// -*- 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; } }