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` ````
```

` ````
@import compass
html, body
background: #1b1b1b
overflow: hidden
```

` ````
###
Demonstrates collision detection between convex and non-convex polygons
and how to detect whether a point vector is contained within a polygon
Possible techniques:
x Bounding box or radii
Inacurate for complex polygons
x SAT (Separating Axis Theorem)
Only handles convex polygons, so non-convex polygons must be subdivided
x Collision canvas. Draw polygon A then polygon B using `source-in`
Slow since it uses getImageData and pixels must be scanned. Algorithm
can be improved by drawing to a smaller canvas but downsampling effects
accuracy and using canvas transformations (scale) throws false positives
- Bounding box + line segment intersection
Test bounding box overlap (fast) then proceed to per edge intersection
detection if necessary. Exit after first intersection is found since
we're not simulating collision responce. This technique fails to detect
nested polygons, but since we're testing moving polygons it's ok(ish)
###
class Vector
constructor: ( @x, @y ) -> @set x, y
set: ( @x = 0.0, @y = 0.0 ) -> @
add: ( vector ) ->
@x += vector.x
@y += vector.y
@
scale: ( scalar ) ->
@x *= scalar
@y *= scalar
@
div: ( scalar ) ->
@x /= scalar
@y /= scalar
@
dot: ( vector ) ->
@x * vector.x + @y * vector.y
min: ( vector ) ->
@x = min @x, vector.x
@y = min @y, vector.y
max: ( vector ) ->
@x = max @x, vector.x
@y = max @y, vector.y
lt: ( vector ) ->
@x < vector.x or @y < vector.y
gt: ( vector ) ->
@x > vector.x or @y > vector.y
normalize: ->
mag = sqrt @x*@x + @y*@y
if mag isnt 0
@x /= mag
@y /= mag
clone: ->
new Vector @x, @y
class Edge
constructor: ( @pointA, @pointB ) ->
intersects: ( other, ray = no ) ->
dy1 = @pointB.y - @pointA.y
dx1 = @pointB.x - @pointA.x
dx2 = @pointA.x - other.pointA.x
dy2 = @pointA.y - other.pointA.y
dx3 = other.pointB.x - other.pointA.x
dy3 = other.pointB.y - other.pointA.y
if dy1 / dx1 isnt dy3 / dx3
d = dx1 * dy3 - dy1 * dx3
if d isnt 0
r = (dy2 * dx3 - dx2 * dy3) / d
s = (dy2 * dx1 - dx2 * dy1) / d
if r >= 0 and ( ray or r <= 1 )
if s >= 0 and s <= 1
return new Vector @pointA.x + r * dx1, @pointA.y + r * dy1
no
class Polygon
constructor: ( @vertices = [], @edges = [] ) ->
@colliding = no
@center = new Vector
@bounds = min: new Vector, max: new Vector
@edges = []
if @vertices.length > 0
@computeCenter()
@computeBounds()
@computeEdges()
translate: ( vector ) ->
@center.add vector
@bounds.min.add vector
@bounds.max.add vector
vertex.add vector for vertex in @vertices
rotate: ( radians, pivot = @center ) ->
s = sin radians
c = cos radians
for vertex in @vertices
dx = vertex.x - pivot.x
dy = vertex.y - pivot.y
vertex.x = c * dx - s * dy + pivot.x
vertex.y = s * dx + c * dy + pivot.y
computeCenter: ->
@center.set 0, 0
@center.add vertex for vertex in @vertices
@center.div @vertices.length
computeBounds: ->
@bounds.min.set Number.MAX_VALUE, Number.MAX_VALUE
@bounds.max.set -Number.MAX_VALUE, -Number.MAX_VALUE
for vertex in @vertices
@bounds.min.min vertex
@bounds.max.max vertex
computeEdges: ->
@edges.length = 0
for vertex, index in @vertices
@edges.push new Edge vertex, @vertices[ (index + 1) % @vertices.length ]
contains: ( vector ) ->
return no if vector.x > this.bounds.max.x or vector.x < this.bounds.min.x
return no if vector.y > this.bounds.max.y or vector.y < this.bounds.min.y
minX = (o) => o.x
minY = (o) => o.y
outside = new Vector(
Math.min.apply( Math, this.vertices.map( minX ) ) - 1,
Math.min.apply( Math, this.vertices.map( minY ) ) - 1)
ray = new Edge vector, outside
intersections = 0
( ++intersections if ray.intersects edge, yes ) for edge in @edges
!!( intersections % 2 )
collides: ( polygon ) ->
overlap = yes
# First perform a simple boundary check
overlap = no if polygon.bounds.min.gt @bounds.max
overlap = no if polygon.bounds.max.lt @bounds.min
# Perform per edge intersection tests if bounds overlap
overlap = no
for edge in @edges
for other in polygon.edges
return yes if edge.intersects other
no
wrap: ( bounds ) ->
ox = (@bounds.max.x - @bounds.min.x) + (bounds.max.x - bounds.min.x)
oy = (@bounds.max.y - @bounds.min.y) + (bounds.max.y - bounds.min.y)
if @bounds.max.x < bounds.min.x then @translate new Vector ox, 0
else if @bounds.min.x > bounds.max.x then @translate new Vector -ox, 0
if @bounds.max.y < bounds.min.y then @translate new Vector 0, oy
else if @bounds.min.y > bounds.max.y then @translate new Vector 0, -oy
draw: ( ctx ) ->
color = if @colliding then '#FF0051' else @color
ctx.strokeStyle = color
ctx.fillStyle = color
# center
ctx.beginPath()
ctx.arc @center.x, @center.y, 5, 0, TWO_PI
ctx.globalAlpha = 0.2
ctx.stroke()
# bounds
ctx.beginPath()
ctx.moveTo @bounds.min.x, @bounds.min.y
ctx.lineTo @bounds.max.x, @bounds.min.y
ctx.lineTo @bounds.max.x, @bounds.max.y
ctx.lineTo @bounds.min.x, @bounds.max.y
ctx.closePath()
ctx.globalAlpha = 0.05
ctx.fill()
# polygon
ctx.beginPath()
ctx.lineTo vertex.x, vertex.y for vertex in @vertices
ctx.closePath()
ctx.globalAlpha = 0.8
ctx.fill()
ctx.globalAlpha = 1
ctx.lineWidth = 2
ctx.stroke()
class Projectile extends Vector
constructor: ->
super
@velocity = new Vector
update: ( dt ) ->
@add @velocity.clone().scale dt
draw: ( ctx ) ->
alpha = if @colliding then 0.5 else 0.05
ctx.strokeStyle = '#fff'
ctx.fillStyle = '#fff'
ctx.beginPath()
ctx.arc @x, @y, 3, 0, TWO_PI
ctx.globalAlpha = alpha
ctx.lineWidth = 12
ctx.stroke()
ctx.globalAlpha = 0.6
ctx.fill()
wrap: ( bounds ) ->
if @x > bounds.max.x then @x = bounds.min.x
else if @x < bounds.min.x then @x = bounds.max.x
if @y > bounds.max.y then @y = bounds.min.y
else if @y < bounds.min.y then @y = bounds.max.y
# Example
Sketch.create
COLORS: [ '#0DB2AC', '#F5DD7E', '#FC8D4D', '#FC694D', '#69D2E7', '#A7DBD8', '#E0E4CC' ]
bounds:
min: new Vector
max: new Vector
makePolygon: ->
sides = random 4, 12
step = TWO_PI / sides
mv = 100
vertices = []
for side in [0..sides-1]
theta = (step * side) + random step
radius = random 30, 90
vertices.push new Vector (radius * cos theta), (radius * sin theta)
polygon = new Polygon vertices
polygon.translate new Vector (random @width), (random @height)
polygon.velocity = new Vector (random -mv, mv), (random -mv, mv)
polygon.color = random @COLORS
polygon.spin = random -1, 1
polygon
makeProjectile: ->
mv = 200
projectile = new Projectile (random @width), (random @height)
projectile.velocity.set (random -mv, mv), (random -mv, mv)
projectile
setup: ->
@projectiles = ( do @makeProjectile for i in [0..8] )
@polygons = ( do @makePolygon for i in [0..12] )
draw: ->
dts = max 0, this.dt / 1000
@globalCompositeOperation = 'lighter'
projectile.colliding = no for projectile in @projectiles
polygon.colliding = no for polygon in @polygons
for polygon, index in @polygons
polygon.translate polygon.velocity.clone().scale dts
polygon.rotate polygon.spin * dts
polygon.computeBounds()
polygon.wrap @bounds
# test collisions
for projectile in @projectiles
if polygon.contains projectile
projectile.colliding = yes
polygon.colliding = yes
break
if not polygon.colliding
for n in [[email protected]] by 1
other = @polygons[ n ]
if polygon.collides other
polygon.colliding = yes
other.colliding = yes
polygon.draw @
for projectile in @projectiles
projectile.update dts
projectile.wrap @bounds
projectile.draw @
resize: ->
@bounds.max.set @width, @height
```

999px

Also see: Tab Triggers