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공유 - 복제, 배포, 전시, 공연 및 공중송신. (포맷 변경도 포함)
변경 - 리믹스, 변형, 2차적 저작물의 작성.
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1. 기본 정보
| 출처 | 출처를 반드시 삽입해 주세요. | 위키미디어 https://commons.wikimedia.org/wiki/File:Sphere_wireframe.svg | |||||||
| 날짜 | 이미지가 만들어진 날짜를 삽입해 주세요. | November 2008 | |||||||
| 저작자 | 이미지의 저작자를 삽입해 주세요. | Geek3 : Sphere wireframe - orthogonal projection of a sphere. The image shows lines, which are drawn as they were painted onto the surface of a sphere. The angular distance between two lines is 10°. The SVG file is created by the below C++-program, which calculates each edge of a line as an ellipse-bow. The backside of the sphere has an opacity of 0.25. The axis tilt is 52.5°. | |||||||
| 저작권 | 이미지의 저작권과 관련된 기타 정보를 삽입해 주세요. | (Source Code-GNU GPL) 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 {{{#!syntax javascript /* sphere - creates a svg vector-graphics file which depicts a wireframe sphere
/* The expressions in this code are not proven to be correct.
#include #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/wiki/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(); } }}} |
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