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「数学デッサン教室 描いて楽しむ数学のかたち」という本に記載のある数式を元にトーラス結び目(7, 2)をopenFrameworksで描写しました
Torus knot.
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#pragma once #include "ofMain.h" class ofApp : public ofBaseApp { public: void setup(); void update(); void draw(); void keyPressed(int key) {}; void keyReleased(int key) {}; void mouseMoved(int x, int y) {}; void mouseDragged(int x, int y, int button) {}; void mousePressed(int x, int y, int button) {}; void mouseReleased(int x, int y, int button) {}; void windowResized(int w, int h) {}; void dragEvent(ofDragInfo dragInfo) {}; void gotMessage(ofMessage msg) {}; void draw_torus(float R, float r, float p, float q); glm::vec3 make_point(float R, float r, float t, float p, float q); ofEasyCam cam; }; |
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#include "ofApp.h" //-------------------------------------------------------------- void ofApp::setup() { ofSetFrameRate(60); ofSetWindowTitle("openFrameworks"); ofBackground(239); ofSetLineWidth(5); ofEnableDepthTest(); } //-------------------------------------------------------------- void ofApp::update() { } //-------------------------------------------------------------- void ofApp::draw() { this->cam.begin(); this->draw_torus(200, 60, 7, 2); this->cam.end(); } //-------------------------------------------------------------- void ofApp::draw_torus(float R, float r, float p, float q) { ofColor color; for (int t_start = ofGetFrameNum() * 0.75; t_start < ofGetFrameNum() * 0.75 + 360; t_start += 30) { ofSetColor(39); for (int t = t_start; t <= t_start + 20; t++) { ofDrawLine(this->make_point(R, r, t, p, q), this->make_point(R, r, t + 1, p, q)); } color.setHsb(ofMap(t_start % 360, 0, 360, 0, 255), 255, 255); ofSetColor(color); ofDrawSphere(this->make_point(R, r, t_start + 25, p, q), 10); } } //-------------------------------------------------------------- glm::vec3 ofApp::make_point(float R, float r, float t, float p, float q) { // 数学デッサン教室 描いて楽しむ数学たち P.39 float x = (R + r * cos(p * t * DEG_TO_RAD)) * cos(q * t * DEG_TO_RAD); float y = (R + r * cos(p * t * DEG_TO_RAD)) * sin(q * t * DEG_TO_RAD); float z = r * sin(p * t * DEG_TO_RAD); return glm::vec3(x, y, z); } //-------------------------------------------------------------- int main() { ofSetupOpenGL(720, 720, OF_WINDOW); ofRunApp(new ofApp()); } |