_minR, double maxR, bool inc_maxR,
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PGen_1D_incrementDirection incdir);
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extern const PGenClassInfo PGen_xyWeb;
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PGen PGen_xyWeb_new(cart2_t b1, cart2_t b2, double rtol, cart2_t offset,
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double minR, bool inc_minR, double maxR, bool inc_maxR);
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/*
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* THE NICE PART (adaptation of lattices2d.py)
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* ===========================================
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*
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* all the functions are prefixed with l2d_
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* convention for argument order: inputs, *outputs, add. params
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*/
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#define BASIS_RTOL 1e-13
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// Bravais lattice types
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typedef enum {
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OBLIQUE = 1,
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RECTANGULAR = 2,
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SQUARE = 4,
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RHOMBIC = 5,
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EQUILATERAL_TRIANGULAR = 3,
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RIGHT_ISOSCELES=SQUARE,
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PARALLELOGRAMMIC=OBLIQUE,
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CENTERED_RHOMBIC=RECTANGULAR,
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RIGHT_TRIANGULAR=RECTANGULAR,
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CENTERED_RECTANGULAR=RHOMBIC,
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ISOSCELE_TRIANGULAR=RHOMBIC,
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RIGHT_ISOSCELE_TRIANGULAR=SQUARE,
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HEXAGONAL=EQUILATERAL_TRIANGULAR
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} LatticeType2;
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#if 0
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// Wallpaper groups
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typedef enum {
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TODO
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} SpaceGroup2;
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#endif
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/*
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* Lagrange-Gauss reduction of a 2D basis.
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* The output shall satisfy |out1| <= |out2| <= |out2 - out1|
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*/
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void l2d_reduceBasis(cart2_t in1, cart2_t in2, cart2_t *out1, cart2_t *out2);
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/*
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* This gives the "ordered shortest triple" of base vectors (each pair from the triple
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* is a base) and there may not be obtuse angle between o1, o2 and between o2, o3
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*/
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void l2d_shortestBase3(cart2_t i1, cart2_t i2, cart2_t *o1, cart2_t *o2, cart2_t *o3);
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/*
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* TODO doc
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* return value is 4 or 6.
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*/
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int l2d_shortestBase46(cart2_t i1, cart2_t i2, cart2_t *o1, cart2_t *o2, cart2_t *o3, cart2_t *o4, cart2_t *o5, cart2_t *o6, double rtol);
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// variant
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int l2d_shortestBase46_arr(cart2_t i1, cart2_t i2, cart2_t *oarr, double rtol);
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// Determines whether angle between inputs is obtuse
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bool l2d_is_obtuse_r(cart2_t i1, cart2_t i2, double rtol);
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bool l2d_is_obtuse(cart2_t i1, cart2_t i2);
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/*
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* Given two basis vectors, returns 2D Bravais lattice type.
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*/
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LatticeType2 l2d_classifyLattice(cart2_t b1, cart2_t b2, double rtol);
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// Other functions in lattices2d.py: TODO?
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// range2D()
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// generateLattice()
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// generateLatticeDisk()
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// cutWS()
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// filledWS()
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// change_basis()
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/*
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* Given basis vectors, returns the corners of the Wigner-Seits unit cell (W1, W2, -W1, W2)
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* for rectangular and square lattice or (w1, w2, w3, -w1, -w2, -w3) otherwise.
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*/
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int l2d_cellCornersWS(cart2_t i1, cart2_t i2, cart2_t *o1, cart2_t *o2, cart2_t *o3, cart2_t *o4, cart2_t *o5, cart2_t *o6, double rtol);
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// variant
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int l2d_cellCornersWS_arr(cart2_t i1, cart2_t i2, cart2_t *oarr, double rtol);
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// Reciprocal bases; returns 0 on success, possibly a non-zero if b1 and b2 are parallel
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int l2d_reciprocalBasis1(cart2_t b1, cart2_t b2, cart2_t *rb1, cart2_t *rb2);
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int l2d_reciprocalBasis2pi(cart2_t b1, cart2_t b2, cart2_t *rb1, cart2_t *rb2);
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double l2d_unitcell_area(cart2_t b1, cart2_t b2);
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// returns the radius of inscribed circle of a hexagon (or rectangle/square if applicable) created by the shortest base triple
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double l2d_hexWebInCircleRadius(cart2_t b1, cart2_t b2);
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/*
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* THE MORE OR LESS OK PART
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* ========================
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*/
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/*
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* General set of points ordered by the r-coordinate.
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* Typically, this will include all lattice inside a certain circle.
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* This structure is internally used by the "lattice generators" below.
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* It does not have its memory management of its own, as it is handled
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* by the "generators". For everything except the generators,
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* this structure shall be read-only.
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*/
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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 *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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// sorts arbitrary points and creates points2d_rordered_t
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points2d_rordered_t *points2d_rordered_frompoints(const point2d *orig_base,
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size_t nmemb, double rtol, double atol);
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// returns a copy but shifted by a constant (actually in a stupid way, but whatever)
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points2d_rordered_t *points2d_rordered_shift(const points2d_rordered_t *orig,
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point2d shift, double rtol, double atol);
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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,
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double factor);
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/* The destructor: use only for results of
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* - points2D_rordered_frompoints,
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* - points2d_rordered_shift,
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* - points2d_rordered_scale.
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*/
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void points2d_rordered_free(points2d_rordered_t *);
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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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ptrdiff_t points2d_rordered_locate_r(const points2d_rordered_t *, double r);
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// returns a "view" (does not copy any of the arrays)
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// -- DO NOT FREE orig BEFORE THE END OF SCOPE OF THE RESULT
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points2d_rordered_t points2d_rordered_annulus(const points2d_rordered_t *orig, double minr, bool minr_inc,
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double maxr, bool maxr_inc);
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/*
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* THE UGLY PART
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* =============
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*/
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/*
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* EQUILATERAL TRIANGULAR LATTICE
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*/
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typedef enum {
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TRIANGULAR_VERTICAL, // there is a lattice base vector parallel to the y-axis
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TRIANGULAR_HORIZONTAL // there is a lattice base vector parallel to the x-axis
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} TriangularLatticeOrientation;
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static inline TriangularLatticeOrientation reverseTriangularLatticeOrientation(TriangularLatticeOrientation o){
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switch(o) {
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case TRIANGULAR_VERTICAL:
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return TRIANGULAR_HORIZONTAL;
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break;
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case TRIANGULAR_HORIZONTAL:
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return TRIANGULAR_VERTICAL;
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break;
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default:
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abort();
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}
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abort();
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}
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// implementation data structures; not needed in the header file
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typedef struct triangular_lattice_gen_privstuff_t triangular_lattice_gen_privstuff_t;
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typedef struct {
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// public:
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points2d_rordered_t ps;
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TriangularLatticeOrientation orientation;
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double a; // lattice vector length
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// not sure if needed:
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bool includes_origin;
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// Denotes an offset of the "origin" point; meaning step hexshift * a / sqrt(2) upwards
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// or leftwards for the horizontal or vertical orientations, respectively.
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int hexshift;
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// private:
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triangular_lattice_gen_privstuff_t *priv;
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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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int halfoffset);
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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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/*
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* HONEYCOMB LATTICE
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*/
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||
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typedef struct {
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// public:
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points2d_rordered_t ps;
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TriangularLatticeOrientation orientation;
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||
double a;
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||
double h;
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||
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// private:
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triangular_lattice_gen_t *tg;
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} honeycomb_lattice_gen_t;
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honeycomb_lattice_gen_t *honeycomb_lattice_gen_init_h(double h, TriangularLatticeOrientation ori);
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||
honeycomb_lattice_gen_t *honeycomb_lattice_gen_init_a(double a, TriangularLatticeOrientation ori);
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||
int honeycomb_lattice_gen_extend_to_steps(honeycomb_lattice_gen_t *g, int maxsteps);
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||
int honeycomb_lattice_gen_extend_to_r(honeycomb_lattice_gen_t *g, double r);
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||
void honeycomb_lattice_gen_free(honeycomb_lattice_gen_t *g);
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||
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#endif // LATTICES_H
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