/**
 * Taylor 1
 *
 * Graphs of functions together with their Taylor polynomials.
 *
 * Matthew Conroy ( jumbo (at) madandmoonly com (you know where the dot goes))
 **/

HScrollbar hs1, hs2, hs3, hs4;

PImage top, bottom;         // Two image to load
int topWidth, bottomWidth;  // The width of the top and bottom images
float lasta, lastb; // to keep track of whether things have changed
int lastm;

float[] coeffs = new float[30]; //array for the coefficients of the taylor polynomials

void setup()
{
  size(700, 560);
  noStroke();
  //hs1 = new HScrollbar(0, height-80, width, 10, 3*5+1);
  //hs2 = new HScrollbar(0, height-60, width, 10, 3*5+1);
  hs3 = new HScrollbar(0, height-40, width, 10, 3*5+1,50);
  hs4 = new HScrollbar(0, height-20, width, 10, 3*5+1,0);


   PFont fontA = loadFont("CourierNew36.vlw");
   textFont(fontA, 18);
}

void draw()
{
  background(255);

  // Get the position of the top scrollbar
  // and convert to a value to display the top image
  //float Pos1 = hs1.getPos();
  //float Pos2 = hs2.getPos();
  float Pos3 = hs3.getPos();
  float Pos4 = hs4.getPos();

  float xx=0;
  float yy=0;
  float xxLast=0,yyLast=0,xx0=0,yy0=0;
  
  float scale=30.0;

 //  float a=0.+1.0*Pos1/width;
 //  float b=(Pos2/width-1./2.)*2*3.1415926535;

  int m = int(Pos3);
  int n = 1+int(Pos4/50);

  smooth();
  strokeWeight(1);
    
    //draw axes
    stroke(33);
    line(0,height/2,width,height/2);
    line(width/2,0,width/2,height);
    
    //draw sine curve
    int numPoints=1000;
    for(int i = 0; i<numPoints; ++i) {
        xx = width*i/numPoints;
        yy = height/2.-scale*sin((xx-width/2)/scale);
        stroke(77);
        if (i>0) {
          line(xx,yy,xxLast,yyLast);
        }
        else {
          xx0=xx;
          yy0=yy;
        }
        xxLast=xx;
        yyLast=yy;
    }

    // calculate taylor polynomial
    int i,j,i4=0, j4=0, fact=1;
    float xcalc=0.0, blah=1;
    float mm=(m-width/2)/scale;
    for(i = 0; i<=n; ++i) {
      i4=i % 4;
      if (i4==0) { coeffs[i] = sin(mm); }
      if (i4==1) { coeffs[i] = cos(mm); }
      if (i4==2) { coeffs[i] = -sin(mm); }
      if (i4==3) { coeffs[i] = -cos(mm); }
    }
    
    // draw taylor polynomial
    float ydiff=0;
    for(i = 0; i<numPoints; ++i) {
        xx=width*i/numPoints;
        xcalc = (xx-width/2)/scale;
        yy=height/2.-scale*coeffs[0];
        fact=1;
        blah=1.0;
        for (j=1; j<=n; ++j) {
          fact=fact*j;
          blah = blah * (xcalc-mm);
          yy=yy-scale*( coeffs[j]*blah/fact);        
        }
        //yy = yy-scale*ydiff;
        stroke(177,10,10);
        if (i>0) {
          line(xx,yy,xxLast,yyLast);
        }
        else {
          xx0=xx;
          yy0=yy;
        }
        xxLast=xx;
        yyLast=yy;
    }     
    
    //draw dot at center
    stroke(0);
    ellipse(m,height/2.-scale*sin((m-width/2.)/scale),4,4);

    //updatePixels();

    stroke(128);
    //hs1.update();
    //hs2.update();
    hs3.update();
    hs4.update();
    //hs1.draw();
    //hs2.draw();
    hs3.draw();
    hs4.draw();
  

  //words

   //text("a="+int(a*100)/100.+" b="+int(b*10)/10.+" m="+z1Fact+" n="+z2Fact,10,height-100);

     fill(0);
     //text("a="+int(100*a)/100.,10,height-100);
     //text("b="+int(100*b)/100.,10+width*0.25,height-100);
     text("b="+int(100*mm)/100.,10+width*0.5,height-60);
     text("n="+n,10+width*0.75,height-60);
     
    // lasta=a;
    // lastb=b;
    // lastm=m;
  //} // end of if things have changed
   
  
  //println(hs1.getPos());
}


class HScrollbar
{
  int swidth, sheight;    // width and height of bar
  int xpos, ypos;         // x and y position of bar
  float spos, newspos;    // x position of slider
  int sposMin, sposMax;   // max and min values of slider
  int loose;              // how loose/heavy
  boolean over;           // is the mouse over the slider?
  boolean locked;
  float ratio;

  HScrollbar (int xp, int yp, int sw, int sh, int l, int sposition) {
    swidth = sw;
    sheight = sh;
    int widthtoheight = sw - sh;
    ratio = (float)sw / (float)widthtoheight;
    xpos = xp;
    ypos = yp-sheight/2;
    // note the width and height of the slider are both sheight
    spos = xpos+sheight/2.+sposition/100.*(swidth-sheight)-sheight/2.;
    newspos = spos;
    sposMin = xpos;
    sposMax = xpos + swidth - sheight;
    loose = l;
  }

  void update() {
    if(over()) {
      over = true;
    } else {
      over = false;
    }
    if(mousePressed && over) {
      locked = true;
    }
    if(!mousePressed) {
      locked = false;
    }
    if(locked) {
      newspos = constrain(mouseX-sheight/2, sposMin, sposMax);
    }
    if(abs(newspos - spos) > 1) {
      spos = spos + (newspos-spos)/loose;
    }
  }

  int constrain(int val, int minv, int maxv) {
    return min(max(val, minv), maxv);
  }

  boolean over() {
    if(mouseX > xpos && mouseX < xpos+swidth &&
    mouseY > ypos && mouseY < ypos+sheight) {
      return true;
    } else {
      return false;
    }
  }

  void draw() {
    fill(255);
    rect(xpos, ypos, swidth, sheight);
    if(over || locked) {
      fill(128);
    } else {
      fill(0);
    }
    rect(spos, ypos, sheight, sheight);
  }

  float getPos() {
    // convert spos to be values between
    // 0 and the total width of the scrollbar
    return spos * ratio;
  }
}