Complex Parabolas 3D - OpenProcessing

mySketch
Complex Free
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var complexRes = 40;  // How many program pixels there are on each side of the square (for a total of complexRes x complexRes pixels).
var squareSize = 12;  // Size of each program pixel in computer pixels.
var input;            // An array representing the complex point z(i,j) at the coordinates (i,j)
var output;           // An array representing the image f(z(i,j)) at the coordinate (i,j)  (computed at a given time t)
​
var mid = complexRes*squareSize/2;
​
var l1Size = 2;       // The source of the function f will be {z=a+bi | max(|a|,|b|)<l1Size}
​
var ii = [0,1];       // = sqrt(-1)
var zero = [0,0];     // = 0
​
var t=0;
var dt = Math.PI/30;
​
// rotation
var cameraHorAngle = Math.PI/10;  //full rotation
var cameraVerAngle = Math.PI/4; // should be in [-PI/2,PI/2]
var cameraDistance = 800;
​
var pause = false;
​
/**
 * Returns the value of the function f at the complex point z, at the real time t.
 */
function f(z, t){
  return addReal(mult(z,z), 2*Math.sin(t));  // z^2 + sin(t)
}
​
function setup() {
  createCanvas((complexRes-1)*squareSize, (complexRes-1)*squareSize, WEBGL);
  background(0);
  colorMode(HSB, 360, 100, 100)
  //normalize = range/complexRes;
  createComplexInput();
  initOutput();
  computeOutput(t);
  updateScreen();
  
  tx = -complexRes*squareSize/2;
  ty = -complexRes*squareSize/2;
}
​
//float[] mouse = new float[]{1,0};
function draw() { 
  
  background(0);
  updateScreen();
  cameraX = Math.sin(cameraHorAngle)*Math.cos(cameraVerAngle);
  cameraY = Math.cos(cameraHorAngle)*Math.cos(cameraVerAngle);
  cameraZ = Math.sin(cameraVerAngle);
  camera(cameraX*cameraDistance,cameraY*cameraDistance,cameraZ*cameraDistance,0,0,0,0,0,-1);
  if (pause){
    return;
  }
  computeOutput(t);
  t+=dt;
  
}
​
/**
 * Creates an input corresponding to the grid of pixels.
 */
function createComplexInput(){
  input = []
  for (let i=0; i<complexRes; i++){
    var innerInput = [];
    input.push(innerInput);
    for (let j=0; j<complexRes; j++){
      var a = (2*j/complexRes-1) * l1Size;
      var b = (2*i/complexRes-1) * l1Size;
      innerInput.push([a,b]);
    }
  }
}
​
/**
 * Initializes the output array.
 */
function initOutput(){
  output = [];
  for (let i=0; i<complexRes; i++){
    var innerOutput = [];
    output.push(innerOutput);
    for (let j=0; j<complexRes; j++){
      innerOutput.push(zero);
    }
  }
}
​
/**
 * Compute the output of f(z,t) at time t on the given input.
 */
function computeOutput(t){
  var result;
  for (let i=0; i<complexRes; i++){
    for (let j=0; j<complexRes; j++){
      result = f(input[i][j], t);
      if (result==null)
        result = zero;
      output[i][j] = result;
    }
  }
}
​
function complexToColor(z){
  // z = a+bi
  a = z[0];
  b = z[1];
  // polar coordinates
  var theta = atan2(b,a);
  var r = (a*a+b*b)*10;
  
  var tt = map(theta,-1*PI,PI,0,360);
  var rr = map(atan(r),0,PI/2,0,100);
  return color(tt,100,rr);
}
​
var drawReal = true;
​
function updateScreen(){
  drawComplexParabola();
  drawAxes();
  if (drawReal){
    drawRealParabola();
  }
}
​
function drawRealParabola(){
  stroke(255);
  noFill();
  strokeWeight(5);
  for (let i=1; i<complexRes; i++){
    beginShape();
    vertex(squareSize*(i-1)-mid, 0, -output[i-1][complexRes/2][0]*50);
    vertex(squareSize*(i)-mid, 0, -output[i][complexRes/2][0]*50);
    endShape();
  }
}
​
function drawComplexParabola(){
  noStroke();
  for (let i=1; i<complexRes; i++){
    for (let j=1; j<complexRes; j++){
      c = complexToColor(output[i][j]);
      fill(c);
      beginShape();
      vertex(squareSize*(i-1)-mid, squareSize*(j-1)-mid, complex_norm(output[i-1][j-1])*50);
      vertex(squareSize*(i)-mid, squareSize*(j-1)-mid, complex_norm(output[i][j-1])*50);
      vertex(squareSize*(i)-mid, squareSize*(j)-mid, complex_norm(output[i][j])*50);
      vertex(squareSize*(i-1)-mid, squareSize*(j)-mid, complex_norm(output[i-1][j])*50);
      endShape();
    }
  }
}
​
function drawAxes(){
  //fill(255);
  //strokeWeight(10);
  //rect(-1000,-squareSize,2000,2*squareSize);
  //rect(-squareSize,-1000,2*squareSize,2000);
  
  stroke(255);
  noFill();
  strokeWeight(5);
  beginShape();
  vertex(-1000,0,0);
  vertex(1000,0,0);
  endShape();
  beginShape();
  vertex(0,-1000,0);
  vertex(0,1000,0);
  endShape();
  
  strokeWeight(5);
  beginShape();
  vertex(0,0,-1000);
  vertex(0,0,1000);
  endShape();
}
​
function complex_norm(z){
  return Math.sqrt(z[0]*z[0] + z[1]*z[1]);
}
​
​
function keyPressed(){
  //print(key);
  if (key=='r'){
    drawReal = !drawReal;
    return;
  }
  if (key=='p'){
    pause = !pause;
    return;
  }
  if (key=='+'){
    cameraDistance -= 50;
    if (cameraDistance < 0){
      cameraDistance = 0;
    }
    return;
  }
  if (key=='-'){
    cameraDistance += 50;
    return;
  }
  if (key=='ArrowUp'){
    cameraVerAngle += Math.PI/20;
    if (cameraVerAngle>Math.PI/2){
      cameraVerAngle=Math.PI/2;
    }
    return;
  }
  if (key=='ArrowDown'){
    cameraVerAngle -= Math.PI/20;
    if (cameraVerAngle<-Math.PI/2){
      cameraVerAngle=-Math.PI/2;
    }
    return;
  }
  if (key=='ArrowLeft'){
    cameraHorAngle -= Math.PI/20;
    return;
  }
  if (key=='ArrowRight'){
    cameraHorAngle += Math.PI/20;
    return;
  }
}