steiner_ellipse_test.h

#include "ofMain.h"

class ofApp : public ofBaseApp
{
public:
    
    ofMesh mesh, ellipse;
    double scale = 200.0;
    
    //--------------------------------------------------------------
    void setup()
    {
        ofBackground(0);
        
        mesh.setMode(OF_PRIMITIVE_LINE_LOOP);
        mesh.addVertices({
            ofVec2f(ofRandom(1.0), ofRandom(-1.0)) * scale,
            ofVec2f(ofRandom(-1.0), ofRandom(-1.0)) * scale,
            ofVec2f(0, ofRandom(1.0)) * scale,
        });
        
        ellipse.setMode(OF_PRIMITIVE_LINE_LOOP);
    }
    
    //--------------------------------------------------------------
    void draw()
    {
        ofSetColor(255);
        
        ofPushMatrix();
        {
            // ベースになる三角形
            ofTranslate(ofGetWidth() * 0.5, ofGetHeight() * 0.5);
            mesh.draw(OF_MESH_WIREFRAME);
        }
        ofPopMatrix();
        
        // 「三角形の重心座標 = 0 を使い(x3, y3)を消去」( http://d.hatena.ne.jp/Hyperion64/20120316/p1 )
        const double x1 = mesh.getVertices().at(0).x,  y1 = mesh.getVertices().at(0).y;
        const double x2 = mesh.getVertices().at(1).x, y2 = mesh.getVertices().at(1).y;
        
        const double a = (x2 * y1 - x1 * y2) / std::sqrt(std::pow(y1, 2.0) + y1 * y2 + std::pow(y2, 2.0));
        const double b = (x2 * y1 - x1 * y2) / std::sqrt(std::pow(x1, 2.0) + x1 * x2 + std::pow(x2, 2.0));
        const double c = -((x1 * (2 * y1 + y2) + x2 * (y1 + 2 * y2)) / std::pow((x2 * y1 - x1 * y2), 2.0));
        
        const double check = (std::pow(x2, 2.0) / std::pow(a, 2.0)) + (std::pow(y2, 2.0) / std::pow(b, 2.0)) + c * x2 * y2;
        ofLog() << check; // = 1
        
        // 楕円
        double resolution = 128.0;
        
        ellipse.clear();
        
        for (int i = 0; i < (int)resolution; ++i)
        {
            double theta = TWO_PI / resolution * i;
            // 楕円の媒介変数表示 x = acosθ, y = b / a・asinθ を使って円周上の座標を決定
            // c を使った回転の適用方法が分からない、、、
            ofVec2f v = ofVec2f(a * std::cos(theta), b * std::sin(theta));
            ellipse.addVertex(v);
        }
        
        ofPushMatrix();
        {
            ofTranslate(ofGetWidth() * 0.5, ofGetHeight() * 0.5);
            ellipse.draw(OF_MESH_WIREFRAME);
        }
        ofPopMatrix();
    }
    
    void mousePressed(int x, int y, int button)
    {
        mesh.clear();
        mesh.addVertices({
            ofVec2f(ofRandom(1.0), ofRandom(-1.0)) * scale,
            ofVec2f(ofRandom(-1.0), ofRandom(-1.0)) * scale,
            ofVec2f(0, ofRandom(1.0)) * scale,
        });
    }
};