Trigonometry & Random March 2, 2010

Trigonometry

Angles and Waves Angles can be measured in degrees or radians Pi is the ratio of the circumference of a circle to its diameter Angles can be converted from degrees to radians with radians() Angles can be converted from radians to degrees with degrees()

Sine

Sine Wave in Processing Angles are specified in radians in sin() and cos() functions size(700, 100); noStroke(); fill(0); float angle = 0.0; for (int x = 0; x <= width; x += 5) { float y = map(sin(angle), -1, 1, 2*height/3, height/3); rect(x, y, 2, 4); angle += PI/20.0; }

Following the sine void setup() { size(700, 100); ellipseMode(CENTER); fill(0); } float angle = 0.0; float time = 0; float yPos = 0; void draw() { background(255); yPos = map(sin(angle), -1, 1, 0.8*height, 0.2*height); ellipse(time, yPos, 20, 20); if (time>width) { time=0; time += 5; angle += PI/20.0;

In a spiral void setup() { size(200,200); noStroke(); smooth(); } float radius = 1.0; int deg = 0; float increment=random(20); void draw() { float angle = radians(deg); float x = width/2 + (cos(angle) * radius); float y = height/2 + (sin(angle) * radius); ellipse(x, y, 6, 6); deg += 11; if(radius>width/2+1) { radius=0; increment=random(20); radius = radius + 0.34;

Earth and Moon sort of void setup() { size(400,400); noStroke(); smooth(); ellipseMode(CENTER); } void drawBody(float angleRot, int radiusOrbit, int radiusDot) { float x = map(sin(angleRot), -1, 1, width/2-radiusOrbit, width/2+radiusOrbit) ; float y = map(cos(angleRot), -1, 1, width/2-radiusOrbit, width/2+radiusOrbit) ; ellipse(x, y, radiusDot, radiusDot) ; float angle = 0 ; void draw() { background(0) ; fill(0,255,0) ; drawBody(angle, width/10, width/10) ; fill(255,255,0) ; drawBody(angle+PI, 4*width/10, width/30) ; angle += 0.01 ;

Rotating Rectangles void drawBody(float angleRot, int radiusOrbit, int radiusDot) { int lowEnd = width/2-radiusOrbit ; int highEnd = width/2+radiusOrbit ; float x = map(sin(angleRot), -1, 1, lowEnd, highEnd) ; float y = map(cos(angleRot), -1, 1, lowEnd, highEnd) ; pushMatrix() ; translate(x, y) ; rotate(-angleRot) ; rect(0, 0, 2*radiusDot, radiusDot) ; popMatrix() ; } Be sure to add rectMode(CENTER) to setup()

Lab Exercise Fill the canvas with a regular, repeating pattern that uses the sine function.

Random Numbers Assume float f; To generate a pseudo random number between 0 and high and assign it to f f = random(high); To generate a pseudo random number between low and high f = random(low, high);

Printing Random Numbers for (int i=0; i<10; i++) { print(i + ". "); println(random(100)); } How do the print statements print and println differ? What’s the + inside of a print

Sample Code float f = random(5.2); // Assign f a float value from 0 to 5.2 int i = random(5.2); // ERROR! Can't assign a float to an int int j = (int)random(5.2); // Assign j an int value from 0 to 5

Perlin Noise A smoother noise void setup() { size(800,200); noStroke(); noiseSeed(0) ; fill(0) ; for (int x=0; x<width; x++) { float yN = noise(x*0.1) * 100 ; ellipse(x,yN, 5, 5) ; float yR = random(1.0) * 100 ; ellipse(x,yR+100, 5, 5) ; }

Noisy Mountains void setup() { size(800,200); background(0,0,200) ; noiseSeed(0) ; stroke(0, 150,0) ; for (int x=0; x<width; x++) { float yN = noise(x*0.01) * 150 ; line(x, yN, x, height) ; }

In-class Lab Modify the groundhog to be a bit more random or noisy Or modify anything else