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# spline.c: spline and spline list (represented as arrays) manipulation.
#
# Copyright (C) 1992, 2011 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 3 of the License, 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, see <http://www.gnu.org/licenses/>.
#
#include "config.h"
#include "bounding-box.h"
#include "spline.h"
#include "vector.h"
/* Return a new spline structure, initialized with (recognizable)
garbage. */
spline_type
new_spline ()
{
spline_type spline;
START_POINT (spline)
= CONTROL1 (spline)
= CONTROL2 (spline)
= END_POINT (spline)
= (real_coordinate_type) { -100.0, -100.0 };
SPLINE_DEGREE (spline) = -1;
return spline;
}
/* Print a spline in human-readable form. */
void
print_spline (FILE *f, spline_type s)
{
if (SPLINE_DEGREE (s) == LINEAR)
fprintf (f, "(%.3f,%.3f)--(%.3f,%.3f).\n",
START_POINT (s).x, START_POINT (s).y,
END_POINT (s).x, END_POINT (s).y);
else if (SPLINE_DEGREE (s) == CUBIC)
fprintf (f, "(%.3f,%.3f)..ctrls(%.3f,%.3f)&(%.3f,%.3f)..(%.3f,%.3f).\n",
START_POINT (s).x, START_POINT (s).y,
CONTROL1 (s).x, CONTROL1 (s).y,
CONTROL2 (s).x, CONTROL2 (s).y,
END_POINT (s).x, END_POINT (s).y);
else
FATAL1 ("print_spline: strange degree (%d)", SPLINE_DEGREE (s));
}
/* Evaluate the spline S at a given T value. This is an implementation
of de Casteljau's algorithm. See Schneider's thesis (reference in
../limn/README), p.37. The variable names are taken from there. */
real_coordinate_type
evaluate_spline (spline_type s, real t)
{
spline_type V[4]; /* We need degree+1 splines, but assert degree <= 3. */
unsigned i, j;
real one_minus_t = 1.0 - t;
polynomial_degree degree = SPLINE_DEGREE (s);
for (i = 0; i <= degree; i++)
V[0].v[i] = s.v[i];
for (j = 1; j <= degree; j++)
for (i = 0; i <= degree - j; i++)
{
real_coordinate_type t1 = Pmult_scalar (V[j - 1].v[i], one_minus_t);
real_coordinate_type t2 = Pmult_scalar (V[j - 1].v[i + 1], t);
V[j].v[i] = Padd (t1, t2);
}
return V[degree].v[0];
}
/* Return a new, empty, spline list. */
spline_list_type *
new_spline_list ()
{
spline_list_type *answer = xmalloc (sizeof (spline_list_type));
SPLINE_LIST_DATA (*answer) = NULL;
SPLINE_LIST_LENGTH (*answer) = 0;
return answer;
}
/* Return a new spline list with SPLINE as the first element. */
spline_list_type *
init_spline_list (spline_type spline)
{
spline_list_type *answer = xmalloc (sizeof (spline_list_type));
SPLINE_LIST_DATA (*answer) = xmalloc (sizeof (spline_type));
SPLINE_LIST_ELT (*answer, 0) = spline;
SPLINE_LIST_LENGTH (*answer) = 1;
return answer;
}
/* Free the storage in a spline list. We don't have to free the
elements, since they are arrays in automatic storage. And we don't
want to free the list if it was empty. */
void
free_spline_list (spline_list_type *spline_list)
{
if (SPLINE_LIST_DATA (*spline_list) != NULL)
safe_free ((address *) &(SPLINE_LIST_DATA (*spline_list)));
}
/* Append the spline S to the list SPLINE_LIST. */
void
append_spline (spline_list_type *l, spline_type s)
{
assert (l != NULL);
SPLINE_LIST_LENGTH (*l)++;
SPLINE_LIST_DATA (*l) = xrealloc (SPLINE_LIST_DATA (*l),
SPLINE_LIST_LENGTH (*l) * sizeof (spline_type));
LAST_SPLINE_LIST_ELT (*l) = s;
}
/* Tack the elements in the list S2 onto the end of S1.
S2 is not changed. */
void
concat_spline_lists (spline_list_type *s1, spline_list_type s2)
{
unsigned this_spline;
unsigned new_length;
assert (s1 != NULL);
new_length = SPLINE_LIST_LENGTH (*s1) + SPLINE_LIST_LENGTH (s2);
XRETALLOC (SPLINE_LIST_DATA (*s1), new_length, spline_type);
for (this_spline = 0; this_spline < SPLINE_LIST_LENGTH (s2); this_spline++)
SPLINE_LIST_ELT (*s1, SPLINE_LIST_LENGTH (*s1)++)
= SPLINE_LIST_ELT (s2, this_spline);
}
/* Return a new, empty, spline list array. */
spline_list_array_type
new_spline_list_array ()
{
spline_list_array_type answer;
SPLINE_LIST_ARRAY_DATA (answer) = NULL;
SPLINE_LIST_ARRAY_LENGTH (answer) = 0;
return answer;
}
/* Free the storage in a spline list array. We don't
want to free the list if it is empty. */
void
free_spline_list_array (spline_list_array_type *spline_list_array)
{
unsigned this_list;
for (this_list = 0;
this_list < SPLINE_LIST_ARRAY_LENGTH (*spline_list_array);
this_list++)
free_spline_list (&SPLINE_LIST_ARRAY_ELT (*spline_list_array, this_list));
if (SPLINE_LIST_ARRAY_DATA (*spline_list_array) != NULL)
safe_free ((address *) &(SPLINE_LIST_ARRAY_DATA (*spline_list_array)));
}
/* Append the spline S to the list SPLINE_LIST_ARRAY. */
void
append_spline_list (spline_list_array_type *l, spline_list_type s)
{
SPLINE_LIST_ARRAY_LENGTH (*l)++;
XRETALLOC (SPLINE_LIST_ARRAY_DATA (*l),
SPLINE_LIST_ARRAY_LENGTH (*l), spline_list_type);
LAST_SPLINE_LIST_ARRAY_ELT (*l) = s;
}
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