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1225 lines
26 KiB
C
1225 lines
26 KiB
C
/******************************************************************************
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This file contains routines that can be bound to a Postgres backend and
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called by the backend in the process of processing queries. The calling
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format for these routines is dictated by Postgres architecture.
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******************************************************************************/
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#include "postgres.h"
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#include <math.h>
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#include "access/gist.h"
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#include "access/rtree.h"
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#include "lib/stringinfo.h"
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#include "utils/builtins.h"
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#include "cubedata.h"
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#define max(a,b) ((a) > (b) ? (a) : (b))
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#define min(a,b) ((a) <= (b) ? (a) : (b))
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#define abs(a) ((a) < (0) ? (-a) : (a))
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extern int cube_yyparse();
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extern void cube_yyerror(const char *message);
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extern void cube_scanner_init(const char *str);
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extern void cube_scanner_finish(void);
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/*
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** Input/Output routines
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*/
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NDBOX *cube_in(char *str);
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NDBOX *cube(text *str);
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char *cube_out(NDBOX * cube);
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NDBOX *cube_f8(double *);
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NDBOX *cube_f8_f8(double *, double *);
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NDBOX *cube_c_f8(NDBOX *, double *);
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NDBOX *cube_c_f8_f8(NDBOX *, double *, double *);
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int4 cube_dim(NDBOX * a);
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double *cube_ll_coord(NDBOX * a, int4 n);
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double *cube_ur_coord(NDBOX * a, int4 n);
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/*
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** GiST support methods
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*/
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bool g_cube_consistent(GISTENTRY *entry, NDBOX * query, StrategyNumber strategy);
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GISTENTRY *g_cube_compress(GISTENTRY *entry);
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GISTENTRY *g_cube_decompress(GISTENTRY *entry);
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float *g_cube_penalty(GISTENTRY *origentry, GISTENTRY *newentry, float *result);
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GIST_SPLITVEC *g_cube_picksplit(bytea *entryvec, GIST_SPLITVEC *v);
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bool g_cube_leaf_consistent(NDBOX * key, NDBOX * query, StrategyNumber strategy);
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bool g_cube_internal_consistent(NDBOX * key, NDBOX * query, StrategyNumber strategy);
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NDBOX *g_cube_union(bytea *entryvec, int *sizep);
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NDBOX *g_cube_binary_union(NDBOX * r1, NDBOX * r2, int *sizep);
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bool *g_cube_same(NDBOX * b1, NDBOX * b2, bool *result);
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/*
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** B-tree support functions
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*/
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bool cube_eq(NDBOX * a, NDBOX * b);
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bool cube_ne(NDBOX * a, NDBOX * b);
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bool cube_lt(NDBOX * a, NDBOX * b);
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bool cube_gt(NDBOX * a, NDBOX * b);
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bool cube_le(NDBOX * a, NDBOX * b);
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bool cube_ge(NDBOX * a, NDBOX * b);
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int32 cube_cmp(NDBOX * a, NDBOX * b);
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/*
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** R-tree support functions
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*/
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bool cube_contains(NDBOX * a, NDBOX * b);
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bool cube_contained(NDBOX * a, NDBOX * b);
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bool cube_overlap(NDBOX * a, NDBOX * b);
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NDBOX *cube_union(NDBOX * a, NDBOX * b);
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NDBOX *cube_inter(NDBOX * a, NDBOX * b);
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double *cube_size(NDBOX * a);
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void rt_cube_size(NDBOX * a, double *sz);
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/*
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** These make no sense for this type, but R-tree wants them
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*/
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bool cube_over_left(NDBOX * a, NDBOX * b);
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bool cube_over_right(NDBOX * a, NDBOX * b);
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bool cube_left(NDBOX * a, NDBOX * b);
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bool cube_right(NDBOX * a, NDBOX * b);
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/*
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** miscellaneous
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*/
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bool cube_lt(NDBOX * a, NDBOX * b);
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bool cube_gt(NDBOX * a, NDBOX * b);
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double *cube_distance(NDBOX * a, NDBOX * b);
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bool cube_is_point(NDBOX * a);
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NDBOX *cube_enlarge(NDBOX * a, double *r, int4 n);
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/*
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** Auxiliary funxtions
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*/
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static double distance_1D(double a1, double a2, double b1, double b2);
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/*****************************************************************************
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* Input/Output functions
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*****************************************************************************/
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/* NdBox = [(lowerleft),(upperright)] */
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/* [(xLL(1)...xLL(N)),(xUR(1)...xUR(n))] */
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NDBOX *
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cube_in(char *str)
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{
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void *result;
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cube_scanner_init(str);
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if (cube_yyparse(&result) != 0)
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cube_yyerror("bogus input");
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cube_scanner_finish();
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return ((NDBOX *) result);
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}
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/* Allow conversion from text to cube to allow input of computed strings */
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/* There may be issues with toasted data here. I don't know enough to be sure.*/
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NDBOX *
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cube(text *str)
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{
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return cube_in(DatumGetCString(DirectFunctionCall1(textout,
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PointerGetDatum(str))));
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}
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char *
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cube_out(NDBOX * cube)
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{
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StringInfoData buf;
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bool equal = true;
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int dim = cube->dim;
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int i;
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int ndig;
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initStringInfo(&buf);
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/*
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* Get the number of digits to display.
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*/
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ndig = DBL_DIG + extra_float_digits;
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if (ndig < 1)
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ndig = 1;
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/*
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* while printing the first (LL) corner, check if it is equal to the
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* second one
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*/
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appendStringInfoChar(&buf, '(');
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for (i = 0; i < dim; i++)
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{
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if (i > 0)
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appendStringInfo(&buf, ", ");
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appendStringInfo(&buf, "%.*g", ndig, cube->x[i]);
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if (cube->x[i] != cube->x[i + dim])
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equal = false;
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}
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appendStringInfoChar(&buf, ')');
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if (!equal)
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{
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appendStringInfo(&buf, ",(");
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for (i = 0; i < dim; i++)
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{
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if (i > 0)
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appendStringInfo(&buf, ", ");
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appendStringInfo(&buf, "%.*g", ndig, cube->x[i + dim]);
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}
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appendStringInfoChar(&buf, ')');
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}
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return buf.data;
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}
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/*****************************************************************************
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* GiST functions
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*****************************************************************************/
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/*
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** The GiST Consistent method for boxes
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** Should return false if for all data items x below entry,
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** the predicate x op query == FALSE, where op is the oper
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** corresponding to strategy in the pg_amop table.
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*/
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bool
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g_cube_consistent(GISTENTRY *entry,
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NDBOX * query,
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StrategyNumber strategy)
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{
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/*
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* if entry is not leaf, use g_cube_internal_consistent, else use
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* g_cube_leaf_consistent
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*/
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if (GIST_LEAF(entry))
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return g_cube_leaf_consistent((NDBOX *) DatumGetPointer(entry->key),
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query, strategy);
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else
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return g_cube_internal_consistent((NDBOX *) DatumGetPointer(entry->key),
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query, strategy);
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}
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/*
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** The GiST Union method for boxes
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** returns the minimal bounding box that encloses all the entries in entryvec
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*/
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NDBOX *
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g_cube_union(bytea *entryvec, int *sizep)
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{
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int numranges,
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i;
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NDBOX *out = (NDBOX *) NULL;
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NDBOX *tmp;
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/*
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* fprintf(stderr, "union\n");
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*/
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numranges = (VARSIZE(entryvec) - VARHDRSZ) / sizeof(GISTENTRY);
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tmp = (NDBOX *) DatumGetPointer((((GISTENTRY *) (VARDATA(entryvec)))[0]).key);
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/*
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* sizep = sizeof(NDBOX); -- NDBOX has variable size
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*/
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*sizep = tmp->size;
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for (i = 1; i < numranges; i++)
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{
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out = g_cube_binary_union(tmp, (NDBOX *)
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DatumGetPointer((((GISTENTRY *) (VARDATA(entryvec)))[i]).key),
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sizep);
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if (i > 1)
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pfree(tmp);
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tmp = out;
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}
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return (out);
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}
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/*
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** GiST Compress and Decompress methods for boxes
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** do not do anything.
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*/
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GISTENTRY *
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g_cube_compress(GISTENTRY *entry)
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{
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return (entry);
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}
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GISTENTRY *
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g_cube_decompress(GISTENTRY *entry)
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{
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return (entry);
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}
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/*
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** The GiST Penalty method for boxes
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** As in the R-tree paper, we use change in area as our penalty metric
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*/
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float *
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g_cube_penalty(GISTENTRY *origentry, GISTENTRY *newentry, float *result)
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{
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NDBOX *ud;
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double tmp1,
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tmp2;
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ud = cube_union((NDBOX *) DatumGetPointer(origentry->key),
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(NDBOX *) DatumGetPointer(newentry->key));
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rt_cube_size(ud, &tmp1);
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rt_cube_size((NDBOX *) DatumGetPointer(origentry->key), &tmp2);
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*result = (float) (tmp1 - tmp2);
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pfree(ud);
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/*
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* fprintf(stderr, "penalty\n"); fprintf(stderr, "\t%g\n", *result);
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*/
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return (result);
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}
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/*
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** The GiST PickSplit method for boxes
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** We use Guttman's poly time split algorithm
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*/
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GIST_SPLITVEC *
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g_cube_picksplit(bytea *entryvec,
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GIST_SPLITVEC *v)
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{
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OffsetNumber i,
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j;
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NDBOX *datum_alpha,
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*datum_beta;
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NDBOX *datum_l,
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*datum_r;
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NDBOX *union_d,
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*union_dl,
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*union_dr;
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NDBOX *inter_d;
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bool firsttime;
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double size_alpha,
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size_beta,
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size_union,
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size_inter;
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double size_waste,
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waste;
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double size_l,
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size_r;
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int nbytes;
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OffsetNumber seed_1 = 0,
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seed_2 = 0;
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OffsetNumber *left,
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*right;
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OffsetNumber maxoff;
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/*
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* fprintf(stderr, "picksplit\n");
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*/
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maxoff = ((VARSIZE(entryvec) - VARHDRSZ) / sizeof(GISTENTRY)) - 2;
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nbytes = (maxoff + 2) * sizeof(OffsetNumber);
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v->spl_left = (OffsetNumber *) palloc(nbytes);
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v->spl_right = (OffsetNumber *) palloc(nbytes);
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firsttime = true;
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waste = 0.0;
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for (i = FirstOffsetNumber; i < maxoff; i = OffsetNumberNext(i))
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{
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datum_alpha = (NDBOX *) DatumGetPointer(((GISTENTRY *) (VARDATA(entryvec)))[i].key);
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for (j = OffsetNumberNext(i); j <= maxoff; j = OffsetNumberNext(j))
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{
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datum_beta = (NDBOX *) DatumGetPointer(((GISTENTRY *) (VARDATA(entryvec)))[j].key);
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/* compute the wasted space by unioning these guys */
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/* size_waste = size_union - size_inter; */
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union_d = cube_union(datum_alpha, datum_beta);
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rt_cube_size(union_d, &size_union);
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inter_d = cube_inter(datum_alpha, datum_beta);
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rt_cube_size(inter_d, &size_inter);
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size_waste = size_union - size_inter;
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pfree(union_d);
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if (inter_d != (NDBOX *) NULL)
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pfree(inter_d);
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/*
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* are these a more promising split than what we've already
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* seen?
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*/
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if (size_waste > waste || firsttime)
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{
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waste = size_waste;
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seed_1 = i;
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seed_2 = j;
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firsttime = false;
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}
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}
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}
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left = v->spl_left;
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v->spl_nleft = 0;
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right = v->spl_right;
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v->spl_nright = 0;
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datum_alpha = (NDBOX *) DatumGetPointer(((GISTENTRY *) (VARDATA(entryvec)))[seed_1].key);
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datum_l = cube_union(datum_alpha, datum_alpha);
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rt_cube_size(datum_l, &size_l);
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datum_beta = (NDBOX *) DatumGetPointer(((GISTENTRY *) (VARDATA(entryvec)))[seed_2].key);
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datum_r = cube_union(datum_beta, datum_beta);
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rt_cube_size(datum_r, &size_r);
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/*
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* Now split up the regions between the two seeds. An important
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* property of this split algorithm is that the split vector v has the
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* indices of items to be split in order in its left and right
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* vectors. We exploit this property by doing a merge in the code
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* that actually splits the page.
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*
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* For efficiency, we also place the new index tuple in this loop. This
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* is handled at the very end, when we have placed all the existing
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* tuples and i == maxoff + 1.
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*/
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maxoff = OffsetNumberNext(maxoff);
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for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
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{
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/*
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* If we've already decided where to place this item, just put it
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* on the right list. Otherwise, we need to figure out which page
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* needs the least enlargement in order to store the item.
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*/
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if (i == seed_1)
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{
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*left++ = i;
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v->spl_nleft++;
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continue;
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}
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else if (i == seed_2)
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{
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*right++ = i;
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v->spl_nright++;
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continue;
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}
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/* okay, which page needs least enlargement? */
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datum_alpha = (NDBOX *) DatumGetPointer(((GISTENTRY *) (VARDATA(entryvec)))[i].key);
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union_dl = cube_union(datum_l, datum_alpha);
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union_dr = cube_union(datum_r, datum_alpha);
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rt_cube_size(union_dl, &size_alpha);
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rt_cube_size(union_dr, &size_beta);
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/* pick which page to add it to */
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if (size_alpha - size_l < size_beta - size_r)
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{
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pfree(datum_l);
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pfree(union_dr);
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datum_l = union_dl;
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size_l = size_alpha;
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*left++ = i;
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v->spl_nleft++;
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}
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else
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{
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pfree(datum_r);
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pfree(union_dl);
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datum_r = union_dr;
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size_r = size_alpha;
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*right++ = i;
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v->spl_nright++;
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}
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}
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*left = *right = FirstOffsetNumber; /* sentinel value, see dosplit() */
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v->spl_ldatum = PointerGetDatum(datum_l);
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v->spl_rdatum = PointerGetDatum(datum_r);
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return v;
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}
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/*
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** Equality method
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*/
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bool *
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g_cube_same(NDBOX * b1, NDBOX * b2, bool *result)
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{
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if (cube_eq(b1, b2))
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*result = TRUE;
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else
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*result = FALSE;
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/*
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* fprintf(stderr, "same: %s\n", (*result ? "TRUE" : "FALSE" ));
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*/
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return (result);
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}
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/*
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** SUPPORT ROUTINES
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*/
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bool
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g_cube_leaf_consistent(NDBOX * key,
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NDBOX * query,
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StrategyNumber strategy)
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{
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bool retval;
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/*
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* fprintf(stderr, "leaf_consistent, %d\n", strategy);
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*/
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switch (strategy)
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{
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case RTLeftStrategyNumber:
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retval = (bool) cube_left(key, query);
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break;
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case RTOverLeftStrategyNumber:
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retval = (bool) cube_over_left(key, query);
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break;
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case RTOverlapStrategyNumber:
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retval = (bool) cube_overlap(key, query);
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break;
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case RTOverRightStrategyNumber:
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retval = (bool) cube_over_right(key, query);
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break;
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case RTRightStrategyNumber:
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retval = (bool) cube_right(key, query);
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break;
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case RTSameStrategyNumber:
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retval = (bool) cube_eq(key, query);
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break;
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case RTContainsStrategyNumber:
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retval = (bool) cube_contains(key, query);
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break;
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case RTContainedByStrategyNumber:
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retval = (bool) cube_contained(key, query);
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break;
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default:
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retval = FALSE;
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}
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return (retval);
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}
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|
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bool
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g_cube_internal_consistent(NDBOX * key,
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NDBOX * query,
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StrategyNumber strategy)
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{
|
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bool retval;
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|
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/*
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* fprintf(stderr, "internal_consistent, %d\n", strategy);
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*/
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switch (strategy)
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{
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case RTLeftStrategyNumber:
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case RTOverLeftStrategyNumber:
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retval = (bool) cube_over_left(key, query);
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break;
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case RTOverlapStrategyNumber:
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retval = (bool) cube_overlap(key, query);
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break;
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case RTOverRightStrategyNumber:
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case RTRightStrategyNumber:
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retval = (bool) cube_right(key, query);
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break;
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case RTSameStrategyNumber:
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case RTContainsStrategyNumber:
|
|
retval = (bool) cube_contains(key, query);
|
|
break;
|
|
case RTContainedByStrategyNumber:
|
|
retval = (bool) cube_overlap(key, query);
|
|
break;
|
|
default:
|
|
retval = FALSE;
|
|
}
|
|
return (retval);
|
|
}
|
|
|
|
NDBOX *
|
|
g_cube_binary_union(NDBOX * r1, NDBOX * r2, int *sizep)
|
|
{
|
|
NDBOX *retval;
|
|
|
|
retval = cube_union(r1, r2);
|
|
*sizep = retval->size;
|
|
|
|
return (retval);
|
|
}
|
|
|
|
|
|
/* cube_union */
|
|
NDBOX *
|
|
cube_union(NDBOX * a, NDBOX * b)
|
|
{
|
|
int i;
|
|
NDBOX *result;
|
|
|
|
if (a->dim >= b->dim)
|
|
{
|
|
result = palloc(a->size);
|
|
memset(result, 0, a->size);
|
|
result->size = a->size;
|
|
result->dim = a->dim;
|
|
}
|
|
else
|
|
{
|
|
result = palloc(b->size);
|
|
memset(result, 0, b->size);
|
|
result->size = b->size;
|
|
result->dim = b->dim;
|
|
}
|
|
|
|
/* swap the box pointers if needed */
|
|
if (a->dim < b->dim)
|
|
{
|
|
NDBOX *tmp = b;
|
|
|
|
b = a;
|
|
a = tmp;
|
|
}
|
|
|
|
/*
|
|
* use the potentially smaller of the two boxes (b) to fill in the
|
|
* result, padding absent dimensions with zeroes
|
|
*/
|
|
for (i = 0; i < b->dim; i++)
|
|
{
|
|
result->x[i] = min(b->x[i], b->x[i + b->dim]);
|
|
result->x[i + a->dim] = max(b->x[i], b->x[i + b->dim]);
|
|
}
|
|
for (i = b->dim; i < a->dim; i++)
|
|
{
|
|
result->x[i] = 0;
|
|
result->x[i + a->dim] = 0;
|
|
}
|
|
|
|
/* compute the union */
|
|
for (i = 0; i < a->dim; i++)
|
|
{
|
|
result->x[i] =
|
|
min(min(a->x[i], a->x[i + a->dim]), result->x[i]);
|
|
result->x[i + a->dim] = max(max(a->x[i],
|
|
a->x[i + a->dim]), result->x[i + a->dim]);
|
|
}
|
|
|
|
return (result);
|
|
}
|
|
|
|
/* cube_inter */
|
|
NDBOX *
|
|
cube_inter(NDBOX * a, NDBOX * b)
|
|
{
|
|
int i;
|
|
NDBOX *result;
|
|
|
|
if (a->dim >= b->dim)
|
|
{
|
|
result = palloc(a->size);
|
|
memset(result, 0, a->size);
|
|
result->size = a->size;
|
|
result->dim = a->dim;
|
|
}
|
|
else
|
|
{
|
|
result = palloc(b->size);
|
|
memset(result, 0, b->size);
|
|
result->size = b->size;
|
|
result->dim = b->dim;
|
|
}
|
|
|
|
/* swap the box pointers if needed */
|
|
if (a->dim < b->dim)
|
|
{
|
|
NDBOX *tmp = b;
|
|
|
|
b = a;
|
|
a = tmp;
|
|
}
|
|
|
|
/*
|
|
* use the potentially smaller of the two boxes (b) to fill in the
|
|
* result, padding absent dimensions with zeroes
|
|
*/
|
|
for (i = 0; i < b->dim; i++)
|
|
{
|
|
result->x[i] = min(b->x[i], b->x[i + b->dim]);
|
|
result->x[i + a->dim] = max(b->x[i], b->x[i + b->dim]);
|
|
}
|
|
for (i = b->dim; i < a->dim; i++)
|
|
{
|
|
result->x[i] = 0;
|
|
result->x[i + a->dim] = 0;
|
|
}
|
|
|
|
/* compute the intersection */
|
|
for (i = 0; i < a->dim; i++)
|
|
{
|
|
result->x[i] =
|
|
max(min(a->x[i], a->x[i + a->dim]), result->x[i]);
|
|
result->x[i + a->dim] = min(max(a->x[i],
|
|
a->x[i + a->dim]), result->x[i + a->dim]);
|
|
}
|
|
|
|
/*
|
|
* Is it OK to return a non-null intersection for non-overlapping
|
|
* boxes?
|
|
*/
|
|
return (result);
|
|
}
|
|
|
|
/* cube_size */
|
|
double *
|
|
cube_size(NDBOX * a)
|
|
{
|
|
int i,
|
|
j;
|
|
double *result;
|
|
|
|
result = (double *) palloc(sizeof(double));
|
|
|
|
*result = 1.0;
|
|
for (i = 0, j = a->dim; i < a->dim; i++, j++)
|
|
*result = (*result) * abs((a->x[j] - a->x[i]));
|
|
|
|
return (result);
|
|
}
|
|
|
|
void
|
|
rt_cube_size(NDBOX * a, double *size)
|
|
{
|
|
int i,
|
|
j;
|
|
|
|
if (a == (NDBOX *) NULL)
|
|
*size = 0.0;
|
|
else
|
|
{
|
|
*size = 1.0;
|
|
for (i = 0, j = a->dim; i < a->dim; i++, j++)
|
|
*size = (*size) * abs((a->x[j] - a->x[i]));
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* The following four methods compare the projections of the boxes
|
|
onto the 0-th coordinate axis. These methods are useless for dimensions
|
|
larger than 2, but it seems that R-tree requires all its strategies
|
|
map to real functions that return something */
|
|
|
|
/* is the right edge of (a) located to the left of
|
|
the right edge of (b)? */
|
|
bool
|
|
cube_over_left(NDBOX * a, NDBOX * b)
|
|
{
|
|
if ((a == NULL) || (b == NULL))
|
|
return (FALSE);
|
|
|
|
return (min(a->x[a->dim - 1], a->x[2 * a->dim - 1]) <=
|
|
min(b->x[b->dim - 1], b->x[2 * b->dim - 1]) &&
|
|
!cube_left(a, b) && !cube_right(a, b));
|
|
}
|
|
|
|
/* is the left edge of (a) located to the right of
|
|
the left edge of (b)? */
|
|
bool
|
|
cube_over_right(NDBOX * a, NDBOX * b)
|
|
{
|
|
if ((a == NULL) || (b == NULL))
|
|
return (FALSE);
|
|
|
|
return (min(a->x[a->dim - 1], a->x[2 * a->dim - 1]) >=
|
|
min(b->x[b->dim - 1], b->x[2 * b->dim - 1]) &&
|
|
!cube_left(a, b) && !cube_right(a, b));
|
|
}
|
|
|
|
|
|
/* return 'true' if the projection of 'a' is
|
|
entirely on the left of the projection of 'b' */
|
|
bool
|
|
cube_left(NDBOX * a, NDBOX * b)
|
|
{
|
|
if ((a == NULL) || (b == NULL))
|
|
return (FALSE);
|
|
|
|
return (min(a->x[a->dim - 1], a->x[2 * a->dim - 1]) <
|
|
min(b->x[0], b->x[b->dim]));
|
|
}
|
|
|
|
/* return 'true' if the projection of 'a' is
|
|
entirely on the right of the projection of 'b' */
|
|
bool
|
|
cube_right(NDBOX * a, NDBOX * b)
|
|
{
|
|
if ((a == NULL) || (b == NULL))
|
|
return (FALSE);
|
|
|
|
return (min(a->x[0], a->x[a->dim]) >
|
|
min(b->x[b->dim - 1], b->x[2 * b->dim - 1]));
|
|
}
|
|
|
|
/* make up a metric in which one box will be 'lower' than the other
|
|
-- this can be useful for sorting and to determine uniqueness */
|
|
int32
|
|
cube_cmp(NDBOX * a, NDBOX * b)
|
|
{
|
|
int i;
|
|
int dim;
|
|
|
|
dim = min(a->dim, b->dim);
|
|
|
|
/* compare the common dimensions */
|
|
for (i = 0; i < dim; i++)
|
|
{
|
|
if (min(a->x[i], a->x[a->dim + i]) >
|
|
min(b->x[i], b->x[b->dim + i]))
|
|
return 1;
|
|
if (min(a->x[i], a->x[a->dim + i]) <
|
|
min(b->x[i], b->x[b->dim + i]))
|
|
return -1;
|
|
}
|
|
for (i = 0; i < dim; i++)
|
|
{
|
|
if (max(a->x[i], a->x[a->dim + i]) >
|
|
max(b->x[i], b->x[b->dim + i]))
|
|
return 1;
|
|
if (max(a->x[i], a->x[a->dim + i]) <
|
|
max(b->x[i], b->x[b->dim + i]))
|
|
return -1;
|
|
}
|
|
|
|
/* compare extra dimensions to zero */
|
|
if (a->dim > b->dim)
|
|
{
|
|
for (i = dim; i < a->dim; i++)
|
|
{
|
|
if (min(a->x[i], a->x[a->dim + i]) > 0)
|
|
return 1;
|
|
if (min(a->x[i], a->x[a->dim + i]) < 0)
|
|
return -1;
|
|
}
|
|
for (i = dim; i < a->dim; i++)
|
|
{
|
|
if (max(a->x[i], a->x[a->dim + i]) > 0)
|
|
return 1;
|
|
if (max(a->x[i], a->x[a->dim + i]) < 0)
|
|
return -1;
|
|
}
|
|
|
|
/*
|
|
* if all common dimensions are equal, the cube with more
|
|
* dimensions wins
|
|
*/
|
|
return 1;
|
|
}
|
|
if (a->dim < b->dim)
|
|
{
|
|
for (i = dim; i < b->dim; i++)
|
|
{
|
|
if (min(b->x[i], b->x[b->dim + i]) > 0)
|
|
return -1;
|
|
if (min(b->x[i], b->x[b->dim + i]) < 0)
|
|
return 1;
|
|
}
|
|
for (i = dim; i < b->dim; i++)
|
|
{
|
|
if (max(b->x[i], b->x[b->dim + i]) > 0)
|
|
return -1;
|
|
if (max(b->x[i], b->x[b->dim + i]) < 0)
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
* if all common dimensions are equal, the cube with more
|
|
* dimensions wins
|
|
*/
|
|
return -1;
|
|
}
|
|
|
|
/* They're really equal */
|
|
return 0;
|
|
}
|
|
|
|
|
|
bool
|
|
cube_eq(NDBOX * a, NDBOX * b)
|
|
{
|
|
return (cube_cmp(a, b) == 0);
|
|
}
|
|
|
|
bool
|
|
cube_ne(NDBOX * a, NDBOX * b)
|
|
{
|
|
return (cube_cmp(a, b) != 0);
|
|
}
|
|
|
|
bool
|
|
cube_lt(NDBOX * a, NDBOX * b)
|
|
{
|
|
return (cube_cmp(a, b) < 0);
|
|
}
|
|
|
|
bool
|
|
cube_gt(NDBOX * a, NDBOX * b)
|
|
{
|
|
return (cube_cmp(a, b) > 0);
|
|
}
|
|
|
|
bool
|
|
cube_le(NDBOX * a, NDBOX * b)
|
|
{
|
|
return (cube_cmp(a, b) <= 0);
|
|
}
|
|
|
|
bool
|
|
cube_ge(NDBOX * a, NDBOX * b)
|
|
{
|
|
return (cube_cmp(a, b) >= 0);
|
|
}
|
|
|
|
|
|
/* Contains */
|
|
/* Box(A) CONTAINS Box(B) IFF pt(A) < pt(B) */
|
|
bool
|
|
cube_contains(NDBOX * a, NDBOX * b)
|
|
{
|
|
int i;
|
|
|
|
if ((a == NULL) || (b == NULL))
|
|
return (FALSE);
|
|
|
|
if (a->dim < b->dim)
|
|
{
|
|
/*
|
|
* the further comparisons will make sense if the excess
|
|
* dimensions of (b) were zeroes Since both UL and UR coordinates
|
|
* must be zero, we can check them all without worrying about
|
|
* which is which.
|
|
*/
|
|
for (i = a->dim; i < b->dim; i++)
|
|
{
|
|
if (b->x[i] != 0)
|
|
return (FALSE);
|
|
if (b->x[i + b->dim] != 0)
|
|
return (FALSE);
|
|
}
|
|
}
|
|
|
|
/* Can't care less about the excess dimensions of (a), if any */
|
|
for (i = 0; i < min(a->dim, b->dim); i++)
|
|
{
|
|
if (min(a->x[i], a->x[a->dim + i]) >
|
|
min(b->x[i], b->x[b->dim + i]))
|
|
return (FALSE);
|
|
if (max(a->x[i], a->x[a->dim + i]) <
|
|
max(b->x[i], b->x[b->dim + i]))
|
|
return (FALSE);
|
|
}
|
|
|
|
return (TRUE);
|
|
}
|
|
|
|
/* Contained */
|
|
/* Box(A) Contained by Box(B) IFF Box(B) Contains Box(A) */
|
|
bool
|
|
cube_contained(NDBOX * a, NDBOX * b)
|
|
{
|
|
if (cube_contains(b, a) == TRUE)
|
|
return (TRUE);
|
|
else
|
|
return (FALSE);
|
|
}
|
|
|
|
/* Overlap */
|
|
/* Box(A) Overlap Box(B) IFF (pt(a)LL < pt(B)UR) && (pt(b)LL < pt(a)UR) */
|
|
bool
|
|
cube_overlap(NDBOX * a, NDBOX * b)
|
|
{
|
|
int i;
|
|
|
|
/*
|
|
* This *very bad* error was found in the source: if ( (a==NULL) ||
|
|
* (b=NULL) ) return(FALSE);
|
|
*/
|
|
if ((a == NULL) || (b == NULL))
|
|
return (FALSE);
|
|
|
|
/* swap the box pointers if needed */
|
|
if (a->dim < b->dim)
|
|
{
|
|
NDBOX *tmp = b;
|
|
|
|
b = a;
|
|
a = tmp;
|
|
}
|
|
|
|
/* compare within the dimensions of (b) */
|
|
for (i = 0; i < b->dim; i++)
|
|
{
|
|
if (min(a->x[i], a->x[a->dim + i]) >
|
|
max(b->x[i], b->x[b->dim + i]))
|
|
return (FALSE);
|
|
if (max(a->x[i], a->x[a->dim + i]) <
|
|
min(b->x[i], b->x[b->dim + i]))
|
|
return (FALSE);
|
|
}
|
|
|
|
/* compare to zero those dimensions in (a) absent in (b) */
|
|
for (i = b->dim; i < a->dim; i++)
|
|
{
|
|
if (min(a->x[i], a->x[a->dim + i]) > 0)
|
|
return (FALSE);
|
|
if (max(a->x[i], a->x[a->dim + i]) < 0)
|
|
return (FALSE);
|
|
}
|
|
|
|
return (TRUE);
|
|
}
|
|
|
|
|
|
/* Distance */
|
|
/* The distance is computed as a per axis sum of the squared distances
|
|
between 1D projections of the boxes onto Cartesian axes. Assuming zero
|
|
distance between overlapping projections, this metric coincides with the
|
|
"common sense" geometric distance */
|
|
double *
|
|
cube_distance(NDBOX * a, NDBOX * b)
|
|
{
|
|
int i;
|
|
double d,
|
|
distance;
|
|
double *result;
|
|
|
|
result = (double *) palloc(sizeof(double));
|
|
|
|
/* swap the box pointers if needed */
|
|
if (a->dim < b->dim)
|
|
{
|
|
NDBOX *tmp = b;
|
|
|
|
b = a;
|
|
a = tmp;
|
|
}
|
|
|
|
distance = 0.0;
|
|
/* compute within the dimensions of (b) */
|
|
for (i = 0; i < b->dim; i++)
|
|
{
|
|
d = distance_1D(a->x[i], a->x[i + a->dim], b->x[i], b->x[i + b->dim]);
|
|
distance += d * d;
|
|
}
|
|
|
|
/* compute distance to zero for those dimensions in (a) absent in (b) */
|
|
for (i = b->dim; i < a->dim; i++)
|
|
{
|
|
d = distance_1D(a->x[i], a->x[i + a->dim], 0.0, 0.0);
|
|
distance += d * d;
|
|
}
|
|
|
|
*result = (double) sqrt(distance);
|
|
|
|
return (result);
|
|
}
|
|
|
|
static double
|
|
distance_1D(double a1, double a2, double b1, double b2)
|
|
{
|
|
/* interval (a) is entirely on the left of (b) */
|
|
if ((a1 <= b1) && (a2 <= b1) && (a1 <= b2) && (a2 <= b2))
|
|
return (min(b1, b2) - max(a1, a2));
|
|
|
|
/* interval (a) is entirely on the right of (b) */
|
|
if ((a1 > b1) && (a2 > b1) && (a1 > b2) && (a2 > b2))
|
|
return (min(a1, a2) - max(b1, b2));
|
|
|
|
/* the rest are all sorts of intersections */
|
|
return (0.0);
|
|
}
|
|
|
|
/* Test if a box is also a point */
|
|
bool
|
|
cube_is_point(NDBOX * a)
|
|
{
|
|
int i,
|
|
j;
|
|
|
|
for (i = 0, j = a->dim; i < a->dim; i++, j++)
|
|
{
|
|
if (a->x[i] != a->x[j])
|
|
return FALSE;
|
|
}
|
|
|
|
return TRUE;
|
|
}
|
|
|
|
/* Return dimensions in use in the data structure */
|
|
int4
|
|
cube_dim(NDBOX * a)
|
|
{
|
|
/* Other things will break before unsigned int doesn't fit. */
|
|
return a->dim;
|
|
}
|
|
|
|
/* Return a specific normalized LL coordinate */
|
|
double *
|
|
cube_ll_coord(NDBOX * a, int4 n)
|
|
{
|
|
double *result;
|
|
|
|
result = (double *) palloc(sizeof(double));
|
|
*result = 0;
|
|
if (a->dim >= n && n > 0)
|
|
*result = min(a->x[n - 1], a->x[a->dim + n - 1]);
|
|
return result;
|
|
}
|
|
|
|
/* Return a specific normalized UR coordinate */
|
|
double *
|
|
cube_ur_coord(NDBOX * a, int4 n)
|
|
{
|
|
double *result;
|
|
|
|
result = (double *) palloc(sizeof(double));
|
|
*result = 0;
|
|
if (a->dim >= n && n > 0)
|
|
*result = max(a->x[n - 1], a->x[a->dim + n - 1]);
|
|
return result;
|
|
}
|
|
|
|
/* Increase or decrease box size by a radius in at least n dimensions. */
|
|
NDBOX *
|
|
cube_enlarge(NDBOX * a, double *r, int4 n)
|
|
{
|
|
NDBOX *result;
|
|
int dim = 0;
|
|
int size;
|
|
int i,
|
|
j,
|
|
k;
|
|
|
|
if (n > CUBE_MAX_DIM)
|
|
n = CUBE_MAX_DIM;
|
|
if (*r > 0 && n > 0)
|
|
dim = n;
|
|
if (a->dim > dim)
|
|
dim = a->dim;
|
|
size = offsetof(NDBOX, x[0]) + sizeof(double) * dim * 2;
|
|
result = (NDBOX *) palloc(size);
|
|
memset(result, 0, size);
|
|
result->size = size;
|
|
result->dim = dim;
|
|
for (i = 0, j = dim, k = a->dim; i < a->dim; i++, j++, k++)
|
|
{
|
|
if (a->x[i] >= a->x[k])
|
|
{
|
|
result->x[i] = a->x[k] - *r;
|
|
result->x[j] = a->x[i] + *r;
|
|
}
|
|
else
|
|
{
|
|
result->x[i] = a->x[i] - *r;
|
|
result->x[j] = a->x[k] + *r;
|
|
}
|
|
if (result->x[i] > result->x[j])
|
|
{
|
|
result->x[i] = (result->x[i] + result->x[j]) / 2;
|
|
result->x[j] = result->x[i];
|
|
}
|
|
}
|
|
/* dim > a->dim only if r > 0 */
|
|
for (; i < dim; i++, j++)
|
|
{
|
|
result->x[i] = -*r;
|
|
result->x[j] = *r;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/* Create a one dimensional box with identical upper and lower coordinates */
|
|
NDBOX *
|
|
cube_f8(double *x1)
|
|
{
|
|
NDBOX *result;
|
|
int size;
|
|
|
|
size = offsetof(NDBOX, x[0]) + sizeof(double) * 2;
|
|
result = (NDBOX *) palloc(size);
|
|
memset(result, 0, size);
|
|
result->size = size;
|
|
result->dim = 1;
|
|
result->x[0] = *x1;
|
|
result->x[1] = *x1;
|
|
return result;
|
|
}
|
|
|
|
/* Create a one dimensional box */
|
|
NDBOX *
|
|
cube_f8_f8(double *x1, double *x2)
|
|
{
|
|
NDBOX *result;
|
|
int size;
|
|
|
|
size = offsetof(NDBOX, x[0]) + sizeof(double) * 2;
|
|
result = (NDBOX *) palloc(size);
|
|
memset(result, 0, size);
|
|
result->size = size;
|
|
result->dim = 1;
|
|
result->x[0] = *x1;
|
|
result->x[1] = *x2;
|
|
return result;
|
|
}
|
|
|
|
/* Add a dimension to an existing cube with the same values for the new
|
|
coordinate */
|
|
NDBOX *
|
|
cube_c_f8(NDBOX * c, double *x1)
|
|
{
|
|
NDBOX *result;
|
|
int size;
|
|
int i;
|
|
|
|
size = offsetof(NDBOX, x[0]) + sizeof(double) * (c->dim + 1) *2;
|
|
result = (NDBOX *) palloc(size);
|
|
memset(result, 0, size);
|
|
result->size = size;
|
|
result->dim = c->dim + 1;
|
|
for (i = 0; i < c->dim; i++)
|
|
{
|
|
result->x[i] = c->x[i];
|
|
result->x[result->dim + i] = c->x[c->dim + i];
|
|
}
|
|
result->x[result->dim - 1] = *x1;
|
|
result->x[2 * result->dim - 1] = *x1;
|
|
return result;
|
|
}
|
|
|
|
/* Add a dimension to an existing cube */
|
|
NDBOX *
|
|
cube_c_f8_f8(NDBOX * c, double *x1, double *x2)
|
|
{
|
|
NDBOX *result;
|
|
int size;
|
|
int i;
|
|
|
|
size = offsetof(NDBOX, x[0]) + sizeof(double) * (c->dim + 1) *2;
|
|
result = (NDBOX *) palloc(size);
|
|
memset(result, 0, size);
|
|
result->size = size;
|
|
result->dim = c->dim + 1;
|
|
for (i = 0; i < c->dim; i++)
|
|
{
|
|
result->x[i] = c->x[i];
|
|
result->x[result->dim + i] = c->x[c->dim + i];
|
|
}
|
|
result->x[result->dim - 1] = *x1;
|
|
result->x[2 * result->dim - 1] = *x2;
|
|
return result;
|
|
}
|