Trigonometry for Designers (Don't Panic!)

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Description

See trig sketch in action

Trigonometry is the secret weapon of many top creative coders. Unfortunately for many designers, though, it was never taught in a visual or interactive way. We try and fix that with this whirlwind tour of the key concepts of SIN and COS and how we can use them to generate circles, spirals and patterns. We also introduce more advanced rendering concepts by introducing pushMatrix() and popMatrix() for handling rotation and scale of our visual elements. We finish off the lesson with an sketch that explores the Golden Ratio.

To follow along in Visual Studio, please download the Processing Sketchbook projection.

The finished sketch for this lesson can be found below:

float ToRadians = PI / 180.0;
float gAngle = 137.5077640844293;
float rotation = 0.0;
float initialRotation = 0.0;
int width, height;
int totalPetals = 300;
Petal[] petals = new Petal[totalPetals];
float radiusGrowth = 1.0049;
float radius = 60;
 
void setup() {
    width = 500;
    height = 550;
    size(width, height);
    noStroke();
    smooth();
    background(0);
    for (int i = 0; i < totalPetals; i++) {
        rotation += gAngle;
        radius *= radiusGrowth;
        Petal petal = new Petal();
        petal.x = width / 2 + cos(rotation * ToRadians) * radius;
        petal.y = height / 2 + sin(rotation * ToRadians) * radius;
        petal.rotation = rotation * ToRadians;
        petal.scale += (i * 2) / totalPetals;
        petal.render();
        petals[i] = petal;
    }
};
 
class Petal {
  float x = 0.0;
  float y = 0.0;
  float rotation = 0.0;
  float scaleVar = 1;
  color baseColor = color(0, 255, 255, 150);   
  color detailColor = color(255, 255, 255, 160);
  color trimColor = color(0, 0, 0);
  void render (){
      pushMatrix();
      translate(this.x, this.y);
      fill(this.baseColor);
      rotate(this.rotation);
      scale(this.scaleVar, this.scaleVar);
      rect(-10, -1, 20, 2);
      ellipse(0, 0, 10, 10);
      fill(this.detailColor);
      ellipse(0, 0, 8, 8);
      fill(this.trimColor);
      ellipse(0, 0, 5, 5);
      popMatrix();
  }
}

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The Discussion

  • User profile image
    rapuke

    Is it possible to bring data from within the Java Script say from a db into Processing?

  • User profile image
    mrpaulb

    That was perfect refresher, great example and top quality presentation. 

    Many thanks

    Paul

  • User profile image
    mk1234

    Enjoying the series but have a question - why do you pronounce
    height the way you do (with a 'th' on the end) as opposed to 'hite'?

    I'm curious.

  • User profile image
    rbarraza

    LOL. Never even noticed that. I DO always say "width and heigh(th)". Totally understand how that could be annoying. Like hearing people say "nuculer", right? I'll try and work on it Wink

  • User profile image
    tomkirbygre​en

    Terrific series. I like to see more coverage of the fundamental maths for 2D graphics.

  • User profile image
    pavan

    Great series.. I would like to see more series.. Thanks for this series..!

  • User profile image
    Zapp

    I totally agree. Enjoyed this alot. Please do another :D

  • User profile image
    Craig

    Really nice presentation!

    Thanks!

  • User profile image
    Nicolas Carlo

    Again, thanks a lot for these videos. One of the best, if not the best, presentations of what the deal is with cos and sin functions.

    Processing comes with a radians() function by the way that helps you convert degrees to radians. And a degrees() function that does the opposite.

  • User profile image
    John Montgomery

    A stimulating tutorial - made me fire up Processing again.
    Much thanks.

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