Processing语言中的向量应用：Pvector

2022-04-10
在Processing语言中，提供了一种向量类，称作Pvector.
这个类中提供了若干种方法：部分方法的实现在代码本色书中有介绍。便于更深入理解其意义。

Methods

set()Set the components of the vector
random2D()Make a new 2D unit vector with a random direction
random3D()Make a new 3D unit vector with a random direction
fromAngle()Make a new 2D unit vector from an angle
copy()Get a copy of the vector
mag()Calculate the magnitude of the vector
magSq()Calculate the magnitude of the vector, squared
add()Adds x, y, and z components to a vector, one vector to another, or two independent vectors
sub()Subtract x, y, and z components from a vector, one vector from another, or two independent vectors
mult()Multiply a vector by a scalar
div()Divide a vector by a scalar
dist()Calculate the distance between two points
dot()Calculate the dot product of two vectors
cross()Calculate and return the cross product
normalize()Normalize the vector to a length of 1
limit()Limit the magnitude of the vector
setMag()Set the magnitude of the vector
heading()Calculate the angle of rotation for this vector
rotate()Rotate the vector by an angle (2D only)
lerp()Linear interpolate the vector to another vector
angleBetween()Calculate and return the angle between two vectors
array()Return a representation of the vector as a float array

以下是向量做加法的示例：
需要注意的是，向量不可以直接用+、-这样的符号运算。而是需要内置的相关方法。

PVector v1, v2;

void setup() {
  noLoop();
  v1 = new PVector(40, 20);
  v2 = new PVector(25, 50); 
}

void draw() {
  ellipse(v1.x, v1.y, 12, 12);
  ellipse(v2.x, v2.y, 12, 12);
  v2.add(v1);
  ellipse(v2.x, v2.y, 24, 24);
}

image.png

注释2：
在代码本色一书中，使用Pvector类来实现物理的移动，就是设计了具有二维位置、具有二维方向的速度和加速度。

基本的知识：速度由加速度累加而得，移动距离即最终位置由速度累加而得。是积分的概念。

例程的运行效果是使圆形跟随鼠标运动。
注释3：
这小圆形在鼠标静止时一直在运动。并未停下来。这个是什么原因？
需思考。

image.png

程序首先使用Pvector定义了一个Mover类：
初始位置在窗口中心，速度为0，并设计了速度上限。否则因为具有加速度，速度会一直增加。

// The Nature of Code
// Daniel Shiffman
// http://natureofcode.com

class Mover {

  // The Mover tracks position, velocity, and acceleration 
  PVector position;
  PVector velocity;
  PVector acceleration;
  // The Mover's maximum speed
  float topspeed;

  Mover() {
    // Start in the center
    position = new PVector(width/2,height/2);
    velocity = new PVector(0,0);
    topspeed = 5;
  }

  void update() {
    
    // Compute a vector that points from position to mouse
    PVector mouse = new PVector(mouseX,mouseY);
    PVector acceleration = PVector.sub(mouse,position);
    // Set magnitude of acceleration
    acceleration.setMag(0.2);
    
    // Velocity changes according to acceleration
    velocity.add(acceleration);
    // Limit the velocity by topspeed
    velocity.limit(topspeed);
    // position changes by velocity
    position.add(velocity);
  }

  void display() {
    stroke(0);
    strokeWeight(2);
    fill(127);
    ellipse(position.x,position.y,48,48);
  }

}

主程序比较简洁：

// The Nature of Code
// Daniel Shiffman
// http://natureofcode.com

// A Mover object
Mover mover;

void setup() {
  size(640,360);
  mover = new Mover(); 
}

void draw() {
  background(255);
  
  // Update the position
  mover.update();
  // Display the Mover
  mover.display(); 
}

Processing语言中的向量应用：Pvector

Methods

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