/* $NetBSD: common.cpp,v 1.1.1.1 2016/01/13 18:41:48 christos Exp $ */
// -*- C++ -*-
/* Copyright (C) 1989, 1990, 1991, 1992, 2003 Free Software Foundation, Inc.
Written by James Clark (jjc@jclark.com)
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, 51 Franklin St - Fifth Floor, Boston, MA 02110-1301, USA. */
#include "pic.h"
#include "common.h"
// output a dashed circle as a series of arcs
void common_output::dashed_circle(const position ¢, double rad,
const line_type <)
{
assert(lt.type == line_type::dashed);
line_type slt = lt;
slt.type = line_type::solid;
double dash_angle = lt.dash_width/rad;
int ndashes;
double gap_angle;
if (dash_angle >= M_PI/4.0) {
if (dash_angle < M_PI/2.0) {
gap_angle = M_PI/2.0 - dash_angle;
ndashes = 4;
}
else if (dash_angle < M_PI) {
gap_angle = M_PI - dash_angle;
ndashes = 2;
}
else {
circle(cent, rad, slt, -1.0);
return;
}
}
else {
ndashes = 4*int(ceil(M_PI/(4.0*dash_angle)));
gap_angle = (M_PI*2.0)/ndashes - dash_angle;
}
for (int i = 0; i < ndashes; i++) {
double start_angle = i*(dash_angle+gap_angle) - dash_angle/2.0;
solid_arc(cent, rad, start_angle, start_angle + dash_angle, lt);
}
}
// output a dotted circle as a series of dots
void common_output::dotted_circle(const position ¢, double rad,
const line_type <)
{
assert(lt.type == line_type::dotted);
double gap_angle = lt.dash_width/rad;
int ndots;
if (gap_angle >= M_PI/2.0) {
// always have at least 2 dots
gap_angle = M_PI;
ndots = 2;
}
else {
ndots = 4*int(M_PI/(2.0*gap_angle));
gap_angle = (M_PI*2.0)/ndots;
}
double ang = 0.0;
for (int i = 0; i < ndots; i++, ang += gap_angle)
dot(cent + position(cos(ang), sin(ang))*rad, lt);
}
// recursive function for dash drawing, used by dashed_ellipse
void common_output::ellipse_arc(const position ¢,
const position &z0, const position &z1,
const distance &dim, const line_type <)
{
assert(lt.type == line_type::solid);
assert(dim.x != 0 && dim.y != 0);
double eps = 0.0001;
position zml = (z0 + z1) / 2;
// apply affine transformation (from ellipse to circle) to compute angle
// of new position, then invert transformation to get exact position
double psi = atan2(zml.y / dim.y, zml.x / dim.x);
position zm = position(dim.x * cos(psi), dim.y * sin(psi));
// to approximate the ellipse arc with one or more circle arcs, we
// first compute the radius of curvature in zm
double a_2 = dim.x * dim.x;
double a_4 = a_2 * a_2;
double b_2 = dim.y * dim.y;
double b_4 = b_2 * b_2;
double e_2 = a_2 - b_2;
double temp = a_4 * zm.y * zm.y + b_4 * zm.x * zm.x;
double rho = sqrt(temp / a_4 / b_4 * temp / a_4 / b_4 * temp);
// compute center of curvature circle
position M = position(e_2 * zm.x / a_2 * zm.x / a_2 * zm.x,
-e_2 * zm.y / b_2 * zm.y / b_2 * zm.y);
// compute distance between circle and ellipse arc at start and end
double phi0 = atan2(z0.y - M.y, z0.x - M.x);
double phi1 = atan2(z1.y - M.y, z1.x - M.x);
position M0 = position(rho * cos(phi0), rho * sin(phi0)) + M;
position M1 = position(rho * cos(phi1), rho * sin(phi1)) + M;
double dist0 = hypot(z0 - M0) / sqrt(z0 * z0);
double dist1 = hypot(z1 - M1) / sqrt(z1 * z1);
if (dist0 < eps && dist1 < eps)
solid_arc(M + cent, rho, phi0, phi1, lt);
else {
ellipse_arc(cent, z0, zm, dim, lt);
ellipse_arc(cent, zm, z1, dim, lt);
}
}
// output a dashed ellipse as a series of arcs
void common_output::dashed_ellipse(const position ¢, const distance &dim,
const line_type <)
{
assert(lt.type == line_type::dashed);
double dim_x = dim.x / 2;
double dim_y = dim.y / 2;
line_type slt = lt;
slt.type = line_type::solid;
double dw = lt.dash_width;
// we use an approximation to compute the ellipse length (found in:
// Bronstein, Semendjajew, Taschenbuch der Mathematik)
double lambda = (dim.x - dim.y) / (dim.x + dim.y);
double le = M_PI / 2 * (dim.x + dim.y)
* ((64 - 3 * lambda * lambda * lambda * lambda )
/ (64 - 16 * lambda * lambda));
// for symmetry we make nmax a multiple of 8
int nmax = 8 * int(le / dw / 8 + 0.5);
if (nmax < 8) {
nmax = 8;
dw = le / 8;
}
int ndash = nmax / 2;
double gapwidth = (le - dw * ndash) / ndash;
double l = 0;
position z = position(dim_x, 0);
position zdot = z;
int j = 0;
int jmax = int(10 / lt.dash_width);
for (int i = 0; i <= nmax; i++) {
position zold = z;
position zpre = zdot;
double ld = (int(i / 2) + 0.5) * dw + int((i + 1) / 2) * gapwidth;
double lold = 0;
double dl = 1;
// find next position for fixed arc length
while (l < ld) {
j++;
lold = l;
zold = z;
double phi = j * 2 * M_PI / jmax;
z = position(dim_x * cos(phi), dim_y * sin(phi));
dl = hypot(z - zold);
l += dl;
}
// interpolate linearly between the last two points,
// using the length difference as the scaling factor
double delta = (ld - lold) / dl;
zdot = zold + (z - zold) * delta;
// compute angle of new position on the affine circle
// and use it to get the exact value on the ellipse
double psi = atan2(zdot.y / dim_y, zdot.x / dim_x);
zdot = position(dim_x * cos(psi), dim_y * sin(psi));
if ((i % 2 == 0) && (i > 1))
ellipse_arc(cent, zpre, zdot, dim / 2, slt);
}
}
// output a dotted ellipse as a series of dots
void common_output::dotted_ellipse(const position ¢, const distance &dim,
const line_type <)
{
assert(lt.type == line_type::dotted);
double dim_x = dim.x / 2;
double dim_y = dim.y / 2;
line_type slt = lt;
slt.type = line_type::solid;
// we use an approximation to compute the ellipse length (found in:
// Bronstein, Semendjajew, Taschenbuch der Mathematik)
double lambda = (dim.x - dim.y) / (dim.x + dim.y);
double le = M_PI / 2 * (dim.x + dim.y)
* ((64 - 3 * lambda * lambda * lambda * lambda )
/ (64 - 16 * lambda * lambda));
// for symmetry we make nmax a multiple of 4
int ndots = 4 * int(le / lt.dash_width / 4 + 0.5);
if (ndots < 4)
ndots = 4;
double l = 0;
position z = position(dim_x, 0);
int j = 0;
int jmax = int(10 / lt.dash_width);
for (int i = 1; i <= ndots; i++) {
position zold = z;
double lold = l;
double ld = i * le / ndots;
double dl = 1;
// find next position for fixed arc length
while (l < ld) {
j++;
lold = l;
zold = z;
double phi = j * 2 * M_PI / jmax;
z = position(dim_x * cos(phi), dim_y * sin(phi));
dl = hypot(z - zold);
l += dl;
}
// interpolate linearly between the last two points,
// using the length difference as the scaling factor
double delta = (ld - lold) / dl;
position zdot = zold + (z - zold) * delta;
// compute angle of new position on the affine circle
// and use it to get the exact value on the ellipse
double psi = atan2(zdot.y / dim_y, zdot.x / dim_x);
zdot = position(dim_x * cos(psi), dim_y * sin(psi));
dot(cent + zdot, slt);
}
}
// return non-zero iff we can compute a center
int compute_arc_center(const position &start, const position ¢,
const position &end, position *result)
{
// This finds the point along the vector from start to cent that
// is equidistant between start and end.
distance c = cent - start;
distance e = end - start;
double n = c*e;
if (n == 0.0)
return 0;
*result = start + c*((e*e)/(2.0*n));
return 1;
}
// output a dashed arc as a series of arcs
void common_output::dashed_arc(const position &start, const position ¢,
const position &end, const line_type <)
{
assert(lt.type == line_type::dashed);
position c;
if (!compute_arc_center(start, cent, end, &c)) {
line(start, &end, 1, lt);
return;
}
distance start_offset = start - c;
distance end_offset = end - c;
double start_angle = atan2(start_offset.y, start_offset.x);
double end_angle = atan2(end_offset.y, end_offset.x);
double rad = hypot(c - start);
double dash_angle = lt.dash_width/rad;
double total_angle = end_angle - start_angle;
while (total_angle < 0)
total_angle += M_PI + M_PI;
if (total_angle <= dash_angle*2.0) {
solid_arc(cent, rad, start_angle, end_angle, lt);
return;
}
int ndashes = int((total_angle - dash_angle)/(dash_angle*2.0) + .5);
double dash_and_gap_angle = (total_angle - dash_angle)/ndashes;
for (int i = 0; i <= ndashes; i++)
solid_arc(cent, rad, start_angle + i*dash_and_gap_angle,
start_angle + i*dash_and_gap_angle + dash_angle, lt);
}
// output a dotted arc as a series of dots
void common_output::dotted_arc(const position &start, const position ¢,
const position &end, const line_type <)
{
assert(lt.type == line_type::dotted);
position c;
if (!compute_arc_center(start, cent, end, &c)) {
line(start, &end, 1, lt);
return;
}
distance start_offset = start - c;
distance end_offset = end - c;
double start_angle = atan2(start_offset.y, start_offset.x);
double total_angle = atan2(end_offset.y, end_offset.x) - start_angle;
while (total_angle < 0)
total_angle += M_PI + M_PI;
double rad = hypot(c - start);
int ndots = int(total_angle/(lt.dash_width/rad) + .5);
if (ndots == 0)
dot(start, lt);
else {
for (int i = 0; i <= ndots; i++) {
double a = start_angle + (total_angle*i)/ndots;
dot(cent + position(cos(a), sin(a))*rad, lt);
}
}
}
void common_output::solid_arc(const position ¢, double rad,
double start_angle, double end_angle,
const line_type <)
{
line_type slt = lt;
slt.type = line_type::solid;
arc(cent + position(cos(start_angle), sin(start_angle))*rad,
cent,
cent + position(cos(end_angle), sin(end_angle))*rad,
slt);
}
void common_output::rounded_box(const position ¢, const distance &dim,
double rad, const line_type <, double fill)
{
if (fill >= 0.0)
filled_rounded_box(cent, dim, rad, fill);
switch (lt.type) {
case line_type::invisible:
break;
case line_type::dashed:
dashed_rounded_box(cent, dim, rad, lt);
break;
case line_type::dotted:
dotted_rounded_box(cent, dim, rad, lt);
break;
case line_type::solid:
solid_rounded_box(cent, dim, rad, lt);
break;
default:
assert(0);
}
}
void common_output::dashed_rounded_box(const position ¢,
const distance &dim, double rad,
const line_type <)
{
line_type slt = lt;
slt.type = line_type::solid;
double hor_length = dim.x + (M_PI/2.0 - 2.0)*rad;
int n_hor_dashes = int(hor_length/(lt.dash_width*2.0) + .5);
double hor_gap_width = (n_hor_dashes != 0
? hor_length/n_hor_dashes - lt.dash_width
: 0.0);
double vert_length = dim.y + (M_PI/2.0 - 2.0)*rad;
int n_vert_dashes = int(vert_length/(lt.dash_width*2.0) + .5);
double vert_gap_width = (n_vert_dashes != 0
? vert_length/n_vert_dashes - lt.dash_width
: 0.0);
// Note that each corner arc has to be split into two for dashing,
// because one part is dashed using vert_gap_width, and the other
// using hor_gap_width.
double offset = lt.dash_width/2.0;
dash_arc(cent + position(dim.x/2.0 - rad, -dim.y/2.0 + rad), rad,
-M_PI/4.0, 0, slt, lt.dash_width, vert_gap_width, &offset);
dash_line(cent + position(dim.x/2.0, -dim.y/2.0 + rad),
cent + position(dim.x/2.0, dim.y/2.0 - rad),
slt, lt.dash_width, vert_gap_width, &offset);
dash_arc(cent + position(dim.x/2.0 - rad, dim.y/2.0 - rad), rad,
0, M_PI/4.0, slt, lt.dash_width, vert_gap_width, &offset);
offset = lt.dash_width/2.0;
dash_arc(cent + position(dim.x/2.0 - rad, dim.y/2.0 - rad), rad,
M_PI/4.0, M_PI/2, slt, lt.dash_width, hor_gap_width, &offset);
dash_line(cent + position(dim.x/2.0 - rad, dim.y/2.0),
cent + position(-dim.x/2.0 + rad, dim.y/2.0),
slt, lt.dash_width, hor_gap_width, &offset);
dash_arc(cent + position(-dim.x/2.0 + rad, dim.y/2.0 - rad), rad,
M_PI/2, 3*M_PI/4.0, slt, lt.dash_width, hor_gap_width, &offset);
offset = lt.dash_width/2.0;
dash_arc(cent + position(-dim.x/2.0 + rad, dim.y/2.0 - rad), rad,
3.0*M_PI/4.0, M_PI, slt, lt.dash_width, vert_gap_width, &offset);
dash_line(cent + position(-dim.x/2.0, dim.y/2.0 - rad),
cent + position(-dim.x/2.0, -dim.y/2.0 + rad),
slt, lt.dash_width, vert_gap_width, &offset);
dash_arc(cent + position(-dim.x/2.0 + rad, -dim.y/2.0 + rad), rad,
M_PI, 5.0*M_PI/4.0, slt, lt.dash_width, vert_gap_width, &offset);
offset = lt.dash_width/2.0;
dash_arc(cent + position(-dim.x/2.0 + rad, -dim.y/2.0 + rad), rad,
5*M_PI/4.0, 3*M_PI/2.0, slt, lt.dash_width, hor_gap_width, &offset);
dash_line(cent + position(-dim.x/2.0 + rad, -dim.y/2.0),
cent + position(dim.x/2.0 - rad, -dim.y/2.0),
slt, lt.dash_width, hor_gap_width, &offset);
dash_arc(cent + position(dim.x/2.0 - rad, -dim.y/2.0 + rad), rad,
3*M_PI/2, 7*M_PI/4, slt, lt.dash_width, hor_gap_width, &offset);
}
// Used by dashed_rounded_box.
void common_output::dash_arc(const position ¢, double rad,
double start_angle, double end_angle,
const line_type <,
double dash_width, double gap_width,
double *offsetp)
{
double length = (end_angle - start_angle)*rad;
double pos = 0.0;
for (;;) {
if (*offsetp >= dash_width) {
double rem = dash_width + gap_width - *offsetp;
if (pos + rem > length) {
*offsetp += length - pos;
break;
}
else {
pos += rem;
*offsetp = 0.0;
}
}
else {
double rem = dash_width - *offsetp;
if (pos + rem > length) {
solid_arc(cent, rad, start_angle + pos/rad, end_angle, lt);
*offsetp += length - pos;
break;
}
else {
solid_arc(cent, rad, start_angle + pos/rad,
start_angle + (pos + rem)/rad, lt);
pos += rem;
*offsetp = dash_width;
}
}
}
}
// Used by dashed_rounded_box.
void common_output::dash_line(const position &start, const position &end,
const line_type <,
double dash_width, double gap_width,
double *offsetp)
{
distance dist = end - start;
double length = hypot(dist);
if (length == 0.0)
return;
double pos = 0.0;
for (;;) {
if (*offsetp >= dash_width) {
double rem = dash_width + gap_width - *offsetp;
if (pos + rem > length) {
*offsetp += length - pos;
break;
}
else {
pos += rem;
*offsetp = 0.0;
}
}
else {
double rem = dash_width - *offsetp;
if (pos + rem > length) {
line(start + dist*(pos/length), &end, 1, lt);
*offsetp += length - pos;
break;
}
else {
position p(start + dist*((pos + rem)/length));
line(start + dist*(pos/length), &p, 1, lt);
pos += rem;
*offsetp = dash_width;
}
}
}
}
void common_output::dotted_rounded_box(const position ¢,
const distance &dim, double rad,
const line_type <)
{
line_type slt = lt;
slt.type = line_type::solid;
double hor_length = dim.x + (M_PI/2.0 - 2.0)*rad;
int n_hor_dots = int(hor_length/lt.dash_width + .5);
double hor_gap_width = (n_hor_dots != 0
? hor_length/n_hor_dots
: lt.dash_width);
double vert_length = dim.y + (M_PI/2.0 - 2.0)*rad;
int n_vert_dots = int(vert_length/lt.dash_width + .5);
double vert_gap_width = (n_vert_dots != 0
? vert_length/n_vert_dots
: lt.dash_width);
double epsilon = lt.dash_width/(rad*100.0);
double offset = 0.0;
dot_arc(cent + position(dim.x/2.0 - rad, -dim.y/2.0 + rad), rad,
-M_PI/4.0, 0, slt, vert_gap_width, &offset);
dot_line(cent + position(dim.x/2.0, -dim.y/2.0 + rad),
cent + position(dim.x/2.0, dim.y/2.0 - rad),
slt, vert_gap_width, &offset);
dot_arc(cent + position(dim.x/2.0 - rad, dim.y/2.0 - rad), rad,
0, M_PI/4.0 - epsilon, slt, vert_gap_width, &offset);
offset = 0.0;
dot_arc(cent + position(dim.x/2.0 - rad, dim.y/2.0 - rad), rad,
M_PI/4.0, M_PI/2, slt, hor_gap_width, &offset);
dot_line(cent + position(dim.x/2.0 - rad, dim.y/2.0),
cent + position(-dim.x/2.0 + rad, dim.y/2.0),
slt, hor_gap_width, &offset);
dot_arc(cent + position(-dim.x/2.0 + rad, dim.y/2.0 - rad), rad,
M_PI/2, 3*M_PI/4.0 - epsilon, slt, hor_gap_width, &offset);
offset = 0.0;
dot_arc(cent + position(-dim.x/2.0 + rad, dim.y/2.0 - rad), rad,
3.0*M_PI/4.0, M_PI, slt, vert_gap_width, &offset);
dot_line(cent + position(-dim.x/2.0, dim.y/2.0 - rad),
cent + position(-dim.x/2.0, -dim.y/2.0 + rad),
slt, vert_gap_width, &offset);
dot_arc(cent + position(-dim.x/2.0 + rad, -dim.y/2.0 + rad), rad,
M_PI, 5.0*M_PI/4.0 - epsilon, slt, vert_gap_width, &offset);
offset = 0.0;
dot_arc(cent + position(-dim.x/2.0 + rad, -dim.y/2.0 + rad), rad,
5*M_PI/4.0, 3*M_PI/2.0, slt, hor_gap_width, &offset);
dot_line(cent + position(-dim.x/2.0 + rad, -dim.y/2.0),
cent + position(dim.x/2.0 - rad, -dim.y/2.0),
slt, hor_gap_width, &offset);
dot_arc(cent + position(dim.x/2.0 - rad, -dim.y/2.0 + rad), rad,
3*M_PI/2, 7*M_PI/4 - epsilon, slt, hor_gap_width, &offset);
}
// Used by dotted_rounded_box.
void common_output::dot_arc(const position ¢, double rad,
double start_angle, double end_angle,
const line_type <, double gap_width,
double *offsetp)
{
double length = (end_angle - start_angle)*rad;
double pos = 0.0;
for (;;) {
if (*offsetp == 0.0) {
double ang = start_angle + pos/rad;
dot(cent + position(cos(ang), sin(ang))*rad, lt);
}
double rem = gap_width - *offsetp;
if (pos + rem > length) {
*offsetp += length - pos;
break;
}
else {
pos += rem;
*offsetp = 0.0;
}
}
}
// Used by dotted_rounded_box.
void common_output::dot_line(const position &start, const position &end,
const line_type <, double gap_width,
double *offsetp)
{
distance dist = end - start;
double length = hypot(dist);
if (length == 0.0)
return;
double pos = 0.0;
for (;;) {
if (*offsetp == 0.0)
dot(start + dist*(pos/length), lt);
double rem = gap_width - *offsetp;
if (pos + rem > length) {
*offsetp += length - pos;
break;
}
else {
pos += rem;
*offsetp = 0.0;
}
}
}
void common_output::solid_rounded_box(const position ¢,
const distance &dim, double rad,
const line_type <)
{
position tem = cent - dim/2.0;
arc(tem + position(0.0, rad),
tem + position(rad, rad),
tem + position(rad, 0.0),
lt);
tem = cent + position(-dim.x/2.0, dim.y/2.0);
arc(tem + position(rad, 0.0),
tem + position(rad, -rad),
tem + position(0.0, -rad),
lt);
tem = cent + dim/2.0;
arc(tem + position(0.0, -rad),
tem + position(-rad, -rad),
tem + position(-rad, 0.0),
lt);
tem = cent + position(dim.x/2.0, -dim.y/2.0);
arc(tem + position(-rad, 0.0),
tem + position(-rad, rad),
tem + position(0.0, rad),
lt);
position end;
end = cent + position(-dim.x/2.0, dim.y/2.0 - rad);
line(cent - dim/2.0 + position(0.0, rad), &end, 1, lt);
end = cent + position(dim.x/2.0 - rad, dim.y/2.0);
line(cent + position(-dim.x/2.0 + rad, dim.y/2.0), &end, 1, lt);
end = cent + position(dim.x/2.0, -dim.y/2.0 + rad);
line(cent + position(dim.x/2.0, dim.y/2.0 - rad), &end, 1, lt);
end = cent + position(-dim.x/2.0 + rad, -dim.y/2.0);
line(cent + position(dim.x/2.0 - rad, -dim.y/2.0), &end, 1, lt);
}
void common_output::filled_rounded_box(const position ¢,
const distance &dim, double rad,
double fill)
{
line_type ilt;
ilt.type = line_type::invisible;
circle(cent + position(dim.x/2.0 - rad, dim.y/2.0 - rad), rad, ilt, fill);
circle(cent + position(-dim.x/2.0 + rad, dim.y/2.0 - rad), rad, ilt, fill);
circle(cent + position(-dim.x/2.0 + rad, -dim.y/2.0 + rad), rad, ilt, fill);
circle(cent + position(dim.x/2.0 - rad, -dim.y/2.0 + rad), rad, ilt, fill);
position vec[4];
vec[0] = cent + position(dim.x/2.0, dim.y/2.0 - rad);
vec[1] = cent + position(-dim.x/2.0, dim.y/2.0 - rad);
vec[2] = cent + position(-dim.x/2.0, -dim.y/2.0 + rad);
vec[3] = cent + position(dim.x/2.0, -dim.y/2.0 + rad);
polygon(vec, 4, ilt, fill);
vec[0] = cent + position(dim.x/2.0 - rad, dim.y/2.0);
vec[1] = cent + position(-dim.x/2.0 + rad, dim.y/2.0);
vec[2] = cent + position(-dim.x/2.0 + rad, -dim.y/2.0);
vec[3] = cent + position(dim.x/2.0 - rad, -dim.y/2.0);
polygon(vec, 4, ilt, fill);
}