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。

• 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