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/* _____ _ __ ________ ___ *\
** / ___/(_) |/ / ___/ |__ \ Simple Mechanics Simulator 2 **
** \__ \/ / /|_/ /\__ \ __/ / copyright (c) 2011 Jakob Odersky **
** ___/ / / / / /___/ / / __/ **
** /____/_/_/ /_//____/ /____/ **
\* */
package sims.collision.narrowphase
import sims.collision._
import sims.math._
class SAT[A <: Collidable: ClassManifest] extends NarrowPhaseDetector[A] {
def collision(pair: (A, A)): Option[Collision[A]] = {
var c = getCollision(pair)
c orElse getCollision(pair.swap)
}
private def getCollision(pair: (A,A)): Option[Collision[A]] = pair match {
case (c1: Circle, c2: Circle) =>
collisionCircleCircle(c1, c2)(pair)
case (p1: ConvexPolygon, p2: ConvexPolygon) =>
sat(pair, p1.sides.map(_.rightNormal0) ++ p2.sides.map(_.rightNormal0))
case _ => None
}
private def collisionCircleCircle(c1: Circle, c2: Circle)(pair: (A, A)) = {
val d = (c2.position - c1.position)
val l = d.length
if (l <= c1.radius + c2.radius) {
val p = c1.position + d.unit * (l - c2.radius)
Some(new Collision[A] {
val item1 = pair._1
val item2 = pair._2
val normal = d.unit
val points = List(p)
val overlap = (c1.radius + c2.radius - l)
})
} else None
}
private def collisionPolyPoly(p1: ConvexPolygon, p2: ConvexPolygon)(pair: (A, A)): Option[Collision[A]] = {
var minOverlap = Double.PositiveInfinity
var reference: ConvexPolygon = null
var incident: ConvexPolygon = null
var referenceSide: Segment = null
var incidentVerticeNumber = 0
for (i <- 0 until p1.sides.length) {
var overlaps = false
for (j <- 0 until p2.vertices.length) {
val s = p1.sides(i)
val v = p2.vertices(j)
val overlap = (s.rightNormal0 dot s.point1) - (s.rightNormal0 dot v)
if (overlap > 0) overlaps = true
if (overlap > 0 && overlap < minOverlap.abs) {
minOverlap = overlap
reference = p1
referenceSide = s
incident = p2
incidentVerticeNumber = j
}
}
if (!overlaps) return None
}
for (i <- 0 until p2.sides.length) {
var overlaps = false
for (j <- 0 until p1.vertices.length) {
val s = p2.sides(i)
val v = p1.vertices(j)
val overlap = (s.rightNormal0 dot s.point1) - (s.rightNormal0 dot v)
if (overlap > 0) overlaps = true
if (overlap > 0 && overlap < minOverlap.abs) {
minOverlap = overlap
reference = p2
referenceSide = s
incident = p1
incidentVerticeNumber = j
}
}
if (!overlaps) return None
}
val i = incidentVerticeNumber
val side1 = incident.sides(i)
val side2 = incident.sides(mod(i-1, incident.sides.length))
val incidentSide = if ((side1.direction dot referenceSide.rightNormal0).abs <
(side2.direction dot referenceSide.rightNormal0).abs) side1
else side2
val clipped: Segment = null //incidentSide clippedToSegment referenceSide
Some(new Collision[A] {
val item1 = reference.asInstanceOf[A]
val item2 = incident.asInstanceOf[A]
val normal = referenceSide.rightNormal0
val points = List(clipped.point1, clipped.point2)
val overlap = minOverlap
})
}
def farthestFeature(collidable: Collidable, direction: Vector2D): Either[Vector2D, Segment] = collidable match {
case c: Circle => Left(c.position + direction.unit * c.radius)
case p: ConvexPolygon => {
var max = p.vertices(0) dot direction.unit
//maximum vertice index
var i = 0
for (j <- 0 until p.vertices.length) {
val d = p.vertices(j) dot direction.unit
if (d > max) {
max = d
i = j
}
}
/* 1) vertex is considered to be the first point of a segment
* 2) polygons vertices are ordered counter-clockwise
*
* implies:
* previous segment is the (i-1)th segment
* next segment is the ith segment */
val prev = if (i == 0) p.sides.last else p.sides(i - 1)
val next = p.sides(i)
// check which segment is less parallel to direction
val side =
if ((prev.direction.unit dot direction).abs <= (next.direction.unit dot direction).abs) prev
else next
Right(side)
}
case _ => throw new IllegalArgumentException("Collidable is of unknown type.")
}
//normal is considered pointing from _1 to _2
//_1 reference, _2 incident
def getCollisionPoints(pair: (A, A), normal: Vector2D, overlap: Double): Array[Vector2D] = {
var points = new scala.collection.mutable.ArrayBuffer[Vector2D]
val feature1 = farthestFeature(pair._1, normal)
//is feature 1 a vertex?
if (feature1.isLeft) {
return Array(feature1.left.get)
}
val feature2 = farthestFeature(pair._2, -normal)
//is feature 2 a vertex?
if (feature2.isLeft) {
return Array(feature2.left.get)
}
//neither feature is a vertex
val side1 = feature1.right.get
val side2 = feature2.right.get
val flipped = (side1.direction.unit dot normal).abs > (side2.direction.unit dot -normal).abs
val reference = if (!flipped) side1 else side2
val incident = if (!flipped) side2 else side1
//both features are sides, clip feature2 to feature1
val clipped: Option[Segment] = None //incident clipped reference
clipped match {
case None => Array()
case Some(Segment(point1, point2)) => Array(point1, point2) filter ((v: Vector2D) => ((v - reference.point1) dot reference.rightNormal0) <= 0)
}
}
def sat(pair: (A, A), axes: Seq[Vector2D]): Option[Collision[A]] = {
var min = Double.PositiveInfinity
var n = axes(0)
for (axis <- axes) {
val overlap = pair._1.project(axis) overlap pair._2.project(axis)
if (overlap < 0) return None
if (overlap < min) {
min = overlap
n = axis
}
}
val pts = getCollisionPoints(pair, n, min)
if (pts.length == 0) return None
Some(new Collision[A] {
val item1 = pair._1
val item2 = pair._2
val normal = n
val points = pts.toSeq
val overlap = min
})
}
}
object SAT {
def apply[A <: Collidable: ClassManifest] = new SAT[A]
}
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