PVector   Origin, Scale;
PVector[]  wv = new PVector[3];
PVector[]  sv = new PVector[3];
PFont fontA;
float  x, y;
int    h=1;
 
void setup() {
  size(500,500);
  smooth();
  noLoop();
  Origin = new PVector(300, 100);
  Scale = new PVector(50, 50); 
  for(int i=0; i<3; i++) {
    wv[i] = new PVector(0, 0);
    sv[i] = new PVector(20, 20);
  }    
  fontA = loadFont("ComicSansMS-Bold-32.vlw");
  textAlign(CENTER);
  textFont(fontA, 8);
}
 
PVector World2Screen(PVector v){
//  v.x=v.x*Scale.x+Origin.x;
//  v.y=height-v.y*Scale.y-Origin.y;
  
  v.mult(Scale);
  v.add(Origin);
  v.y=height-v.y;
  return v;
}
 
void draw() {
  background(200);
  fill(0);
  stroke(0);
  rectMode(CENTER);
  drawAxis();
  drawFunction();
  secant(5, 4, 0.000001);
  newtonraphson(5, 0.000001);
  bisection(-3, 4, 0.000001);
}

void secant(float xi, float xi_minus, float e) {
  int i=0;
  float xi_plus;
  
  while(abs(ft(xi)) > e) {
    xi_plus = xi - ft(xi)/ft_slope(xi,xi_minus);
    xi_minus = xi;
    xi = xi_plus;
    println("[Secant Iteration "+i+"]: The root is "+xi+" <with error"+abs(ft(xi))+">");
    i++;
  }    
}

void newtonraphson(float xi, float e) {
  int i=0;
  while(abs(ft(xi)) > e) {
    xi = xi - ft(xi)/ft_prime(xi);
    println("[NewtonRaphson Iteration "+i+"]: The root is "+xi+" <with error"+abs(ft(xi))+">");
    i++;
  }    
}

void bisection(float xl, float xh, float e) {
    float xm;
    xm = (ft(xh)*xl - ft(xl)*xh) / (ft(xh) - ft(xl));
//    xm = (xh + xl) / 2.0;
    if(ft(xm) == (float)0) return;
    else if((ft(xm)*ft(xl)) < (float)0) xh = xm;
    else if((ft(xm)*ft(xh)) < (float)0) xl = xm;
    else {
        println("Something worng --> cannot find the root.");
        return;
    }

    println("[Recursion " + h + "]: The root is " + xm + " <with error "+(xh-xl)+">"); 
    h++;
    if((xh - xl) <= e) return;
    else bisection(xl, xh, e);
}

void drawFunction() {
  float x=-1, y;
  
  y=ft(x);
  wv[0].set(x,y,0);
  sv[0]=World2Screen(wv[0]);  
  for(x=-3; x<5; x+=0.025) {
    y=ft(x);
    wv[1].set(x,y,0);
    sv[1]=World2Screen(wv[1]);  
    line(sv[0].x, sv[0].y, sv[1].x, sv[1].y);
    sv[0].set(sv[1].x, sv[1].y, 0);
  }
} 
 
void drawAxis() {
  
  sv[0]=World2Screen(wv[0]);  
  ellipse(sv[0].x, sv[0].y, 5, 5);
  text("O", sv[0].x-5, sv[0].y+10);

  wv[0].set(-3,0,0);
  wv[1].set(5,0,0);
  sv[0]=World2Screen(wv[0]);  
  sv[1]=World2Screen(wv[1]);  
  line(sv[0].x, sv[0].y, sv[1].x, sv[1].y);  
 
  wv[0].set(0,-1,0);
  wv[1].set(0,5,0);
  sv[0]=World2Screen(wv[0]);  
  sv[1]=World2Screen(wv[1]);  
  line(sv[0].x, sv[0].y, sv[1].x, sv[1].y);  

  for(int i=1; i<=5; i++) {
    wv[0].set(i,0,0);
    sv[0]=World2Screen(wv[0]);  
    line(sv[0].x, sv[0].y-5, sv[0].x, sv[0].y+5);
    text(i, sv[0].x, sv[0].y+15);
  }   
  for(int i=1; i<=5; i++) {
    wv[0].set(0,i,0);
    sv[0]=World2Screen(wv[0]);  
    line(sv[0].x-5, sv[0].y, sv[0].x+5, sv[0].y);
    text(i, sv[0].x-15, sv[0].y);
  }   
} 

float ft(float x)
{
  return log(x+5)+x;
}

float ft_prime(float x)
{
  return 1/(x+5)+1;
}

float ft_slope(float x1, float x2)
{
  return ((ft(x1)-ft(x2))/(x1-x2));
}