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https://github.com/terkelg/math

Math snippets with graphic programming in mind.
https://github.com/terkelg/math

math math-snippets spring velocity

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Math snippets with graphic programming in mind.

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README 

        
# Math Snippets

> Math snippets with graphic programming in mind.



This is work in progress.

**To-do:**

- [ ] Convert all snippets to JS (Some are Action Script)

- [ ] Add live code examples

- [ ] Add simple desciptions



## Contents

 - [Snippets](https://github.com/terkelg/math/blob/master/README.md#snippets)

	- [Radias & Degrees](https://github.com/terkelg/math#radians--degrees)

	- [Calculate side lengths](https://github.com/terkelg/math#calculate-side-lengths)

	- [Rotate a 2D point](https://github.com/terkelg/math#rotate-a-2d-point)

	- [Linear distance bwetween 2 points](https://github.com/terkelg/math#linear-distance-2-points)

	- [Linear distance between 2 vectors](https://github.com/terkelg/math#linear-distance-between-2-vectors)

	- [Length of a vector (Magnitude)](https://github.com/terkelg/math#length-of-a-vector)

	- [Add and substract vectors](https://github.com/terkelg/math#add-and-substract-vectors)

	- [Normalize vector](https://github.com/terkelg/math#normalize-vector)

	- [Dot product vectors](https://github.com/terkelg/math#dot-product-vectors)

	- [Finding angle between 2 points](https://github.com/terkelg/math#finding-angle-between-2-points)

	- [Finding angle between 2 vectors](https://github.com/terkelg/math#finding-angle-between-2-vectors)

	- [Cross Product](https://github.com/terkelg/math#cross-product)

	- [Rotate to the mouse (or any point)](https://github.com/terkelg/math#rotate-to-the-mouse-or-any-point)

	- [Create waves](https://github.com/terkelg/math#create-waves)

	- [Hex to decimal](https://github.com/terkelg/math#hex-to-decimal)

	- [Decimal to hex](https://github.com/terkelg/math#decimal-to-hex)

	- [Combine component colors](https://github.com/terkelg/math#combine-component-colors)

	- [Extract component colors](https://github.com/terkelg/math#extract-component-colors)

	- [Draw a curve through a point](https://github.com/terkelg/math#draw-a-curve-through-a-point)

	- [Convert angular velocity to x, y velocity](https://github.com/terkelg/math#convert-angular-velocity-to-x-y-velocity)

	- [Convert angular acceleration or any other force to x and y](https://github.com/terkelg/math#convert-angular-acceleration-or-any-other-force-to-x-and-y)

	- [Add acceleration to velocity](https://github.com/terkelg/math#add-acceleration-to-velocity)

	- [Add velocity to position](https://github.com/terkelg/math#add-velocity-to-position)

	- [Testing for out of bound](https://github.com/terkelg/math#testing-for-out-of-bound)

	- [Apply friction (correct way)](https://github.com/terkelg/math#apply-friction-correct-way)

	- [Apply friction (the easy way)](https://github.com/terkelg/math#apply-friction-the-easy-way)

	- [Simple easing, long form](https://github.com/terkelg/math#simple-easing-long-form)

	- [Simple easing, abbreviated form](https://github.com/terkelg/math#simple-easing-abbreviated-form)

	- [Simple easing, short form](https://github.com/terkelg/math#simple-easing-short-form)

	- [Simple spring, long form](https://github.com/terkelg/math#simple-spring-long-form)

	- [Simple spring, abbreviated form](https://github.com/terkelg/math#simple-spring-abbreviated-form)

	- [Simple spring, short form](https://github.com/terkelg/math#simple-spring-short-form)

	- [Offset spring](https://github.com/terkelg/math#offset-spring)

	- [Distance-based collision detection](https://github.com/terkelg/math#distance-based-collision-detection)

	- [Multiple-objects collision detection](https://github.com/terkelg/math#multiple-objects-collision-detection)

	- [Coordinate rotation](https://github.com/terkelg/math#coordinate-rotation)

	- [Reverse coordiante rotation](https://github.com/terkelg/math#reverse-coordiante-rotation)

	- [Conservation of momentum in ActionScript (with a shortcut)](https://github.com/terkelg/math#conservation-of-momentum-in-actionscript-with-a-shortcut)

	- [Gravity implementation](https://github.com/terkelg/math#gravity-implementation)

 - [Resources](https://github.com/terkelg/math#resources)



## Snippets



### Radians & Degrees



```

radians = degrees * Math.PI / 180;

degrees = radians * 180 / Math.PI;

```



```js

// JavaScript

var angleInDegrees = 45;

var radians = angleInDegrees * Math.PI / 180;

var backToDegrees = radians * 180 / Math.PI;

```



### Calculate side lengths

#### SOHCAHTOA



###### Calculate basic trigonometric functions

```

Sine of an angle = opposite / hypotenuse

Cosine of an angle = adjacent / hypotenuse

Tangent of angle = opposite / adjacent

```



```js

// Javascript

var hyp = 100;

var angleDegrees = 45;

var angleRadians = angleDegrees * Math.PI / 180;



var opposite = Math.sin( angleRadians ) * hyp;

var adjacent = Math.cos( angleRadians ) * hyp;

var tangent  = opposite / adjacent;

```



### Rotate a 2D point

```js

var vec2 = {x: 2, y: 3};

var rotatedVector = rotate2D(vec2, angle);



function rotate2D(vector, angle)

{

	var theta = angle * Math.PI / 180; // radians

	var matrix = [  Math.cos(theta),  Math.sin(theta), 

					-Math.sin(theta), Math.cos(theta)

					];

					

	return { 

		x: matrix[0] * vector.x + matrix[1] * vector.y, 

		y: matrix[2] * vector.x + matrix[3] * vector.y

	};

}



```



### Linear distance between 2 points

```

dx = x2 - x1;

dy = y2 - y1;

dist = Math.sqrt(dx*dx + dy*dy);

```



```js

// JavaScript

var x1 = 3;

var x2 = 5;

var distance = x2 — x1;

```



### Linear distance between 2 vectors

#### a² + b² = c²



```js

// Javascript

var v1 = {x: 4, y: -9};

var v2 = {x: 5, y: 15};



var distance = Math.sqrt( Math.pow((v2.x — v1.x), 2) + Math.pow((v2.y — v1.y), 2) );

```



### Length of a vector

#### Magnitude 



```js

// Javascript

// 2D -> hypotenuse

var v = {x: 4, y:-9};

var length = Math.sqrt( (Math.pow(v.x, 2) + Math.pow(v.y, 2)) );



// 3D

var v = {x: 4, y:-9, z: 0.5};

var length = Math.sqrt( (Math.pow(v.x, 2) + Math.pow(v.y, 2) + Math.pow(v.z, 2) ));

```



### Add and substract vectors



```js

var v1 = {x: 2, y: 3};

var v2 = {x: 2, y: -2};

var addedVec = {x: v1.x + v2.x, y: v1.y + v2.y};

var subVec = {x: v1.x - v2.x, y: v1.y - v2.y};

```



### Normalize vector



```js

// Javascript

// 2D

var v = {x: 4, y:-9};

var length = Math.sqrt( (Math.pow(v.x, 2) + Math.pow(v.y,2)) );

var n = {x: v.x / length, y: v.y / length};



// 3D

var v = {x: 4, y:-9, z: 3};

var length = Math.sqrt( Math.pow(v.x, 2) + Math.pow(v.y,2) + Math.pow(v.z,2) );

var n = {x: v.x / length, y: v.y / length, z: v.z / length};

```



### Dot product vectors



```js

// Javascript

var v1 = {x: 4, y: 5, z: 9};

var v2 = {x: 5, y: 9, z: -5};

var dot = (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z);

```



### Finding angle between 2 points



```js

//Javascript

var x = -3;

var y = -2;

var radians = Math.atan2(x, y);

var degrees = radians * 180 / Math.PI;

```



### Finding angle between 2 vectors



```js

// Javascript

var v1 = {x: 4, y: 5, z: 9};

var v2 = {x: 5, y: 9, z: -5};

var dot = (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z);



var lengthv1 = length(v1); // see length

var lengthv2 = length(v2); // see length



var radians = Math.acos(dot / (lengthv1 * lengthv2));

var angle = radians * 180 / Math.PI;

```



### Cross Product



```js

// Javascript

var v1 = {x: 1, y: 2, z: 3};

var v2 = {x: 3, y: 2, z: 1};

var cross = {

	x: v1.y*v2.z - v1.z*v2.y, 

	y: v1.z*v2.x - v1.x*v2.z, 

	z: v1.x*v2.y - v1.y*v2.x

};

```



### Rotate to the mouse (or any point)

```js

var dx = mouseX - spriteX;

var dy = mouseY - spriteY;

sprite.rotation = Math.atan2(dy, dx) * 180 / Math.PI;

```



### Create waves

```js

// value can be properties like x, y, alpha, rotation etc.

public function onEnterFrame(event:Event) {

  value = center + Math.sin(angle) * range;

  angle += speed;

}

```



### Hex to decimal

```

trace(hexValue);

```



### Decimal to hex

```

trace(decimalValue.toString(16));

```



### Combine component colors

```

color24 = red << 16 | green << 8 | blue;

color32 = alpha << 24 | red << 16 | green << 8 | blue;

```



### Extract component colors

```

red = color24 >> 16;

green = color24 >> 8 & 0xFF;

blue = color24 & 0xFF;



alpha = color32 >> 24;

red = color24 >> 16 & 0xFF;

green = color24 >> 8 & 0xFF;

blue = color24 & 0xFF;

```



### Draw a curve through a point

```

//xt, yt is the point to draw through

// x0, y0, x2, y2 is the end points

x1 = xt * 2 - (x0 - x2) / 2;

y1 = yt * 2 - (y0 - y2) / 2;

moveTo(x0, y0);

curveTo(x1, y1, x2, y2);

```



### Convert angular velocity to x, y velocity

```

vx = Math.cos(angle) * speed;

vy = Math.sin(angle) * speed;

```



### Convert angular acceleration or any other force to x and y

```

ax = Math.cos(angle) * force;

ay = Math.sin(angle) * force;

```



### Add acceleration to velocity

```

vx += ax;

vy += ay;

```



### Add velocity to position

```

sprite.x += vx;

sprite.y += vy;

```



### Testing for out of bound

```

if(sprite.x - sprite.width / 2 > right) ||

  sprite.x - sprite.width / 2 < left ||

  sprite.y - sprite.height / 2 > bottom ||

  sprite.y - sprite.height / 2 < top)

{

  //remove or reposition sprite

}

```



### Apply friction (correct way)

```

speed = Math.sqrt(vx*vx + vy*vy);

angle = Math.atan2(vy, vx);

if(speed > friction)

{

  speed -= friction;

} else {

  speed = 0;

}

vx = Math.cos(angle) * speed;

vy = Math.sin(angle) * speed;

```



### Apply friction (the easy way)

```

vx *= friction;

vy *= friction;

```



### Simple easing, long form

```

var dx = targetX - sprite.x;

var dy = targetY - sprite.y;

vx = dx * easing;

vy = dy * easing;

sprite.x += vx;

sprite.y += vy;

```



### Simple easing, abbreviated form

```

vx = (targetX - sprite.x) * easing;

vy = (targetY - sprite.y) * easing;

sprite.x += vx;

sprite.y += vy;

```



### Simple easing, short form

```

sprite.x += (targetX - sprite.x) * easing;

sprite.y += (targetY - sprite.y) * easing;

```



### Simple spring, long form

```

var ax = (targetX - sprite.x) * spring;

var ay = (targetY - sprite.y) * spring;

vx += ax;

vy += ay;

vx *= friction;

vy *= friction;

sprite.x += vx;

sprite.y += vy;

```



### Simple spring, abbreviated form

```

vx = (targetX - sprite.x) * spring;

vy = (targetY - sprite.y) * spring;

vx *= friction;

vy *= friction;

sprite.x += vx;

sprite.y += vy;

```



### Simple spring, short form

```

vx = (targetX - sprite.x) * spring;

vy = (targetY - sprite.y) * spring;

sprite.x += (vx *= friction);

sprite.y += (vy *= friction);

```



### Offset spring

```

var dx = sprite.x - fixedX;

var dy = sprite.y - fixedY;

var angle = Math.atan2(dy, dx);

var targetX = fixedX + Math.cos(angle) * springLength;

var targetY = fixedY + Math.sin(angle) * springLength;

// Spring to targetX and targetY;

```



### Distance-based collision detection

```

// Starting with spriteA and spriteB

// If using a plain sprite, or obejct without a radius property

// you can use with and height divided by 2



var dx = spriteB.x - spriteA.x;

var dy = spriteB.y - spriteA.y;

var dist = Math.sqrt(dx*dx + dy*dy);

if(dist < spriteA.radius + spriteB.radius)

{

  // handle collision

}

```



### Multiple-objects collision detection

```

var numObjects = 10;

for (var i = 0; i < numObjects; i++)

{

  var objectA = objects[i];

  for (var j = i+1; j < numObjects; j++)

  {

    var objectB = objects[j];

    // perform collision detection

    // between objectA and objectB

  }

}

```



### Coordinate rotation

```

x1 = Math.cos(angle) * x - Math.sin(angle) * y;

y1 = Math.cos(angle) * y + Math.sin(angle) * x;

```



### Reverse coordiante rotation

```

x1 = Math.cos(angle) * x + Math.sin(angle) * y;

y1 = Math.cos(angle) * y - Math.sin(angle) * x;

```



### Conservation of momentum in ActionScript (with a shortcut)

```js

var vxTotal = vx0 - vx1;

vx0 = ((ball0.mass - ball1.mass) * vx0 + 2 * ball1.mass * vx1) / (ball0.mass + ball1.mass);

vx1 = vxTotal + vx0;

```



### Gravity implementation

```js

function gravitate(partA, partB) {

  var dx = partB.x - partA.x;

  var dy = partB.y - partA.y;

  var distSQ  = dx*dx + dy*dy;

  var dist = Math.sqrt(distSQ);

  var force = partA.mass * partB.mass / distSQ;

  var ax = force * dx / dist;

  var ay = force * dy / dist;

  partA.vx += ax / partA.mass;

  partA.vy += ay / partA.mass;

  partB.vx += ax / partB.mass;

  partB.vy += ay / partB.mass;

}

```



# Resources

- [Coding Math](https://www.youtube.com/channel/UCF6F8LdCSWlRwQm_hfA2bcQ) ([Github](https://github.com/bit101/codingmath))

- [Generative Art by Matt Pearson](https://www.manning.com/books/generative-art)

- [Math as code](https://github.com/Jam3/math-as-code)

- [BetterExplained.com](http://betterexplained.com/)

- [Essence of linear algebra](https://www.youtube.com/watch?v=kjBOesZCoqc)