taylor

ofApp.cpp

#include "ofMain.h"

double frac_table[101];

double frac(int n) {
    double v = 1;
    for(int i = 1; i <= n; i++) {
        v *= i;
    }
    return v;
}

void init_frac_table() {
    for(int i = 0; i < 101; i++) {
        frac_table[i] = frac(i);
        ofLogNotice() << i << ", " << frac_table[i];
    }
}

double dsin(double x, int n) {
    n = n % 4;
    return ((n % 2) ? cos(x) : sin(x)) * ((n / 2 % 2) ? -1 : 1);
}

double a = 0.0;
int n = 10;

double taylor_sin(double x) {
    double v = 0.0;
    for(int i = n; 0 <= i; i--) {
        v += dsin(a, i) * pow(x - a, i) / frac_table[i];
    }
    return v;
}

double f(double x) {
    return sin(x) * sin(2 * x);
}

double taylor_f(double x) {
    return taylor_sin(x) * taylor_sin(2 * x);
}

class ofApp : public ofBaseApp {
    bool bSimple;
    
public:
    void setup() {
        a = 0.2;
        n = 10;
        init_frac_table();
        
        bSimple = true;
        
        ofEnableSmoothing();
    }
    
    void update() {
        a = ofMap(ofGetMouseX(), 0, ofGetWidth(), -10, 10);
    }
    
    void drawFunc(double (*fun)(double)) {
        glBegin(GL_LINE_STRIP);
        for(int i = 0; i < 1000; i++) {
            float x = ofMap(i, 0, 1000, -10, 10);
            glVertex2d(ofMap(i, 0, 1000, 0, ofGetWidth()), ofMap(fun(x), -1, 1, ofGetHeight() / 8, - ofGetHeight() / 8));
        }
        glEnd();
    }
    
    void draw() {
        ofBackground(0, 0, 0);
        
        for(int i = 0; i <= 100; i++) {
            ofSetColor(255, 255, 255, i % 10 == 0 ? 127 : 64);
            if(i == 50) ofSetColor(255);
            ofLine(i * 0.01 * ofGetWidth(), 0, i * 0.01 * ofGetWidth(), ofGetHeight());
        }
        
        ofSetColor(255, 0, 0);
        ofLine(ofGetMouseX(), 0, ofGetMouseX(), ofGetHeight());
        
        ofPushMatrix();
        {
            ofTranslate(0, ofGetHeight() / 2);
            
            ofSetColor(0, 0, 255);
            if(bSimple) drawFunc(sin);
            else drawFunc(f);
            
            ofSetColor(0, 255, 0);
            if(bSimple) drawFunc(taylor_sin);
            else drawFunc(taylor_f);
        }
        ofPopMatrix();
        
        ofSetColor(255, 255, 255);
        ofDrawBitmapString(string("n = ") + ofToString(n), 20, 20);
    }
    
    void keyPressed(int key) {
        switch (key) {
            case OF_KEY_UP:
                n++;
                if(100 < n) n = 100;
                break;
            case OF_KEY_DOWN:
                n--;
                if(n < 0) n = 0;
                break;
            case ' ':
                bSimple ^= true;
                break;
            default:
                break;
        }
    }
};

int main() {
    ofSetupOpenGL(1024, 512, OF_WINDOW);
    ofRunApp(new ofApp);
}