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// -*- C++ -*-
/* Copyright (C) 1989, 1990, 1991, 1992, 2000, 2001, 2002, 2003, 2004
Free Software Foundation, Inc.
Written by Gaius Mulley <gaius@glam.ac.uk>
using adjust_arc_center() from printer.cpp, written by James Clark.
This file is part of groff.
groff 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.
groff 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 groff; see the file COPYING. If not, write to the Free Software
Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
#include <stdio.h>
#include <math.h>
#undef MAX
#define MAX(a, b) (((a) > (b)) ? (a) : (b))
#undef MIN
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
// This utility function adjusts the specified center of the
// arc so that it is equidistant between the specified start
// and end points. (p[0], p[1]) is a vector from the current
// point to the center; (p[2], p[3]) is a vector from the
// center to the end point. If the center can be adjusted,
// a vector from the current point to the adjusted center is
// stored in c[0], c[1] and 1 is returned. Otherwise 0 is
// returned.
#if 1
int adjust_arc_center(const int *p, double *c)
{
// We move the center along a line parallel to the line between
// the specified start point and end point so that the center
// is equidistant between the start and end point.
// It can be proved (using Lagrange multipliers) that this will
// give the point nearest to the specified center that is equidistant
// between the start and end point.
double x = p[0] + p[2]; // (x, y) is the end point
double y = p[1] + p[3];
double n = x*x + y*y;
if (n != 0) {
c[0]= double(p[0]);
c[1] = double(p[1]);
double k = .5 - (c[0]*x + c[1]*y)/n;
c[0] += k*x;
c[1] += k*y;
return 1;
}
else
return 0;
}
#else
int printer::adjust_arc_center(const int *p, double *c)
{
int x = p[0] + p[2]; // (x, y) is the end point
int y = p[1] + p[3];
// Start at the current point; go in the direction of the specified
// center point until we reach a point that is equidistant between
// the specified starting point and the specified end point. Place
// the center of the arc there.
double n = p[0]*double(x) + p[1]*double(y);
if (n > 0) {
double k = (double(x)*x + double(y)*y)/(2.0*n);
// (cx, cy) is our chosen center
c[0] = k*p[0];
c[1] = k*p[1];
return 1;
}
else {
// We would never reach such a point. So instead start at the
// specified end point of the arc. Go towards the specified
// center point until we reach a point that is equidistant between
// the specified start point and specified end point. Place
// the center of the arc there.
n = p[2]*double(x) + p[3]*double(y);
if (n > 0) {
double k = 1 - (double(x)*x + double(y)*y)/(2.0*n);
// (c[0], c[1]) is our chosen center
c[0] = p[0] + k*p[2];
c[1] = p[1] + k*p[3];
return 1;
}
else
return 0;
}
}
#endif
/*
* check_output_arc_limits - works out the smallest box that will encompass
* an arc defined by an origin (x, y) and two
* vectors (p0, p1) and (p2, p3).
* (x1, y1) -> start of arc
* (x1, y1) + (xv1, yv1) -> center of circle
* (x1, y1) + (xv1, yv1) + (xv2, yv2) -> end of arc
*
* Works out in which quadrant the arc starts and
* stops, and from this it determines the x, y
* max/min limits. The arc is drawn clockwise.
*/
void check_output_arc_limits(int x_1, int y_1,
int xv_1, int yv_1,
int xv_2, int yv_2,
double c_0, double c_1,
int *minx, int *maxx,
int *miny, int *maxy)
{
int radius = (int)sqrt(c_0 * c_0 + c_1 * c_1);
// clockwise direction
int xcenter = x_1 + xv_1;
int ycenter = y_1 + yv_1;
int xend = xcenter + xv_2;
int yend = ycenter + yv_2;
// for convenience, transform to counterclockwise direction,
// centered at the origin
int xs = xend - xcenter;
int ys = yend - ycenter;
int xe = x_1 - xcenter;
int ye = y_1 - ycenter;
*minx = *maxx = xs;
*miny = *maxy = ys;
if (xe > *maxx)
*maxx = xe;
else if (xe < *minx)
*minx = xe;
if (ye > *maxy)
*maxy = ye;
else if (ye < *miny)
*miny = ye;
int qs, qe; // quadrants 0..3
if (xs >= 0)
qs = (ys >= 0) ? 0 : 3;
else
qs = (ys >= 0) ? 1 : 2;
if (xe >= 0)
qe = (ye >= 0) ? 0 : 3;
else
qe = (ye >= 0) ? 1 : 2;
// make qs always smaller than qe
if ((qs > qe)
|| ((qs == qe) && (double(xs) * ye < double(xe) * ys)))
qe += 4;
for (int i = qs; i < qe; i++)
switch (i % 4) {
case 0:
*maxy = radius;
break;
case 1:
*minx = -radius;
break;
case 2:
*miny = -radius;
break;
case 3:
*maxx = radius;
break;
}
*minx += xcenter;
*maxx += xcenter;
*miny += ycenter;
*maxy += ycenter;
}
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