书名：代码本色：用编程模拟自然系统
作者：Daniel Shiffman
译者：周晗彬
ISBN：978-7-115-36947-5
第6章目录
6.13 群集
1、群集行为
- 群集是动物的群体性行为，许多生物都有这种特性，比如鸟类、鱼类和昆虫。1986年，Craig Reynolds用计算机模拟了群集行为，并将算法写在自己的论文中。
2、群集行为的模拟：
- 1.我们会用转向力计算公式（转向力 = 所需速度 - 当前速度）实现群集的规则。
- 2.这些转向力将由群体行为产生，小车要根据所有其他小车的状态计算转向力。
- 3.我们需要结合多个转向力，并对它们进行加权。
- 4.模拟结果是一个复杂系统——智能的群体行为将从简单的群集规则中产生，系统中没有控制中心和领导者。
我们已经完成了前3点，本节的重心在于把它们结合在一起，观察最后的运行结果。
3、群集的3个规则。
- 1.分离（又叫“躲避”） 避免与邻居发生碰撞。
- 2.对齐（又叫“复制”） 转向力的方向和邻居保持一致。
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3.聚集（又叫“集中”） 朝着邻居的中心转向（留在群体内）。
4、Boid对象
Boid对象描述群集系统中的元素，我们希望Boid对象也有一个函数管理所有上述行为，我们把这个函数称为flock()函数。
void flock(ArrayList<Boid> boids) {
PVector sep = separate(boids); 3种群集规则
PVector ali = align(boids);
PVector coh = cohesion(boids);
sep.mult(1.5); 3种转向力的权重（尝试使用不同的值！）
ali.mult(1.0);
coh.mult(1.0);
applyForce(sep); 施加转向力
applyForce(ali);
applyForce(coh);
}
5、示例
示例代码6-9 群集
Flock flock;
void setup() {
size(640,360);
flock = new Flock();
// Add an initial set of boids into the system
for (int i = 0; i < 200; i++) {
Boid b = new Boid(width/2,height/2);
flock.addBoid(b);
}
}
void draw() {
background(255);
flock.run();
// Instructions
fill(0);
text("Drag the mouse to generate new boids.",10,height-16);
}
// Add a new boid into the System
void mouseDragged() {
flock.addBoid(new Boid(mouseX,mouseY));
}
Flock .pde
class Flock {
ArrayList<Boid> boids; // An ArrayList for all the boids
Flock() {
boids = new ArrayList<Boid>(); // Initialize the ArrayList
}
void run() {
for (Boid b : boids) {
b.run(boids); // Passing the entire list of boids to each boid individually
}
}
void addBoid(Boid b) {
boids.add(b);
}
}
Boid.pde
class Boid {
PVector position;
PVector velocity;
PVector acceleration;
float r;
float maxforce; // Maximum steering force
float maxspeed; // Maximum speed
Boid(float x, float y) {
acceleration = new PVector(0,0);
velocity = new PVector(random(-1,1),random(-1,1));
position = new PVector(x,y);
r = 3.0;
maxspeed = 3;
maxforce = 0.05;
}
void run(ArrayList<Boid> boids) {
flock(boids);
update();
borders();
render();
}
void applyForce(PVector force) {
// We could add mass here if we want A = F / M
acceleration.add(force);
}
// We accumulate a new acceleration each time based on three rules
void flock(ArrayList<Boid> boids) {
PVector sep = separate(boids); // Separation
PVector ali = align(boids); // Alignment
PVector coh = cohesion(boids); // Cohesion
// Arbitrarily weight these forces
sep.mult(1.5);
ali.mult(1.0);
coh.mult(1.0);
// Add the force vectors to acceleration
applyForce(sep);
applyForce(ali);
applyForce(coh);
}
// Method to update position
void update() {
// Update velocity
velocity.add(acceleration);
// Limit speed
velocity.limit(maxspeed);
position.add(velocity);
// Reset accelertion to 0 each cycle
acceleration.mult(0);
}
// A method that calculates and applies a steering force towards a target
// STEER = DESIRED MINUS VELOCITY
PVector seek(PVector target) {
PVector desired = PVector.sub(target,position); // A vector pointing from the position to the target
// Normalize desired and scale to maximum speed
desired.normalize();
desired.mult(maxspeed);
// Steering = Desired minus Velocity
PVector steer = PVector.sub(desired,velocity);
steer.limit(maxforce); // Limit to maximum steering force
return steer;
}
void render() {
// Draw a triangle rotated in the direction of velocity
float theta = velocity.heading2D() + radians(90);
fill(175);
stroke(0);
pushMatrix();
translate(position.x,position.y);
rotate(theta);
beginShape(TRIANGLES);
vertex(0, -r*2);
vertex(-r, r*2);
vertex(r, r*2);
endShape();
popMatrix();
}
// Wraparound
void borders() {
if (position.x < -r) position.x = width+r;
if (position.y < -r) position.y = height+r;
if (position.x > width+r) position.x = -r;
if (position.y > height+r) position.y = -r;
}
// Separation
// Method checks for nearby boids and steers away
PVector separate (ArrayList<Boid> boids) {
float desiredseparation = 25.0f;
PVector steer = new PVector(0,0,0);
int count = 0;
// For every boid in the system, check if it's too close
for (Boid other : boids) {
float d = PVector.dist(position,other.position);
// If the distance is greater than 0 and less than an arbitrary amount (0 when you are yourself)
if ((d > 0) && (d < desiredseparation)) {
// Calculate vector pointing away from neighbor
PVector diff = PVector.sub(position,other.position);
diff.normalize();
diff.div(d); // Weight by distance
steer.add(diff);
count++; // Keep track of how many
}
}
// Average -- divide by how many
if (count > 0) {
steer.div((float)count);
}
// As long as the vector is greater than 0
if (steer.mag() > 0) {
// Implement Reynolds: Steering = Desired - Velocity
steer.normalize();
steer.mult(maxspeed);
steer.sub(velocity);
steer.limit(maxforce);
}
return steer;
}
// Alignment
// For every nearby boid in the system, calculate the average velocity
PVector align (ArrayList<Boid> boids) {
float neighbordist = 50;
PVector sum = new PVector(0,0);
int count = 0;
for (Boid other : boids) {
float d = PVector.dist(position,other.position);
if ((d > 0) && (d < neighbordist)) {
sum.add(other.velocity);
count++;
}
}
if (count > 0) {
sum.div((float)count);
sum.normalize();
sum.mult(maxspeed);
PVector steer = PVector.sub(sum,velocity);
steer.limit(maxforce);
return steer;
} else {
return new PVector(0,0);
}
}
// Cohesion
// For the average position (i.e. center) of all nearby boids, calculate steering vector towards that position
PVector cohesion (ArrayList<Boid> boids) {
float neighbordist = 50;
PVector sum = new PVector(0,0); // Start with empty vector to accumulate all positions
int count = 0;
for (Boid other : boids) {
float d = PVector.dist(position,other.position);
if ((d > 0) && (d < neighbordist)) {
sum.add(other.position); // Add position
count++;
}
}
if (count > 0) {
sum.div(count);
return seek(sum); // Steer towards the position
} else {
return new PVector(0,0);
}
}
}
6、运行结果
