1. Trigonometry & Random
March 2, 2010

2. Trigonometry

3. 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()

4. Sine

5. 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; }

6. 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;

7. 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 ;

8. 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 ;

9. 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()

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

11. 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);

12. 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

13. 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

14. 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) ; }

15. 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) ; }

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