Plotting (x,y,z) for helicoid

Processing Coding Questions
1

Hello,
I’m trying to render a helicoid in java by making an array list of vectors and then plotting the shape. Not entirely confident that my approach is a particularly good one but would appreciate any feedback and/or reason why the plots are so erratic.


import peasy.*;

ArrayList<PVector> points = new ArrayList<PVector>();
float p;
PeasyCam cam;

void setup() {
  size(800, 800, P3D);
  background(20);
  colorMode(HSB);
  //cam = new PeasyCam(this , 5000);
}

void draw() {
  noFill();
  stroke(200,180,200);
  strokeWeight(5);
  

  translate(width / 2, height / 2);

  points.add(new PVector(x(p++), y(p++), z(p++)));

  
  beginShape();
  for (PVector v : points) {
    vertex(v.x, v.y, v.z);
  }
  endShape();
  
}

// HELICOID

float x(float p) {
  return 100 * cos(p);
}

float y(float p) {
  return 200 * -sin(p);
}

float z(float p) {
  return 20 * pow(tan(PI/2 + p) , -1); // return p?
}

Many thanks,
Callum

1 Like
2

Hello !

And welcome to the processing forum. Nice to have you here!

I think to add 1 three times to the angle p was just to much (it’s in radians, not degree!).

And also the function z is problematic!

Warm regards,

Chrisir

Full Code




import peasy.*;

ArrayList<PVector> points = new ArrayList<PVector>();
float p;
PeasyCam cam;

void setup() {
  size(800, 800, P3D);
  background(20);
  colorMode(HSB);
  avoidClipping(); 
  cam = new PeasyCam(this, 5000);
}

void draw() {
  background(20);
  lights(); 

  points.add(new PVector(x(p), y(p), z(p)));
  p+=0.0521;

  showData();

  cam.beginHUD();
  fill(255);
  text("Helicoid. Use peasycam.", 19, 19); 
  cam.endHUD();
}

//---------------------------------------------------------------------------

void showData() {
  // show data in points

  noFill();
  stroke(200, 180, 200);
  strokeWeight(5);

  translate(width / 2, height / 2);

  beginShape();
  for (PVector v : points) {
    vertex(v.x, v.y, v.z);
  }
  endShape();
}

//---------------------------------------------------------------------------
// HELICOID

float x(float p) {
  return 100 * cos(p);
}

float y(float p) {
  return 200 * sin(p);
}

float z(float p) {
  // return 20 * pow(tan(PI/2 + p), -1); // return p?
  //return tan(PI/2 + p); // return p?
  return 10*p;
}

// --------------------------------------------------------------------------

void avoidClipping() {
  // avoid clipping :
  // https : //
  // forum.processing.org/two/discussion/4128/quick-q-how-close-is-too-close-why-when-do-3d-objects-disappear
  perspective(PI/3.0, (float) width/height, 1, 1000000);
}//func
//
1 Like
3

new version with a for-loop for the radius at each angle

I tried to close the plane nicely using TRIANGLE_STRIP but to no avail. Needs further work.

Cf. https://github.com/Kango/3DSketches/tree/master/Moebius4

see https://en.wikipedia.org/wiki/Helicoid



import peasy.*;

ArrayList<PVector> points = new ArrayList<PVector>();
float p;
PeasyCam cam;

int i;

void setup() {
  size(800, 800, P3D);
  background(20);
  colorMode(HSB);
  avoidClipping(); 
  cam = new PeasyCam(this, 5000);
}

void draw() {
  background(20);
  lights(); 

  for (i=20; i<100; i+=10) {
    points.add(new PVector(x(p), y(p), z(p)));
  }
  p+=0.0521;

  showData();

  cam.beginHUD();
  fill(255);
  text("Helicoid. Use peasycam.", 19, 19); 
  cam.endHUD();
}

//---------------------------------------------------------------------------

void showData() {
  // show data in points

  noFill();
  stroke(200, 180, 200);
  strokeWeight(5);

  translate(width / 2, height / 2);

  beginShape(TRIANGLE_STRIP);
  for (PVector v : points) {
    vertex(v.x, v.y, v.z);
  }
  endShape();
}

//---------------------------------------------------------------------------
// HELICOID

float x(float p) {
  return i * cos(p);
}

float y(float p) {
  return (i+100) * -sin(p);
}

float z(float p) {
  // return 20 * pow(tan(PI/2 + p), -1); // return p?
  //return tan(PI/2 + p); // return p?
  return 10*p;
}

// --------------------------------------------------------------------------

void avoidClipping() {
  // avoid clipping :
  // https : //
  // forum.processing.org/two/discussion/4128/quick-q-how-close-is-too-close-why-when-do-3d-objects-disappear
  perspective(PI/3.0, (float) width/height, 1, 1000000);
}//func
//
1 Like
4

ahh thank you! Wasn’t aware of the you could avoid clipping so cheers dude!
Hopefully I’ll be able to make a hyperbolic helicoid from here!

1 Like
5

p is in radians. I misspelled that. I corrected it now.

I also put lights() in.

It looked at this, but I couldn’t make it work, your z():

return 20 * pow(tan(PI/2 + p), -1); // return p?
6

Hello,

There are some references to clipping on the Processing site:

:)

3 Likes
7

I got my parametric equations from this site:
https://www.encyclopediaofmath.org/index.php/Helicoid

However most other sources suggest z = c * theta so I’m not sure what that expression particularly does.

2 Likes