# “Canvas animation every Monday” – wave motion

Time：2021-9-9

In the previous section, we introduced the contents of trigonometric functions in canvas animation and an arrow animation that rotates with the mouse. This section mainly introduces the waveform motion of trigonometric function. include:

1. Smooth motion

2. Linear motion

3. Pulse motion

### 1. Waveform of sin function

The waveform of sin function must be familiar to the young people. Its graph is as follows: If you want to get`sin`The value of the function between [0,2 π] can be estimated in this way in the case of discontinuity.

``````for(var angle=0; angle<Math.PI*2; angle+=0.1){
console.log(Math.sin(angle)); // Print the sin value corresponding to the angle
}``````

### 1. Smooth movement

First introduce`Math.sin(angle)`First application of——Smooth motion

Smoothing refers to a smooth motion state of an object. On the contrary, it is a mechanical and simple state from 0 to 1 and then to – 1 and 0. The smooth motion is closer to the natural motion state, which is similar to the left-right swing of water plants in the water flow. There is a change in speed in the swing process.

We use`Math.sin`The first motion that the function imitates is this motion similar to the swing of water and grass. In addition, because`sin`The value of the function is between [- 1,1]. So in the actual code, you need to multiply it by a larger value (that is, amplitude, you know) to make its swing look obvious. The swing of water grass is shown in the figure below,Online presentation address The specific codes are as follows

``````//Aquatic plants
function Aqu(color, num, amp){
this.startPoint = [];
this.endPointX = [];
this.endPointY = [];
this.amp = [];
this.beta = 0;
this.color = (color == undefined)?"#3b154e":color;
this.num = (num == undefined)?80:num;
}

Aqu.prototype.init = function(){
for(var i=0; i<this.num; i++){
this.startPoint[i] = Math.random()*20 + i*10;
this.endPointX[i] = this.startPoint[i];
this.endPointY[i] = canvas.height/1.5 - Math.random()*50;
this.amp[i] = Math.random()*10 + 40;
}
}

Aqu.prototype.draw = function(ctx){
ctx.save();
ctx.lineWidth = 14;
ctx.lineCap = "round";
ctx.globalAlpha = 0.8;
ctx.strokeStyle =this.color;

//Application of math.sin
this.beta += del*0.0012;
var l = Math.sin(this.beta);

for(var i=0; i<this.num; i++){
ctx.beginPath();
ctx.moveTo(this.startPoint[i], canvas.height);

//Periodically change the vertex x coordinate of aquatic plants
this.endPointX[i] = this.startPoint[i] + l*this.amp[i]

ctx.stroke();
}
ctx.restore();
}

var canvas = document.getElementById('canvas'),
ctx = canvas.getContext('2d');
canvas.height = 400;
canvas.width = 800;

//Example aquatic plants
var oAqu = new Aqu();
//Initialization
oAqu.init();

var oldTime = new Date().getTime(),
del = null, newTime = null;

(function drawFrmae(){
window.requestAnimationFrame(drawFrmae);
ctx.clearRect(0, 0, canvas.width, canvas.height);

newTime = new Date().getTime();
del = new Date().getTime() - oldTime;
oldTime = newTime;

oAqu.draw(ctx);
}())``````

Is it more fluent than mechanical addition and subtraction? Of course, you can also control the swing speed by changing the incremental angle value in math. Sin (this. Beta).

### 2. Linear motion

Linear motion is the simplest kind of motion. When an object moves in a certain direction at a uniform speed, it is linear motion. The principle is very simple. Please check the specific code`linear-vertical-motion.html`

``````<script>
var canvas = document.getElementById('canvas'),
context = canvas.getContext('2d');

var angle = 0,
range = 50,
xspeed = 1,
yspeed = 0.05;

var ball = new Ball();

(function drawFrame(){
window.requestAnimationFrame(drawFrame,canvas);
context.clearRect(0,0,canvas.width,canvas.height);

ball.x += xspeed; // Horizontal, moving horizontally along the x-axis

}
//Vertical, because the angle of the angle does not change, the ordinate remains unchanged
ball.y = canvas.height/2+Math.sin(angle)*range;

// angle += 0.05; // Uncomment and see what happens?
ball.draw(context);
})();
}
</script>``````

Actually, if you put`angle += 0.05`If you cancel the annotation, you will find that the trajectory of the ball is consistent with the image of sin function.

### 3. Pulse motion

In addition to the velocity acting on the object, the sin function can still act on the size change of the object. Pulse motion is the application of sin function to the change of object size. The specific code is as follows. Please check the detailed code`plusing-motion.html`

``````window.onload = function(){
var canvas = document.getElementById('canvas');
var context  = canvas.getContext('2d');

var angle = 0,
range = 0.5,
speed = 0.05,
centerScale = 1;

var ball = new Ball();
ball.x = canvas.width/2;
ball.y = canvas.height/2;

(function drawFrame(){
window.requestAnimationFrame(drawFrame,canvas);
context.clearRect(0,0,canvas.width,canvas.height);

//The change of sin value leads to the change of ball.scalex and ball.scaley attributes
ball.scaleX = ball.scaleY = centerScale + Math.sin(angle)*range;
angle += speed;

ball.draw(context);
})();
}``````

Therefore, you should know that in addition to the position attribute, we can also combine the sin function with other attributes to form different motion forms.

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