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/* math.c: define some simple array operations, and other functions.
Copyright (C) 1992 Free Software Foundation, Inc.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
#include "config.h"
/* Numerical errors sometimes make a floating point number just slightly
larger or smaller than its true value. When it matters, we need to
compare with some tolerance, REAL_EPSILON, defined in kbase.h. */
const boolean
epsilon_equal (real v1, real v2)
{
return
v1 == v2 /* Usually they'll be exactly equal, anyway. */
|| fabs (v1 - v2) <= REAL_EPSILON;
}
/* Return the Euclidean distance between P1 and P2. */
const real
distance (real_coordinate_type p1, real_coordinate_type p2)
{
return hypot (p1.x - p2.x, p1.y - p2.y);
}
/* Same thing, for integer points. */
const real
int_distance (coordinate_type p1, coordinate_type p2)
{
return hypot ((double) p1.x - p2.x, (double) p1.y - p2.y);
}
/* Return the arc cosine of V, in degrees in the range zero to 180. V
is taken to be in radians. */
const real
acosd (real v)
{
real a;
if (epsilon_equal (v, 1.0))
v = 1.0;
else if (epsilon_equal (v, -1.0))
v = -1.0;
errno = 0;
a = acos (v);
if (errno == ERANGE || errno == EDOM)
FATAL_PERROR ("acosd");
return a * 180.0 / M_PI;
}
/* The slope of the line defined by COORD1 and COORD2. */
const real
slope (real_coordinate_type coord1, real_coordinate_type coord2)
{
assert (coord2.x - coord1.x != 0);
return (coord2.y - coord1.y) / (coord2.x - coord1.x);
}
/* Turn an integer point into a real one, and vice versa. */
const real_coordinate_type
int_to_real_coord (coordinate_type int_coord)
{
real_coordinate_type real_coord;
real_coord.x = int_coord.x;
real_coord.y = int_coord.y;
return real_coord;
}
const coordinate_type
real_to_int_coord (real_coordinate_type real_coord)
{
coordinate_type int_coord;
int_coord.x = ROUND (real_coord.x);
int_coord.y = ROUND (real_coord.y);
return int_coord;
}
/* See if two points (described by their row and column) are adjacent. */
const boolean
points_adjacent_p (int row1, int col1, int row2, int col2)
{
int row_diff = abs (row1 - row2);
int col_diff = abs (col1 - col2);
return
(row_diff == 1 && col_diff == 1)
|| (row_diff == 0 && col_diff == 1)
|| (row_diff == 1 && col_diff == 0);
}
/* Find the largest and smallest elements in an array of reals. */
void
find_bounds (real *values, unsigned value_count, real *min, real *max)
{
unsigned this_value;
/* We must use FLT_MAX and FLT_MIN, instead of the corresponding
values for double, because gcc uses the native atof to parse
floating point constants, and many atof's choke on the extremes. */
*min = FLT_MAX;
*max = FLT_MIN;
for (this_value = 0; this_value < value_count; this_value++)
{
if (values[this_value] < *min)
*min = values[this_value];
if (values[this_value] > *max)
*max = values[this_value];
}
}
/* Map a range of numbers, some positive and some negative, into all
positive, with the greatest being at one and the least at zero.
This allocates new memory. */
real *
map_to_unit (real *values, unsigned value_count)
{
real smallest, largest;
int this_value;
real *mapped_values = xmalloc (sizeof (real) * value_count);
find_bounds (values, value_count, &smallest, &largest);
largest -= smallest; /* We never care about largest itself. */
for (this_value = 0; this_value < value_count; this_value++)
mapped_values[this_value] = (values[this_value] - smallest) / largest;
return mapped_values;
}
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