class Vec3D extends PVector { 

  public Vec3D() {
    super(0,0,0);  
  }

  public Vec3D(float x, float y, float z) {
    super(x,y,z);
  }

  public Vec3D(PVector old) {
    super(old.x, old.y, old.z);
  }

  public Vec3D cross(Vec3D p) {
    Vec3D r = new Vec3D(super.cross(p));
    return r;
  }


  public Vec3D normalized() {
    float mag = (float) Math.sqrt(x * x + y * y + z * z);
    if (mag > 0) {
      mag = 1f / mag;
      x *= mag;
      y *= mag;
      z *= mag;
    }
    return this;
  }
  
}

class VivianiCurve {

  int curve_length = 100; // number of points that represent the curve
  Vec3D points[];
  float a = 50;

  VivianiCurve(int l) {
    curve_length = l;
    points = new Vec3D[curve_length];
    sample();
  }

  void sample() {
    float theta = 0.1;
    float p = 2.4;
    float q = 1.6;
    float dt = ((TWO_PI) / 100)*3;

    for (int i=0; i<curve_length; i++) {
      points[i] = sample(theta);
      theta += dt; 
    }
  }
  
  float getPeriod()  {
    return TWO_PI*3;
  }

  Vec3D sample(float theta) {
    float x = a*(1+cos(theta));
    float y = a*sin(theta);
    float z = 2*a*sin( theta/2 );

    return new Vec3D(x,y,z);
  }

  Vec3D[] getPoints() {
    return points; 
  } 

  public Vec3D derivateI(float t) {
    Vec3D r = new Vec3D();
    r.x = - a * sin(t);
    r.y =  cos(t);
    r.z = a * cos( t/2 );
    return r;
  }

  public Vec3D derivateII(float t) {
    Vec3D r = new Vec3D();
    r.x = cos(t);
    r.y = - sin(t);
    r.z = - sin( t/2 );
    return r;
  }

  Vec3D getTangent(float t) {
    Vec3D tangentVector = derivateI(t);
    return tangentVector.normalized();
  }

  Vec3D getNormal(float t) {
    return getBinormal(t).cross(getTangent(t)).normalized();
  }

  Vec3D getBinormal(float t) {
    Vec3D derivataI = derivateI(t);
    Vec3D derivataII = derivateII(t);
    Vec3D binormalVector = derivataI.cross(derivataII);
    return binormalVector.normalized();
  }  
}

void drawFrenetFrame() {
  float t = map(mouseX, 0, width, 0, viviani.getPeriod());
  Vec3D point = viviani.sample(t);
  
  Vec3D temp = viviani.getTangent(t);
  drawVector(point.x, point.y, point.z, point.x+temp.x*10, point.y+temp.y*10, point.z+temp.z*10);
  
  temp = viviani.getBinormal(t);
  drawVector(point.x, point.y, point.z, point.x+temp.x*10, point.y+temp.y*10, point.z+temp.z*10);
  
  temp = viviani.getNormal(t);
  drawVector(point.x, point.y, point.z, point.x+temp.x*10, point.y+temp.y*10, point.z+temp.z*10);
}

void drawAxis() {
  stroke(150);
  drawVector(0,0,0, 10, 0, 0);
  stroke(150);
  beginShape();
  drawVector(0,0,0, 0, 10, 0);
  endShape();  
  stroke(150);
  beginShape();
  drawVector(0,0,0, 0, 0, 10);  
  endShape();
}

void drawVector(float v1x, float v1y, float v1z,float v2x, float v2y, float v2z) {
  beginShape();
  vertex(v1x,v1y,v1z);
  vertex(v2x,v2y,v2z);
  endShape();
}

void drawCurve(Vec3D points[]) {
  beginShape();
  for(int i=0; i<points.length; i++) {
    vertex(points[i].x, points[i].y, points[i].z);

  }

  endShape();
}

import processing.opengl.*;
import javax.media.opengl.*;

PFont font;
VivianiCurve viviani;

float rotx=0, roty=0, mX=0, mY=0;

void setup() {
  size(600,400, OPENGL);
  smooth();
  
  font = loadFont("font.vlw");
  textFont(font, 14);

  viviani = new VivianiCurve(100);
}

void draw() {

  background(230);  
  noFill();
  lights();

  stroke(80);
  fill(80);
 
  text("Viviani's curve."+
       "\n    move the mouse to change Frenet-frame position"+
       "\n    drag to rotate", 
       20, 20);

  translate(width/2, height/2);
  rotateX(rotx);
  rotateY(roty);

  drawAxis();

  stroke(80);
  noFill();
  drawCurve(viviani.getPoints());

  drawFrenetFrame();
}

void mousePressed() {
  mX = mouseX;
  mY = mouseY;
}

void mouseDragged() {
  rotx += (mY-mouseY) * 0.01;
  roty += (mX-mouseX) * 0.01;
  mousePressed();
}