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// -*- C++ -*-
/* Copyright (C) 1989, 1990, 1991, 1992, 2000, 2001, 2002
Free Software Foundation, Inc.
Written by Gaius Mulley <gaius@glam.ac.uk>
using adjust_arc_center() from printer.cc, 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.
*
* [I'm sure there is a better way to do this, but
* I don't know how. Please can someone let me
* know or "improve" this function.]
*/
void check_output_arc_limits(int x1, int y1,
int xv1, int yv1,
int xv2, int yv2,
double c0, double c1,
int *minx, int *maxx,
int *miny, int *maxy)
{
int radius = (int)sqrt(c0*c0 + c1*c1);
int x2 = x1 + xv1 + xv2; // end of arc is (x2, y2)
int y2 = y1 + yv1 + yv2;
// firstly lets use the `circle' limitation
*minx = x1 + xv1 - radius;
*maxx = x1 + xv1 + radius;
*miny = y1 + yv1 - radius;
*maxy = y1 + yv1 + radius;
/* now to see which min/max can be reduced and increased for the limits of
* the arc
*
* Q2 | Q1
* -----+-----
* Q3 | Q4
*
*
* NB. (x1+xv1, y1+yv1) is at the origin
*
* below we ask a nested question
* (i) from which quadrant does the first vector start?
* (ii) into which quadrant does the second vector go?
* from the 16 possible answers we determine the limits of the arc
*/
if (xv1 > 0 && yv1 > 0) {
// first vector in Q3
if (xv2 >= 0 && yv2 >= 0 ) {
// second in Q1
*maxx = x2;
*miny = y1;
}
else if (xv2 < 0 && yv2 >= 0) {
// second in Q2
*maxx = x2;
*miny = y1;
}
else if (xv2 >= 0 && yv2 < 0) {
// second in Q4
*miny = MIN(y1, y2);
}
else if (xv2 < 0 && yv2 < 0) {
// second in Q3
if (x1 >= x2) {
*minx = x2;
*maxx = x1;
*miny = MIN(y1, y2);
*maxy = MAX(y1, y2);
}
else {
// xv2, yv2 could all be zero?
}
}
}
else if (xv1 > 0 && yv1 < 0) {
// first vector in Q2
if (xv2 >= 0 && yv2 >= 0) {
// second in Q1
*maxx = MAX(x1, x2);
*minx = MIN(x1, x2);
*miny = y1;
}
else if (xv2 < 0 && yv2 >= 0) {
// second in Q2
if (x1 < x2) {
*maxx = x2;
*minx = x1;
*miny = MIN(y1, y2);
*maxy = MAX(y1, y2);
}
else {
// otherwise almost full circle anyway
}
}
else if (xv2 >= 0 && yv2 < 0) {
// second in Q4
*miny = y2;
*minx = x1;
}
else if (xv2 < 0 && yv2 < 0) {
// second in Q3
*minx = MIN(x1, x2);
}
}
else if (xv1 <= 0 && yv1 <= 0) {
// first vector in Q1
if (xv2 >= 0 && yv2 >= 0) {
// second in Q1
if (x1 < x2) {
*minx = x1;
*maxx = x2;
*miny = MIN(y1, y2);
*maxy = MAX(y1, y2);
}
else {
// nearly full circle
}
}
else if (xv2 < 0 && yv2 >= 0) {
// second in Q2
*maxy = MAX(y1, y2);
}
else if (xv2 >= 0 && yv2 < 0) {
// second in Q4
*miny = MIN(y1, y2);
*maxy = MAX(y1, y2);
*minx = MIN(x1, x2);
}
else if (xv2 < 0 && yv2 < 0) {
// second in Q3
*minx = x2;
*maxy = y1;
}
}
else if (xv1 <= 0 && yv1 > 0) {
// first vector in Q4
if (xv2 >= 0 && yv2 >= 0) {
// second in Q1
*maxx = MAX(x1, x2);
}
else if (xv2 < 0 && yv2 >= 0) {
// second in Q2
*maxy = MAX(y1, y2);
*maxx = MAX(x1, x2);
}
else if (xv2 >= 0 && yv2 < 0) {
// second in Q4
if (x1 >= x2) {
*miny = MIN(y1, y2);
*maxy = MAX(y1, y2);
*minx = MIN(x1, x2);
*maxx = MAX(x2, x2);
}
else {
// nearly full circle
}
}
else if (xv2 < 0 && yv2 < 0) {
// second in Q3
*maxy = MAX(y1, y2);
*minx = MIN(x1, x2);
*maxx = MAX(x1, x2);
}
}
// this should *never* happen but if it does it means a case above is wrong
// this code is only present for safety sake
if (*maxx < *minx) {
fprintf(stderr, "assert failed *minx > *maxx\n");
fflush(stderr);
*maxx = *minx;
}
if (*maxy < *miny) {
fprintf(stderr, "assert failed *miny > *maxy\n");
fflush(stderr);
*maxy = *miny;
}
}
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