1.
•
F = -kx
k
F = -kx
ma = -kx
x = -sin k t
m
x = Csin(!t + "
x

2.
springForce = -stiffness * stretch
springForce = -stiffness * (position - restPosition)

3.
•
springForce = stiffness * (restPositon -
position)
velocity = friction * (velocity + springFroce)

4.
float stiffness = 0.1; //
float damping = 0.9; //
float velocity = 0.0; //
float targetY; //
float y; //
void setup() {
size(400, 400);
noStroke();
}
void draw() {
fill(0, 12);
rect(0, 0, width, height);
fill(255);
float force = stiffness * (targetY - y); // f = -kx
velocity = damping * (velocity + force); //
y += velocity; //
rect(10, y, width - 20, 10); //
targetY = mouseY; // Y
}

5.
•
F = ma
a=F/m
acceleration = springForce / mass

6.
//2
float y1, y2; //
float velocity1, velocity2; //
float mass1 = 1.0; // 1
float mass2 = 6.0; // 2
float stiffness = 0.1; //
float damping = 0.9; //
void setup() {
size(400, 400);
noStroke();
}
void draw() {
fill(0, 12);
rect(0, 0, width, height);
fill(255);
float targetY = mouseY; //
// 1
float forceA = stiffness * (targetY - y1); //
float accelerationY1 = forceA / mass1; //
velocity1 = damping * (velocity1 + accelerationY1); //
y1 += velocity1; //

7.
rect(0, y1, width/2, 15);
// 2
float forceB = stiffness * (targetY - y2); //
float accelerationY2 = forceB / mass2; //
velocity2 = damping * (velocity2 + accelerationY2); //
y2 += velocity2; //
rect(width/2, y2, width/2, 15);
}

8.
float stiffness = 0.05;
float damping = 0.9;
float mass = 3.0;
float gravity = 0.0;
float velocityX = 0.0, velocityY = 0.0;
float targetX, targetY;
float x, y;
void setup() {
size(600, 600);
smooth();
}
void draw() {
background(0);
//X
float forceX = stiffness * (targetX - x);
float accelerationX = forceX / mass;
velocityX = damping * (velocityX + accelerationX);
x += velocityX;
//Y
float forceY = stiffness * (targetY - y);
forceY += gravity;
float accelerationY = forceY / mass;
velocityY = damping * (velocityY + accelerationY);
y += velocityY;

9.
//
noStroke();
fill(255);
ellipse(x, y, 40, 40);
//
stroke(127);
noFill();
line(mouseX, mouseY, x, y);
//
targetX = mouseX;
targetY = mouseY;
}

10.
//Spring2D
Spring2D s1, s2;
float gravity = 5.0;
float mass = 2.0;
void setup() {
size(400, 400);
smooth();
fill(0);
// x , y , ,
s1 = new Spring2D(0.0, width / 2, mass, gravity);
s2 = new Spring2D(0.0, width / 2, mass, gravity);
}
void draw() {
background(204);
s1.update(mouseX, mouseY);
s1.display(mouseX, mouseY);
s2.update(s1.x, s1.y);
s2.display(s1.x, s1.y);
}

11.
// class Spring2D
//
class Spring2D {
float vx, vy;
float x, y;
float gravity;
float mass;
float radius = 10;
float stiffness = 0.2;
float damping = 0.7;
//
Spring2D(float xpos, float ypos, float m, float g) {
x = xpos;
y = ypos;
mass = m;
gravity = g;
}
//
void update(float targetX, float targetY) {
float forceX = (targetX - x) * stiffness;
float ax = forceX / mass;
vx = damping * (vx + ax);
x += vx;
float forceY = (targetY - y) * stiffness;

12.
forceY += gravity;
float ay = forceY / mass;
vy = damping * (vy + ay);
y += vy;
}
//
void display(float nx, float ny) {
noStroke();
ellipse(x, y, radius*2, radius*2);
stroke(255);
line(x, y, nx, ny);
}
}

13.
//
int numSprings = 10; //
Spring2D[] s = new Spring2D[numSprings];
float gravity = 5.0;
float mass = 5.0;
float stiffness = 0.2;
float damping = 0.8;
void setup() {
size(600, 600);
smooth();
fill(0);
for (int i = 0; i < numSprings; i++) {
s[i] = new Spring2D(width / 2, i*(height / numSprings), mass, gravity,
stiffness, damping);
}
}
void draw() {
background(204);
s[0].update(mouseX, mouseY);
s[0].display(mouseX, mouseY);
for (int i = 1; i < numSprings; i++) {
s[i].update(s[i-1].x, s[i-1].y);
s[i].display(s[i-1].x, s[i-1].y);
}
}

14.
import traer.physics.*;
ParticleSystem physics;
Particle mouse;
Particle[] p;
Spring[] s;
void setup(){
size( 400, 400 );
smooth();
//Physics
physics = new ParticleSystem( 1.0, 0.05 );
p = new Particle[10];
s = new Spring[10];
//
for(int i = 0; i < p.length; i++){
p[i] = physics.makeParticle( 1.0, width/2, 20 * i, 0);
if(i > 0){
s[i] = physics.makeSpring( p[i], p[i-1], 1.0, 0.1, 20);
}
}
//
p[0].makeFixed();
}

15.
void draw(){
background(0);
physics.tick();
//
p[0].moveTo(mouseX, mouseY, 0);
//
for(int i = 0; i < p.length; i++){
noStroke();
fill(128);
ellipse( p[i].position().x(), p[i].position().y(), 10, 10 );
if(i > 0){
stroke(255);
line(p[i].position().x(), p[i].position().y(),
p[i-1].position().x(), p[i-1].position().y());
}
}
}

16.
p[0] p[1]
p[2]
p[3]
...
p[n]
p[1] p[2]
p[3]
p[4]
for(int i = 0; i < n; i++){
...
•
•
for(j = i + 1; j < n; j++){ p[n]
•
p[2] p[3]
•
} p[4]
•
} p[5]
...
...
p[n] p[n]

17.
import processing.opengl.*;
import traer.physics.*;
ParticleSystem physics;
Particle[] particles;
int num = 80;
void setup(){
size(800, 800, OPENGL );
fill(255);
smooth();
rectMode(CENTER);
physics = new ParticleSystem(0, 0.0);
particles = new Particle[num];
for (int i = 0; i < num; i++){
particles[i] = physics.makeParticle(0.2, random(width),
random(height), 0);
for (int j = i + 1; j < num; j++){
particles[j] = physics.makeParticle(0.2, random(width),
random(height), 0);
particles[j].setMass(0.5);
physics.makeSpring(particles[i], particles[j], 0.1, 0.0, width/2);
}
}
}

18.
void draw(){
physics.tick(0.01);
background(0);
for (int i = 0; i < num; i++){
rect(particles[i].position().x(), particles[i].position().y(), 8, 8);
}
}

19.
import processing.opengl.*;
import traer.physics.*;
ParticleSystem physics;
Particle[] particles;
int num = 80;
void setup(){
size(800, 800, OPENGL );
fill(255);
smooth();
rectMode(CENTER);
physics = new ParticleSystem(0, 0.0);
particles = new Particle[num];
for (int i = 0; i < num; i++){
particles[i] = physics.makeParticle(0.2, random(width),
random(height), 0);
for (int j = i + 1; j < num; j++){
particles[j] = physics.makeParticle(0.2, random(width),
random(height), 0);
particles[j].setMass(0.5);
physics.makeSpring(particles[i], particles[j], 0.1, 0.0, width/2);
}
}
}

20.
void draw(){
physics.tick(0.01);
background(0);
for (int i = 0; i < num; i++){
fill(255);
noStroke();
rect(particles[i].position().x(), particles[i].position().y(), 8, 8);
stroke(127,50);
//Spring line
for (int j = i + 1; j < num; j++){
line(particles[j].position().x(), particles[j].position().y(),
particles[i].position().x(), particles[i].position().y());
}
}
}

21.
import processing.opengl.*;
import traer.physics.*;
ParticleSystem physics;
Particle[] particles;
int num = 80;
void setup(){
size(800, 800, OPENGL );
fill(255);
smooth();
rectMode(CENTER);
physics = new ParticleSystem(0, 0.0);
particles = new Particle[num];
for (int i = 0; i < num; i++){
particles[i] = physics.makeParticle(0.2, random(width), random(height), 0);
for (int j = i + 1; j < num; j++){
particles[j]
= physics.makeParticle(0.2, random(width), random(height), 0);
particles[j].setMass(0.5);
physics.makeSpring(particles[i], particles[j], 0.1, 0.0, width/2);
}
}
}

22.
void draw(){
physics.tick(0.01);
background(0);
for (int i = 0; i < num; i++){
rect(particles[i].position().x(), particles[i].position().y(), 4, 4);
for (int j = i + 1; j < num; j++){
float l = dist(particles[j].position().x(),
particles[j].position().y(),
particles[i].position().x(),
particles[i].position().y());
stroke(255, 100 - l);
line(particles[j].position().x(),
particles[j].position().y(),
particles[i].position().x(),
particles[i].position().y());
}
}
}

23.
import processing.opengl.*;
import traer.physics.*;
ParticleSystem physics;
Particle[] particles;
int num = 80;
void setup(){
size(800, 800, OPENGL );
smooth();
fill(255);
rectMode(CENTER);
physics = new ParticleSystem(0, 0.0);
particles = new Particle[num];
for (int i = 0; i < num; i++){
particles[i] = physics.makeParticle(0.2, random(width), random(height), 0);
for (int j = i + 1; j < num; j++){
particles[j]
= physics.makeParticle(0.2, random(width), random(height), 0);
particles[j].setMass(0.5);
physics.makeAttraction(particles[i], particles[j], 1000, width);
}
}
}

24.
void draw(){
physics.tick(1);
background(0);
for (int i = 0; i < num; i++)
{
rect(particles[i].position().x(), particles[i].position().y(), 3, 3);
for (int j = i + 1; j < num; j++)
{
float l = dist(particles[j].position().x(),
particles[j].position().y(),
particles[i].position().x(),
particles[i].position().y());
stroke(255, 100 - l);
line(particles[j].position().x(),
particles[j].position().y(),
particles[i].position().x(),
particles[i].position().y());
}
}
}