File:Sphere Wireframe.svg
W3C-validity not checked.
Source Code
This image can be completely generated by the following source code. If you have the gnu compiler collection installed, the programm can be compiled by the following commands:
g++ sphere_wireframe.cpp -o sphere_wireframe
and run :
./sphere_wireframe > Sphere_wireframe.svg
It creates file Sphere_wireframe.svg in working directory. This file can be viewed using rsvg-view program :
rsvg-view Sphere_wireframe.svg
Here is cpp code in file : sphere_wireframe.cpp
/* sphere - creates a svg vector-graphics file which depicts a wireframe sphere
*
* Copyright (C) 2008 Wikimedia foundation
*
* 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 2, 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, you can either send email to this
* program's author (see below) or write to:
* The Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor
* Boston, MA 02110-1301 USA
*/
/* The expressions in this code are not proven to be correct.
* Hence this code probably contains lots of bugs. Be aware! */
#include <iostream>
#include <cmath>
#include <cstdlib>
#include <cstring>
using namespace std;
const double PI = 3.1415926535897932;
const double DEG = PI / 180.0;
/********************************* settings **********************************/
int n_lon = 18; // number of latitude fields (18 => 10° each)
int n_lat = 18; // half number of longitude fields (18 => 10° each)
double lon_offset = 2.5 * DEG; // offset of the meridians
double w = 52.5 * DEG; // axial tilt (0° => axis is perpendicular to image plane)
double stripe_grad = 0.5 * DEG; // width of each line
int image_size = 400; // width and height of the image in pixels
double back_opacity = 0.25; // opacity of the sphere's backside
char color[] = "#334070"; // color of lines
int istep = 2; // svg code indentation step
/*****************************************************************************/
double sqr(double x)
{
return(x * x);
}
// commands for svg-code:
void indent(int n, bool in_tag = false)
{
n *= istep;
if (in_tag) n += istep + 1;
for (int i = 0; i < n; i++) cout << " ";
}
void M()
{
cout << "M ";
}
void Z()
{
cout << "Z ";
}
void xy(double x, double y)
{
cout << x << ",";
cout << y << " ";
}
void arc(double a, double b, double x_axis_rot, bool large_arc, bool sweep)
{ // draws an elliptic arc
if (b < 0.5E-6)
{ // flat ellipses are not rendered properly => use line
cout << "L ";
}
else
{
cout << "A ";
cout << a << ","; // semi-major axis
cout << b << " "; // semi-minor axis
cout << x_axis_rot << " ";
cout << large_arc << " ";
cout << sweep << " ";
}
}
void circle(bool clockwise)
{
M();
xy(-1, 0);
arc(1, 1, 0, 0, !clockwise);
xy(1, 0);
arc(1, 1, 0, 0, !clockwise);
xy(-1, 0);
Z();
}
void start_svg_file()
{
cout << "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n";
cout << "<svg id=\"Sphere_wireframe\"\n";
cout << " version=\"1.1\"\n";
cout << " baseProfile=\"full\"\n";
cout << " xmlns=\"http://www.w3.org/2000/svg\"\n";
cout << " xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n";
cout << " width=\"" << image_size << "\"\n";
cout << " height=\"" << image_size << "\">\n\n";
cout << " <title>Sphere wireframe</title>\n\n";
cout << " <desc>\n";
cout << " about: http://commons.wikimedia.org/key/Image:Sphere_wireframe.svg\n";
cout << " rights: GNU Free Documentation license,\n";
cout << " Creative Commons Attribution ShareAlike license\n";
cout << " </desc>\n\n";
cout << " <g id=\"sphere\" transform=\"scale(" << 0.5 * image_size;
cout << ", " << -0.5 * image_size << ") translate(1, -1)\">\n";
}
void end_svg_file()
{
cout << " </g>\n</svg>\n";
}
int main (int argc, char *argv[])
{
// accept -lat and -lon as parameter
for (int i = 2; i < argc; i++)
{
if (isdigit(argv[i][0]) || (sizeof(argv[i]) > sizeof(char)
&& isdigit(argv[i][1])
&& (argv[i][0] == '.' || argv[i][0] == '-')))
{
if (strcmp(argv[i - 1], "-lon") == 0)
{
lon_offset = atof(argv[i]) * DEG;
}
if (strcmp(argv[i - 1], "-lat") == 0)
{
w = atof(argv[i]) * DEG;
}
}
}
double cosw = cos(w), sinw = sin(w);
double d = 0.5 * stripe_grad;
start_svg_file();
int ind = 2; // initial indentation level
indent(ind);
cout << "<g id=\"sphere_back\" transform=\"rotate(180)\" ";
cout << "opacity=\"" << back_opacity << "\">\n";
indent(++ind);
cout << "<g id=\"sphere_half\">\n";
// meridians
indent(++ind); cout << "<g id=\"meridians\"\n";
indent(ind++, true);
cout << "style=\"stroke:none; fill:" << color << "; fill_rule:evenodd\">\n";
double a = abs(cos(d));
for (int i_lon = 0; i_lon < n_lat; i_lon++)
{ // draw one meridian
double longitude = lon_offset + (i_lon * 180.0 / n_lat) * DEG;
double lon[2];
lon[0] = longitude + d;
lon[1] = longitude - d;
indent(ind);
cout << "<path id=\"meridian";
cout << i_lon << "\"\n";
indent(ind, true);
cout << "d=\"";
double axis_rot = atan2(-1.0 / tan(longitude), cosw);
if (sinw < 0)
axis_rot += PI;
double w2 = sin(longitude) * sinw;
double b = abs(w2 * cos(d));
double sinw1 = sin(d) / sqrt(1.0 - sqr(sin(longitude) * sinw));
if (abs(sinw1) >= 1.0)
{ // stripe covers edge of the circle
double w3 = sqrt(1.0 - sqr(w2)) * sin(d);
circle(false);
// ellipse
M();
xy(sin(axis_rot) * w3 - cos(axis_rot) * a,
-cos(axis_rot) * w3 - sin(axis_rot) * a);
arc(a, b, axis_rot / DEG, 0, 0);
xy(sin(axis_rot) * w3 + cos(axis_rot) * a,
-cos(axis_rot) * w3 + sin(axis_rot) * a);
arc(a, b, axis_rot / DEG, 0, 0);
xy(sin(axis_rot) * w3 - cos(axis_rot) * a,
-cos(axis_rot) * w3 - sin(axis_rot) * a);
Z();
}
else
{ // draw a disrupted ellipse bow
double w1 = asin(sinw1);
M();
xy(-cos(axis_rot + w1), -sin(axis_rot + w1));
arc(a, b, axis_rot / DEG, 1, 0);
xy(cos(axis_rot - w1), sin(axis_rot - w1));
arc(1, 1, 0, 0, 1);
xy(cos(axis_rot + w1), sin(axis_rot + w1));
arc(a, b, axis_rot / DEG, 0, 1);
xy(-cos(axis_rot - w1), -sin(axis_rot - w1));
arc(1, 1, 0, 0, 1);
xy(-cos(axis_rot + w1), -sin(axis_rot + w1));
}
Z();
cout << "\" />\n";
}
indent(--ind); cout << "</g>\n";
cout << endl;
// circles of latitude
indent(ind); cout << "<g id=\"circles_of_latitude\"\n";
indent(ind, true);
cout << "style=\"stroke:none; fill:" << color << "; fill_rule:evenodd\">\n";
ind++;
for (int i_lat = 1; i_lat < n_lon; i_lat++)
{ // draw one circle of latitude
double latitude = (i_lat * 180.0 / n_lon - 90.0) * DEG;
double lat[2];
lat[0] = latitude + d;
lat[1] = latitude - d;
double x[2], yd[2], ym[2];
for (int i = 0; i < 2; i++)
{
x[i] = abs(cos(lat[i]));
yd[i] = abs(cosw * cos(lat[i]));
ym[i] = sinw * sin(lat[i]);
}
double h[4]; // height of each point above image plane
h[0] = sin(lat[0] + w);
h[1] = sin(lat[0] - w);
h[2] = sin(lat[1] + w);
h[3] = sin(lat[1] - w);
if (h[0] > 0 || h[1] > 0 || h[2] > 0 || h[3] > 0)
{ // at least any part visible
indent(ind);
cout << "<path id=\"circle_of_latitude";
cout << i_lat << "\"\n";
indent(ind, true);
cout << "d=\"";
for (int i = 0; i < 2; i++)
{
if ((h[2*i] >= 0 && h[2*i+1] >= 0)
&& (h[2*i] > 0 || h[2*i+1] > 0))
{ // complete ellipse
M();
xy(-x[i], ym[i]); // startpoint
for (int z = 1; z > -2; z -= 2)
{
arc(x[i], yd[i], 0, 1, i);
xy(z * x[i], ym[i]);
}
Z();
if (h[2-2*i] * h[3-2*i] < 0)
{ // partly ellipse + partly circle
double yp = sin(lat[1-i]) / sinw;
double xp = sqrt(1.0 - sqr(yp));
if (sinw < 0)
{
xp = -xp;
}
M();
xy(-xp, yp);
arc(x[1-i], yd[1-i], 0,
sin(lat[1-i]) * cosw > 0, cosw >= 0);
xy(xp, yp);
arc(1, 1, 0, 0, cosw >= 0);
xy(-xp, yp);
Z();
}
else if (h[2-2*i] <= 0 && h[3-2*i] <= 0)
{ // stripe covers edge of the circle
circle(cosw < 0);
}
}
}
if ((h[0] * h[1] < 0 && h[2] <= 0 && h[3] <= 0)
|| (h[0] <= 0 && h[1] <= 0 && h[2] * h[3] < 0))
{
// one slice visible
int i = h[0] <= 0 && h[1] <= 0;
double yp = sin(lat[i]) / sinw;
double xp = sqrt(1.0 - yp * yp);
M();
xy(-xp, yp);
arc(x[i], yd[i], 0, sin(lat[i]) * cosw > 0, cosw * sinw >= 0);
xy(xp, yp);
arc(1, 1, 0, 0, cosw * sinw < 0);
xy(-xp, yp);
Z();
}
else if (h[0] * h[1] < 0 && h[2] * h[3] < 0)
{
// disrupted ellipse bow
double xp[2], yp[2];
for (int i = 0; i < 2; i++)
{
yp[i] = sin(lat[i]) / sinw;
xp[i] = sqrt(1.0 - sqr(yp[i]));
if (sinw < 0) xp[i] = -xp[i];
}
M();
xy(-xp[0], yp[0]);
arc(x[0], yd[0], 0, sin(lat[0]) * cosw > 0, cosw >= 0);
xy(xp[0], yp[0]);
arc(1, 1, 0, 0, 0);
xy(xp[1], yp[1]);
arc(x[1], yd[1], 0, sin(lat[1]) * cosw > 0, cosw < 0);
xy(-xp[1], yp[1]);
arc(1, 1, 0, 0, 0);
xy(-xp[0], yp[0]);
Z();
}
cout << "\" />\n";
}
}
for (int i = 0; i < 3; i++)
{
indent(--ind);
cout << "</g>\n";
}
indent(ind--);
cout << "<use id=\"sphere_front\" xlink:href=\"#sphere_half\" />\n";
end_svg_file();
}
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.
