diff options
Diffstat (limited to 'src/main/scala/sims')
39 files changed, 1930 insertions, 0 deletions
diff --git a/src/main/scala/sims/collision/AABB.scala b/src/main/scala/sims/collision/AABB.scala new file mode 100644 index 0000000..f3a0b71 --- /dev/null +++ b/src/main/scala/sims/collision/AABB.scala @@ -0,0 +1,28 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.geometry._ + +/** + * Axis Aligned Bounding Boxes (AABBs) are rectangles that frame a shape. + * Their X-Axis and Y-Axis orientation makes it easy to test two AABBs for overlap. + * @param minVertex Position vector of the bottom-left vertex + * @param maxVertex Position vector of the upper-right vertex + */ +case class AABB(val minVertex: Vector2D, + val maxVertex: Vector2D) +{ + /** + * Checks this AABB with <code>box</code> for overlap. + * @param box AABB with which to check for overlap*/ + def overlaps(box: AABB): Boolean = { + val d1 = box.minVertex - maxVertex + val d2 = minVertex - box.maxVertex + !(d1.x > 0 || d1.y > 0 || d2.x > 0 || d2.y > 0) + } +} diff --git a/src/main/scala/sims/collision/CircleCollision.scala b/src/main/scala/sims/collision/CircleCollision.scala new file mode 100644 index 0000000..04cf2d7 --- /dev/null +++ b/src/main/scala/sims/collision/CircleCollision.scala @@ -0,0 +1,22 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.geometry._ +import sims.dynamics._ + +/**Collision between two circles.*/ +case class CircleCollision(c1: Circle, c2: Circle) extends Collision { + val shape1 = c1 + val shape2 = c2 + val normal = (c2.pos - c1.pos).unit + val points = { + val distance = (c2.pos - c1.pos).length + val p = shape1.pos + normal * (distance - c2.radius) + List(p) + } +} diff --git a/src/main/scala/sims/collision/Collision.scala b/src/main/scala/sims/collision/Collision.scala new file mode 100644 index 0000000..65111c6 --- /dev/null +++ b/src/main/scala/sims/collision/Collision.scala @@ -0,0 +1,108 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.dynamics._ +import sims.geometry._ + +/**Collision between two shapes. Contains methods to compute the collision response.*/ +abstract class Collision extends Constraint { + + /**First colliding shape (reference shape).*/ + val shape1: Shape + + /**Second colliding shape (incident shape).*/ + val shape2: Shape + + /**Collision points.*/ + val points: Iterable[Vector2D] + + /**Normal vector to the collision face.*/ + val normal: Vector2D + + /* C = delta + * Cdot = (vp2 - vp1) dot n + * = v2 + (w2 cross r2) - v2 - (w1 cross r1) + * = v2 + (w2 cross (p - x2)) - v2 - (w1 cross(p - x1)) + * J = [-n -((p-x1) cross n) n ((p-x2) cross n)]*/ + def correctVelocity(h: Double) = { + val coefficientOfRestitution = shape1.restitution * shape2.restitution + for (p <- points) { + val b1 = shape1.body + val b2 = shape2.body + val relativeNormalVelocity = (b2.velocityOfPoint(p) - b1.velocityOfPoint(p)) dot normal + val Cdot = relativeNormalVelocity + relativeNormalVelocity * coefficientOfRestitution + if (Cdot <= 0) { + val r1 = p - b1.pos + val r2 = p - b2.pos + val cr1 = r1 cross normal + val cr2 = r2 cross normal + val invMass = 1/b1.mass * (normal dot normal) + 1/b1.I * cr1 * cr1 + 1/b2.mass * (normal dot normal) + 1/b2.I * cr2 * cr2 + val m = if (invMass == 0.0) 0.0 else 1/invMass + val lambda = -m * Cdot + //wenn fixed, dann ist Masse unendlich => kein 'if (fixed != true)' + b1.linearVelocity += -normal * lambda / b1.mass + b1.angularVelocity += -(r1 cross normal) * lambda / b1.I + b2.linearVelocity += normal * lambda / b2.mass + b2.angularVelocity += (r2 cross normal) * lambda / b2.I + correctFriction(p, (-normal * lambda).length / h, h) + } + } + } + + /* Cdot = vt = [v2 + (w2 cross r2) - v1 - (w2 cross r2)] dot t + * J = [-t -(r2 cross t) t (r1 cross t)] + * 1/m = J * M * JT + * = 1/m1 * (t dot t) + 1/m2 * (t dot t) + 1/I1 * (r1 cross u)^2 + 1/I2 * (r2 cross u)^2*/ + def correctFriction(point: Vector2D, normalForce: Double, h: Double) = { + val b1 = shape1.body + val b2 = shape2.body + val tangent = normal.leftNormal + val Cdot = (b2.velocityOfPoint(point) - b1.velocityOfPoint(point)) dot tangent + val r1 = point - b1.pos + val r2 = point - b2.pos + val cr1 = r1 cross tangent + val cr2 = r2 cross tangent + val invMass = 1/b1.mass * (tangent dot tangent) + 1/b1.I * cr1 * cr1 + 1/b2.mass * (tangent dot tangent) + 1/b2.I * cr2 * cr2 + val m = if (invMass == 0.0) 0.0 else 1/invMass + val lambda = -m * Cdot + val cf = shape1.friction * shape2.friction + val cl = math.min(math.max(-normalForce * cf * h, lambda), normalForce * cf * h) + val impulse = tangent * cl + b1.applyImpulse(-impulse, point) + b2.applyImpulse(impulse, point) + } + + def correctPosition(h: Double) = { + val b1 = shape1.body + val b2 = shape2.body + + for (p <- points) { + val overlap = shape1.project(normal) overlap shape2.project(normal) + val C = Collision.ToleratedOverlap - overlap + if (C <= 0.0) { + val r1 = p - b1.pos + val r2 = p - b2.pos + val cr1 = r1 cross normal + val cr2 = r2 cross normal + val invMass = 1/b1.mass + 1/b1.I * cr1 * cr1 + 1/b2.mass + 1/b2.I * cr2 * cr2 + val m = if (invMass == 0.0) 0.0 else 1/invMass + val impulse = -normal.unit * m * C + b1.pos += -impulse / b1.mass + b1.rotation += -(r1 cross impulse) / b1.I + b2.pos += impulse / b2.mass + b2.rotation += (r2 cross impulse) / b2.I + } + } + } +} + +object Collision { + + /**Tolerated overlap. Collision response will only be applied if the overlap of two shapes exceeds the tolerated overlap.*/ + val ToleratedOverlap: Double = 0.01 +} diff --git a/src/main/scala/sims/collision/Detector.scala b/src/main/scala/sims/collision/Detector.scala new file mode 100644 index 0000000..96af5dc --- /dev/null +++ b/src/main/scala/sims/collision/Detector.scala @@ -0,0 +1,21 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + + +import sims.geometry._ +import sims.dynamics._ + +/**A world detects its collisions through concrete implementations of this class.*/ +abstract class Detector { + + /**The world whose shapes are to be checked for collisions.*/ + val world: World + + /**Returns all collisions between shapes in the world <code>world</code>.*/ + def collisions: Seq[Collision] +}
\ No newline at end of file diff --git a/src/main/scala/sims/collision/GridDetector.scala b/src/main/scala/sims/collision/GridDetector.scala new file mode 100644 index 0000000..2196195 --- /dev/null +++ b/src/main/scala/sims/collision/GridDetector.scala @@ -0,0 +1,123 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.dynamics._ +import sims.geometry._ +import scala.collection._ +import scala.collection.mutable.ArrayBuffer +import scala.collection.mutable.HashMap + +/**A concrete implementation of <code>Detector</code>. <code>GridDetector</code> divides the world into a grid + * for faster collision detection.*/ +class GridDetector(override val world: World) extends Detector { + + /**Array of collision detection methods. These methods return <code>true</code> if two shapes are colliding.*/ + val detectionMethods = new ArrayBuffer[PartialFunction[(Shape, Shape), Boolean]] + detectionMethods += { + case (c1: Circle, c2: Circle) => { //collision if distance <= sum of radiuses + val d = (c1.pos - c2.pos).length + val rSum = c1.radius + c2.radius + d - rSum <= 0 + } + + case (p1: ConvexPolygon, p2: ConvexPolygon) => { //SAT + val sides = p1.sides ++ p2.sides + val axes = sides map (_.n0) + axes.forall((a: Vector2D) => p1.project(a) overlaps p2.project(a)) + } + + case (p: ConvexPolygon, c: Circle) => { //distance form center to sides or vertices + val distances = for (s <- p.sides) yield (s distance c.pos) + distances.exists(_ - c.radius <= 0) || (p contains c.pos) + } + + case (c: Circle, p: ConvexPolygon) => { //distance form center to sides or vertices + val distances = for (s <- p.sides) yield (s distance c.pos) + distances.exists(_ - c.radius <= 0) || (p contains c.pos) + } + } + + /**Array of methods returning collisions. It is assumed that both shapes are colliding.*/ + val collisionMethods = new ArrayBuffer[PartialFunction[(Shape, Shape), Collision]] + collisionMethods += { + case (c1: Circle, c2: Circle) => CircleCollision(c1, c2) + case (p1: ConvexPolygon, p2: ConvexPolygon) => PolyCollision(p1, p2) + case (p: ConvexPolygon, c: Circle) => PolyCircleCollision(p, c) + case (c: Circle, p: ConvexPolygon) => PolyCircleCollision(p, c) + } + + /**Checks the pair of shapes <code>p</code> for collision. + * @param p Pair of shapes.*/ + def colliding(p: Pair) = { + if (detectionMethods.exists(_.isDefinedAt(p))) + detectionMethods.find(_.isDefinedAt(p)).get.apply(p) + else throw new IllegalArgumentException("No collision method for colliding pair!") + } + + /**Returns the collision between both shapes of the pair <code>p</code>. + * @param p Pair of shapes.*/ + def collision(p: Pair): Collision = { + if (collisionMethods.exists(_.isDefinedAt(p))) + collisionMethods.find(_.isDefinedAt(p)).get.apply(p) + else throw new IllegalArgumentException("No collision found in colliding pair!") + } + + /**Width and height of a grid cell.*/ + var gridSide: Double = 2 + + /**Returns potential colliding pairs of shapes of the world <code>world</code>. + * <p> + * A potential colliding pair is a pair of two shapes that comply with the following criteria: + * <ul> + * <li>The shapes are situated in the same grid cell.</li> + * <li>Their AABBs overlap.</li> + * <li>The shapes do not belong to the same body.</li> + * <li>At least one shape is not fixed.</li> + * <li>Both shapes are {@link dynamics.Shape#collidable}.</li> + * </ul>*/ + def getPairs = { + val grid = new HashMap[(Int, Int), List[Shape]] + def gridCoordinates(v: Vector2D) = ((v.x / gridSide).toInt, (v.y / gridSide).toInt) + def addToGrid(s: Shape) = { + val aabb = s.AABB + val minCell = gridCoordinates(aabb.minVertex) + val maxCell = gridCoordinates(aabb.maxVertex) + val coords = for(i <- (minCell._1 to maxCell._1); j <- (minCell._2 to maxCell._2)) yield (i, j) + for (c <- coords) { + if (grid.contains(c)) + {if (grid(c).forall(_ ne s)) grid(c) = s :: grid(c)} + else + grid += (c -> List(s)) + } + } + for(s <- world.shapes) addToGrid(s) + var ps: List[Pair] = Nil + for(cell <- grid.valuesIterator) { + ps = ps ::: (for (s1: Shape <- cell; s2: Shape <- cell; + if (s1 ne s2); + if (s1.body ne s2.body); + if (s1.collidable && s2.collidable); + if (s1.AABB overlaps s2.AABB); + if (!s1.transientShapes.contains(s2) && !s2.transientShapes.contains(s1))) yield Pair(s1, s2) + ).distinct + } + ps.toSeq + } + + private var cache = (world.time, getPairs) + + /**All potential colliding pairs of the world. + * @see getPairs*/ + def pairs = {if (world.time != cache._1) cache = (world.time, getPairs); cache._2} + + /**Returns all colliding pairs.*/ + def collidingPairs: Seq[Pair] = for(p <- pairs; if (colliding(p))) yield p + + /**Returns all collisions.*/ + def collisions: Seq[Collision] = for(p <- pairs; if (colliding(p))) yield collision(p) +} diff --git a/src/main/scala/sims/collision/Overlap.scala b/src/main/scala/sims/collision/Overlap.scala new file mode 100644 index 0000000..97ecdd6 --- /dev/null +++ b/src/main/scala/sims/collision/Overlap.scala @@ -0,0 +1,11 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.geometry._ + +case class Overlap(poly: ConvexPolygon, sideNum: Int, overlap: Double) diff --git a/src/main/scala/sims/collision/Pair.scala b/src/main/scala/sims/collision/Pair.scala new file mode 100644 index 0000000..a01fb00 --- /dev/null +++ b/src/main/scala/sims/collision/Pair.scala @@ -0,0 +1,24 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.dynamics._ + +/**Pair of shapes.*/ +case class Pair(s1: Shape, s2: Shape){ + + override def equals(other: Any) = { //overriden to prevent removal during "GridDetector.getPairs" + other match { + case Pair(a, b) => ((a eq this.s1) && (b eq this.s2)) || ((b eq this.s1) && (a eq this.s2)) + case _ => false + } + } +} + +object Pair { + implicit def pair2Tuple(x: Pair) = (x.s1, x.s2) +} diff --git a/src/main/scala/sims/collision/PolyCircleCollision.scala b/src/main/scala/sims/collision/PolyCircleCollision.scala new file mode 100644 index 0000000..20f1d49 --- /dev/null +++ b/src/main/scala/sims/collision/PolyCircleCollision.scala @@ -0,0 +1,36 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.dynamics._ +import sims.geometry._ + +/**Collision between a convex polygon and a circle.*/ +case class PolyCircleCollision(p: ConvexPolygon, c: Circle) extends Collision { + require(p.isInstanceOf[Shape]) + val shape1 = p.asInstanceOf[Shape] + val shape2 = c + + val normal = { + //minimum overlap + var min = (p.sides(0) distance c.pos) - c.radius + var axis = p.sides(0).n0 + for (s <- p.sides; val delta = (s distance c.pos) - c.radius) if (delta <= 0 && delta < min) { + min = delta + axis = s.n0 + } + for (v <- p.vertices; val delta = (v - c.pos).length - c.radius) if (delta <= 0 && delta <= min){ + min = delta + axis = (c.pos - v).unit + } + axis + } + + val points = List( + c.pos - normal * c.radius + ) +} diff --git a/src/main/scala/sims/collision/PolyCollision.scala b/src/main/scala/sims/collision/PolyCollision.scala new file mode 100644 index 0000000..5296f41 --- /dev/null +++ b/src/main/scala/sims/collision/PolyCollision.scala @@ -0,0 +1,53 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.collision + +import sims.geometry._ +import sims.dynamics._ +import scala.collection.mutable.Map + +/**Collision between two convex polygons.*/ +case class PolyCollision(p1: ConvexPolygon, p2: ConvexPolygon) extends Collision { + require(p1.isInstanceOf[Shape]) + require(p2.isInstanceOf[Shape]) + + def overlap(axis: Vector2D) = { + // println((p1.project(axis) overlap p2.project(axis)).toString + " to " + (p2.project(axis) overlap p1.project(axis))) + p1.project(axis) overlap p2.project(axis) + } + + lazy val overlaps = (for (i <- 0 until p2.sides.length) yield Overlap(p2, i, overlap(p2.sides(i).n0))) ++ + (for (i <- 0 until p1.sides.length) yield Overlap(p1, i, overlap(p1.sides(i).n0))) + + private var potMinOverlap = overlaps.find(_.overlap > 0.0) + require(potMinOverlap != None) + private var _minOverlap: Overlap = potMinOverlap.get + var minOverlap: Overlap = { + for (o <- overlaps) if ((o.overlap < _minOverlap.overlap) && (o.overlap > 0.0)) _minOverlap = o + _minOverlap + } + + + private lazy val refPoly = minOverlap.poly + private lazy val incPoly = if (minOverlap.poly eq p1) p2 else p1 + + lazy val shape1 = refPoly.asInstanceOf[Shape] + lazy val shape2 = incPoly.asInstanceOf[Shape] + + lazy val normal = refPoly.sides(minOverlap.sideNum).n0 + lazy val points = (for (v <- incPoly.vertices; if refPoly.contains(v)) yield v)++ + (for (v <- refPoly.vertices; if incPoly.contains(v)) yield v) + + /* ++ + (for (s <- incPoly.sides; + val clip = s.clipToSegment(refPoly.sides((refPoly.sides.length - (minOverlap.sideNum + 1)) % refPoly.sides.length)); + if (clip != None)) yield clip.get) ++ + (for (s <- incPoly.sides; + val clip = s.clipToSegment(refPoly.sides((refPoly.sides.length - (minOverlap.sideNum - 1)) % refPoly.sides.length)); + if (clip != None)) yield clip.get) + */ +} diff --git a/src/main/scala/sims/dynamics/Body.scala b/src/main/scala/sims/dynamics/Body.scala new file mode 100644 index 0000000..8c0e2ee --- /dev/null +++ b/src/main/scala/sims/dynamics/Body.scala @@ -0,0 +1,141 @@ + +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +import sims.geometry._ +import sims.dynamics.joints._ + +/**A two dimensional rigid body is made out of shapes. + * @param shps shapes that belong to this body.*/ +class Body(shps: Shape*){ + + /**Unique identification number.*/ + val uid = Body.nextUid + + /**Shapes that belong to this body.*/ + val shapes: List[Shape] = shps.toList + + //Shapes are added during initialisation. + for (s <- shapes) { + s.body = this + s.refLocalPos = s.pos - pos + s.rotation0 = s.rotation + } + + private var isFixed: Boolean = false + + /**Returns whether this body is fixed or not.*/ + def fixed = isFixed + + /**Fixes or frees this body. By fixing, linear and angular velocities are set to zero.*/ + def fixed_=(value: Boolean) = { + if (value) {linearVelocity = Vector2D.Null; angularVelocity = 0.0} + isFixed = value + } + + /**Flag for a world to monitor the properties of this body. + * @see World#monitors*/ + var monitor: Boolean = false + + /**Returns the position of this body. The position is equivalent to the center of mass. + * @return position of this body*/ + def pos: Vector2D = // COM = sum(pos*mass)/M + (Vector2D.Null /: shapes)((v: Vector2D, s: Shape) => v + s.pos * s.mass) / + (0.0 /: shapes)((i: Double, s: Shape) => i + s.mass) + + /**Sets the position of this body. By doing so all its shapes are translated. + * @param newPos new position*/ + def pos_=(newPos: Vector2D) = { + val stepPos = pos + shapes.foreach((s: Shape) => s.pos = s.pos - stepPos + newPos) + } + + /**Contains the current rotation of this body.*/ + private var _rotation: Double = 0.0 + + /**Returns the current rotation of this body.*/ + def rotation: Double = _rotation + + /**Sets the rotation of this body. Position and rotation of shapes are modified accordingly. + * @param r new rotation*/ + def rotation_=(newRotation: Double) = { + _rotation = newRotation + val stepPos = pos + for (s <- shapes) { + s.rotation = newRotation + s.rotation0 + s.pos = stepPos + (s.refLocalPos rotate (newRotation)) + } + } + + /**Linear velocity of this body.*/ + var linearVelocity: Vector2D = Vector2D.Null + + /**Angular velocity of this body.*/ + var angularVelocity: Double = 0 + + /**Linear velocity of the given point on this body (in world coordinates).*/ + def velocityOfPoint(point: Vector2D) = linearVelocity + ((point - pos).leftNormal * angularVelocity) + + /**Resulting force on the COM of this body.*/ + var force: Vector2D = Vector2D.Null + + /**Resulting torque on this body.*/ + var torque: Double = 0 + + /**Returns the mass of this body. If the body is free, its mass is the sum of the masses of its shapes. + * If the body is fixed, its mass is infinite (<code>Double.PositiveInfinity</code>). + * @return this body's mass*/ + def mass: Double = if (fixed) Double.PositiveInfinity else (0.0 /: shapes)((i: Double, s: Shape) => i + s.mass) + + /**Returns the moment of inertia for rotations about the COM of this body. + * It is calculated using the moments of inertia of this body's shapes and the parallel axis theorem. + * If the body is fixed, its moment of inertia is infinite (<code>Double.PositiveInfinity</code>). + * @return moment of inertia for rotations about the COM of this body*/ + def I: Double = if (fixed) Double.PositiveInfinity else + (0.0 /: (for (s <- shapes) yield (s.I + s.mass * ((s.pos - pos) dot (s.pos - pos)))))(_+_) + + /**Applies a force to the COM of this body. + * @param force applied force*/ + def applyForce(force: Vector2D) = if (!fixed) this.force += force + + /**Applies a force to a point on this body. Warning: the point is considered to be contained within this body. + * @param force applied force + * @param point position vector of the point (in world coordinates)*/ + def applyForce(force: Vector2D, point: Vector2D) = if (!fixed) {this.force += force; torque += (point - pos) cross force} + + /**Applies an impulse to the COM of this body. + * @param impulse applied impulse*/ + def applyImpulse(impulse: Vector2D) = if (!fixed) linearVelocity += impulse / mass + + /**Applies an impulse to a point on this body. Warning: the point is considered to be contained within this body. + * @param impulse applied impulse + * @param point position vector of the point (in world coordinates)*/ + def applyImpulse(impulse: Vector2D, point: Vector2D) = if (!fixed) {linearVelocity += impulse / mass; angularVelocity += ((point - pos) cross impulse) / I} + + /**Checks if the point <code>point</code> is contained in this body.*/ + def contains(point: Vector2D) = shapes.exists(_.contains(point)) + + override def toString: String = { + "Body" + uid + " " + shapes + " fixed=" + fixed + " m=" + mass + " I=" + I + " pos=" + pos + " rot=" + rotation + " v=" + linearVelocity + " w=" + angularVelocity + " F=" + force + " tau=" + torque + } + + /**Creates a new body containing this body's shapes and the shape <code>s</code>. + * @param s new shape + * @return new body*/ + def ~(s: Shape) = new Body((s :: shapes): _*) + + /**Creates a new body containing this body's shapes and the shapes of another body <code>b</code>. + * @param b body with extra shapes + * @return new body*/ + def ~(b: Body) = new Body((this.shapes ::: b.shapes): _*) +} + +object Body { + private var uidCounter = -1 + private def nextUid = {uidCounter += 1; uidCounter} +}
\ No newline at end of file diff --git a/src/main/scala/sims/dynamics/Circle.scala b/src/main/scala/sims/dynamics/Circle.scala new file mode 100644 index 0000000..d6db07d --- /dev/null +++ b/src/main/scala/sims/dynamics/Circle.scala @@ -0,0 +1,34 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +import sims.geometry._ +import sims.collision._ + +/** + * A circle. + * @param radius radius of this circle + * @param density density of this circle + */ +case class Circle(radius: Double, density: Double) extends Shape{ + + val volume = math.Pi * radius * radius + + val I = mass * radius * radius / 2 + + def AABB = new AABB(pos - Vector2D(radius,radius), + pos + Vector2D(radius,radius)) + + def project(axis: Vector2D) = if (axis.x != 0) Projection(axis, + (pos.project(axis).x / axis.x) - radius, + (pos.project(axis).x / axis.x) + radius) + else Projection(axis, + (pos.project(axis).y / axis.y) - radius, + (pos.project(axis).y / axis.y) + radius) + + def contains(point: Vector2D) = (point - pos).length <= radius +} diff --git a/src/main/scala/sims/dynamics/Constraint.scala b/src/main/scala/sims/dynamics/Constraint.scala new file mode 100644 index 0000000..eaa6952 --- /dev/null +++ b/src/main/scala/sims/dynamics/Constraint.scala @@ -0,0 +1,21 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +/**All constraints in SiMS implement this trait. + * Position and velocity can be corrected for each constraint. + * The implementation of constraints was inspired by Erin Catto's box2d.*/ +trait Constraint { + + /**Corrects the velocities of bodies according to this constraint. + * @param h a time interval, used for converting forces and impulses*/ + def correctVelocity(h: Double): Unit + + /**Corrects the positions of bodies according to this constraint. + * @param h a time interval, used for converting forces and impulses*/ + def correctPosition(h: Double): Unit +} diff --git a/src/main/scala/sims/dynamics/Rectangle.scala b/src/main/scala/sims/dynamics/Rectangle.scala new file mode 100644 index 0000000..89ab4c0 --- /dev/null +++ b/src/main/scala/sims/dynamics/Rectangle.scala @@ -0,0 +1,38 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +import sims.geometry._ +import sims.collision._ + +/**A rectangle is a polygon. + * @param halfWidth this rectangle's half width + * @param halfHeight this rectangle's half height + * @param density density of this rectangle + */ +case class Rectangle(halfWidth: Double, + halfHeight : Double, + density: Double) extends Shape with ConvexPolygon{ + + val volume = halfWidth * halfHeight * 4 + + val I = 1.0 / 12.0 * mass * ((2 * halfWidth) * (2 * halfWidth) + (2 * halfHeight) * (2 * halfHeight)) + + /**Returns the vectors from the center to the vertices of this rectangle. + * The first vertex is the upper-right vertex at a rotation of 0. + * Vertices are ordered counter-clockwise.*/ + def halfDiags: Array[Vector2D] = Array(Vector2D(halfWidth, halfHeight), + Vector2D(-halfWidth, halfHeight), + Vector2D(-halfWidth, -halfHeight), + Vector2D(halfWidth, -halfHeight)) map (_ rotate rotation) + + /**Returns the position vectors of this rectangle's vertices. + * The first vertex is the upper-right vertex at a rotation of 0. + * Vertices are ordered counter-clockwise.*/ + def vertices = for (h <- halfDiags) yield pos + h + +}
\ No newline at end of file diff --git a/src/main/scala/sims/dynamics/RegularPolygon.scala b/src/main/scala/sims/dynamics/RegularPolygon.scala new file mode 100644 index 0000000..6f08ca1 --- /dev/null +++ b/src/main/scala/sims/dynamics/RegularPolygon.scala @@ -0,0 +1,35 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +import math._ +import sims.geometry._ + +/**A regular polygon with <code>n</code> sides whose excircle has a radius <code>radius</code>. + * @param n nmber of sides. + * @param radius radius of the excircle + * @param density density of this regular polygon + * @throws IllegalArgumentException if <code>n</code> is smaller than 3 */ +case class RegularPolygon(n: Int, radius: Double, density: Double) extends Shape with ConvexPolygon{ + require(n >= 3, "A polygon must have at least 3 sides.") + + /**Height of one of the constituting triangles.*/ + private val h: Double = radius * cos(Pi / n) + /**Half width of one of the constituting triangles.*/ + private val b: Double = radius * sin(Pi / n) + + def halfDiags = (for (i: Int <- (0 until n).toArray) yield (Vector2D(0, radius) rotate (2 * Pi * i / n))) map (_ rotate rotation) + + def vertices = for (h <- halfDiags) yield pos + h + + val volume = n * h * b + + /**Moment of inertia of one of the constituting triangles about the center of this polygon.*/ + private val Ic: Double = density * b * (3 * b + 16) * h * h * h * h / 54 + + val I = n * Ic +} diff --git a/src/main/scala/sims/dynamics/Shape.scala b/src/main/scala/sims/dynamics/Shape.scala new file mode 100644 index 0000000..47a4199 --- /dev/null +++ b/src/main/scala/sims/dynamics/Shape.scala @@ -0,0 +1,97 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +import sims.geometry._ +import sims.collision._ + +/** +* An abstract shape. +*/ +abstract class Shape{ + + /**Unique identification number.*/ + val uid: Int = Shape.nextUid + + /**Flag determining this shapes ability to collide with other shapes.*/ + var collidable: Boolean = true + + /**Part of the coefficient of restitution for a collision between this shape and another. + * The coefficient of restitution is calculated out of the product of this part and the other shape's part.*/ + var restitution: Double = 0.7 + + /**Part of the coefficient of friction for a collision between this shape and another. + * The coefficient of friction is calculated out of the product of this part and the other shape's part.*/ + var friction: Double = 0.707 + + /**Position of this shape's COM (in world coordinates).*/ + var pos: Vector2D = Vector2D.Null + + /**Rotation of this shape about its COM.*/ + var rotation: Double = 0 + + /**Initial rotation. Rotation of this shape before it was added to a body.*/ + var rotation0 = 0.0 + + /**Local position of this shape's body COM to its COM at a body rotation of zero.*/ + var refLocalPos: Vector2D = Vector2D.Null + + /**Density. (Mass per area)*/ + val density: Double + + /**Volume. The volume is actually equivalent to this shape's area (SiMS is in 2D) + * and is used with this shape's density to calculate its mass.*/ + val volume: Double + + /**Returns the mass of this shape. The mass is given by volume times density. + @return mass of this shape*/ + def mass = volume * density + + /**Moment of inertia for a rotation about this shape's COM.*/ + val I: Double + + /**Containing body.*/ + private var _body: Body = _ + + /**Returns this shape's containing body.*/ + def body = _body + + /**Sets this shape's containing body.*/ + private[dynamics] def body_=(b: Body) = _body = b + + /**Returns this shape's axis aligned bounding box.*/ + def AABB: AABB + + /**Returns the projection of this shape onto the line given by the directional vector <code>axis</code>. + * @param axis directional vector of the line + * @return projection of this shape*/ + def project(axis: Vector2D): Projection + + /**Checks if the point <code>point</code> is contained in this shape.*/ + def contains(point: Vector2D): Boolean + + /**Creates a new body made out of tis shape. + @return a body made out of tis shape*/ + def asBody = new Body(this) + + /**Shapes with which this shape cannot collide.*/ + val transientShapes: collection.mutable.Set[Shape] = collection.mutable.Set() + + /**Creates a new body out of this shape and the shape <code>s</code>.*/ + def ~(s: Shape) = new Body(this, s) + + /**Creates a new body out of this shape and the shapes of body <code>b</code>.*/ + def ~(b: Body) = { + val shapes = this :: b.shapes + new Body(shapes: _*) + } +} + +object Shape { + private var uidCounter = -1 + private def nextUid = {uidCounter += 1; uidCounter} +} diff --git a/src/main/scala/sims/dynamics/World.scala b/src/main/scala/sims/dynamics/World.scala new file mode 100644 index 0000000..f24a3fd --- /dev/null +++ b/src/main/scala/sims/dynamics/World.scala @@ -0,0 +1,164 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics + +import sims.geometry._ +import sims.collision._ +import sims.dynamics.joints._ +import scala.collection.mutable.ArrayBuffer + +/**A world contains and simulates a system of rigid bodies and joints.*/ +class World { + + /**Time intervals in which this world simulates.*/ + var timeStep: Double = 1.0 / 60 + + /**Number of constraint corrections per time step.*/ + var iterations: Int = 10 + + /**Gravity in this world.*/ + var gravity = Vector2D(0, -9.81) + + /**Bodies contained in this world.*/ + val bodies = new ArrayBuffer[Body] + + /**Joints contained in this world.*/ + val joints = new ArrayBuffer[Joint] + + /**Monitoring methods for bodies. + * <p> + * The first element of the tuple is the method's title and the second the method. + * Example usage: monitors += ("Y-Position", _.pos.y.toString) + * This will calculate all bodies - whose <code>monitor</code> field is set to + * <code>true</code> - second position components.*/ + val monitors = new ArrayBuffer[(String, Body => Any)] + + /**Collsion detector who manages collision detection in this world.*/ + val detector: Detector = new GridDetector(this) + + /**Warning if a body's velocity exceeds the speed of light.*/ + var overCWarning = false + + /**Flag to enable collision detection.*/ + var enableCollisionDetection = true + + /**Flag to enable position correction for constraints.*/ + var enablePositionCorrection = true + + /**Minimal, non-zero linear velocity.*/ + var minLinearVelocity: Double = 0.0001 + + /**Minimal, non-zero angular velocity.*/ + var minAngularVelocity: Double = 0.0001 + + /**Returns all shapes of all bodies in this world.*/ + def shapes = for (b <- bodies; s <- b.shapes) yield s + + /**Adds the given body to this world.*/ + def +=(body: Body) = bodies += body + + /**Adds the given joint to this world.*/ + def +=(joint: Joint): Unit = joints += joint + + /**Adds the given prefabricated system of bodies and joints to this world.*/ + def +=(p: sims.prefabs.Prefab): Unit = { + for (b <- p.bodies) this += b + for (j <- p.joints) this += j + } + + /**Adds the given sequence of bodies to this world.*/ + def ++=(bs: Seq[Body]): Unit = for(b <- bs) this += b + + /**Removes the given body from this world.*/ + def -=(body: Body): Unit = bodies -= body + + /**Removes the given joint from this world.*/ + def -=(joint: Joint): Unit = joints -= joint + + /**Removes the given prefabricated system of bodies and joints from this world.*/ + def -=(p: sims.prefabs.Prefab): Unit = { + for (b <- p.bodies) this -= b + for (j <- p.joints) this -= j + } + + /**Removes the given sequence of bodies from this world.*/ + def --=(bs: Seq[Body]) = for(b <- bs) this -= b + + /**Removes all bodies, joints and monitoring methods from this world.*/ + def clear() = {joints.clear(); bodies.clear(); monitors.clear()} + + /**Current time in this world.*/ + var time: Double = 0.0 + + /**Simulates a time step of the duration <code>timeStep</code>. + * <p> + * The time step is simulated in the following phases: + * <ol> + * <li>Forces are applied to bodies.</li> + * <li>Accelerations are integrated.</li> + * <li>Velocities are corrected.</li> + * <li>Velocities are integrated.</li> + * <li>Postions are corrected.</li> + * <li>The method <code>postStep()</code> is executed.</li> + * </ol>*/ + def step() = { + time += timeStep + + //force applying objects + for (j <- joints) j match {case f: ForceJoint => f.applyForce; case _ => ()} + + //integration of acclerations, yields velocities + for (b <- bodies) { + b.applyForce(gravity * b.mass) + b.linearVelocity = b.linearVelocity + (b.force / b.mass) * timeStep + b.angularVelocity = b.angularVelocity + (b.torque / b.I) * timeStep + } + + //correction of velocities + for (i <- 0 until iterations){ + for(c <- joints) c.correctVelocity(timeStep) + if (enableCollisionDetection) for (c <- detector.collisions) c.correctVelocity(timeStep) + } + + //integration of velocities, yields positions + for (b <- bodies) { + //warning when body gets faster than speed of light + if (b.linearVelocity.length >= 300000000) overCWarning = true + if (b.linearVelocity.length < minLinearVelocity) b.linearVelocity = Vector2D.Null + if (b.angularVelocity.abs < minAngularVelocity) b.angularVelocity = 0.0 + b.pos = b.pos + b.linearVelocity * timeStep + b.rotation = b.rotation + b.angularVelocity * timeStep + b.force = Vector2D.Null + b.torque = 0.0 + } + + //correction of positions + if (enablePositionCorrection) for (i <- 0 until iterations){ + for (c <- joints) c.correctPosition(timeStep) + if (enableCollisionDetection) for (c <- detector.collisions) c.correctPosition(timeStep) + } + + postStep() + } + + /**Initially empty method that is executed after each time step. This method + * may be overriden to create custom behaviour in a world.*/ + def postStep() = {} + + /**Returns information about this world.*/ + def info = { + "Bodies = " + bodies.length + "\n" + + "Shapes = " + shapes.length + "\n" + + "Joints = " + joints.length + "\n" + + "Collisions = " + detector.collisions.length + "\n" + + "Monitors = " + monitors.length + "\n" + + "Gravity = " + gravity + "m/s^2\n" + + "Timestep = " + timeStep + "s\n" + + "Time = " + time + "s\n" + + "Iterations = " + iterations + } +} diff --git a/src/main/scala/sims/dynamics/joints/DistanceJoint.scala b/src/main/scala/sims/dynamics/joints/DistanceJoint.scala new file mode 100644 index 0000000..1bf9b46 --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/DistanceJoint.scala @@ -0,0 +1,77 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics.joints + +import sims.dynamics._ +import sims.geometry._ + +/** DistanceJoints keep their connection points at a constant distance. + * @param node1 first associated body + * @param anchor1 first connection point + * @param node2 second associated body + * @param anchor2 second connection point*/ +case class DistanceJoint(node1: Body, anchor1: Vector2D, node2: Body, anchor2: Vector2D) extends Joint{ + def this(node1: Body, node2: Body) = this(node1, node1.pos, node2, node2.pos) + + /**Distance between the two connection points at initialisation (the desired distance).*/ + val distance = (anchor2 - anchor1).length + + private val a1 = anchor1 - node1.pos + private val a2 = anchor2 - node2.pos + private val initRotation1 = node1.rotation + private val initRotation2 = node2.rotation + + /**Returns the connection point on body one (in world coordinates).*/ + def connection1 = (a1 rotate (node1.rotation - initRotation1)) + node1.pos + + /**Returns the connection point on body two (in world coordinates).*/ + def connection2 = (a2 rotate (node2.rotation - initRotation2)) + node2.pos + + /**Relative position of the connection points.*/ + def x = connection2 - connection1 + + /**Relative velocity of the connection points.*/ + def v = node2.velocityOfPoint(connection2) - node1.velocityOfPoint(connection1) + + /* x = connection2 - connection1 + * C = ||x|| - L + * u = x / ||x|| + * v = v2 + w2 cross r2 - v1 - w1 cross r1 + * Cdot = u dot v + * J = [-u -(r1 cross u) u (r2 cross u)] + * 1/m = J * M^-1 * JT + * = 1/m1 * u * u + 1/m2 * u * u + 1/I1 * (r1 cross u)^2 + 1/I2 * (r2 cross u)^2*/ + override def correctVelocity(h: Double) = { + val x = this.x //relative position + val v = this.v //relative velocity + val r1 = (connection1 - node1.pos) + val r2 = (connection2 - node2.pos) + val cr1 = r1 cross x.unit + val cr2 = r2 cross x.unit + val Cdot = x.unit dot v //velocity constraint + val invMass = 1/node1.mass + 1/node1.I * cr1 * cr1 + 1/node2.mass + 1/node2.I * cr2 * cr2 //=J M^-1 JT + val m = if (invMass == 0.0) 0.0 else 1/invMass //avoid division by zero + val lambda = -m * Cdot //=-JV/JM^-1JT + val impulse = x.unit * lambda //P=J lambda + node1.applyImpulse(-impulse, connection1) + node2.applyImpulse(impulse, connection2) + } + + override def correctPosition(h: Double) = { + val C = x.length - distance + val cr1 = (connection1 - node1.pos) cross x.unit + val cr2 = (connection2 - node2.pos) cross x.unit + val invMass = 1/node1.mass + 1/node1.I * cr1 * cr1 + 1/node2.mass + 1/node2.I * cr2 * cr2 + val m = if (invMass == 0.0) 0.0 else 1/invMass + val impulse = -x.unit * m * C + node1.pos -= impulse / node1.mass + node2.pos += impulse / node2.mass + node1.rotation -= ((connection1 - node1.pos) cross impulse) / node1.I + node2.rotation += ((connection2 - node2.pos) cross impulse) / node2.I + } + +}
\ No newline at end of file diff --git a/src/main/scala/sims/dynamics/joints/ForceJoint.scala b/src/main/scala/sims/dynamics/joints/ForceJoint.scala new file mode 100644 index 0000000..2074ee4 --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/ForceJoint.scala @@ -0,0 +1,14 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics.joints + +/**A joint which can apply a force to its anchor bodies, thus adding or removing energy to the system.*/ +trait ForceJoint { + + /**Applies a force on the anchor bodies.*/ + def applyForce(): Unit +} diff --git a/src/main/scala/sims/dynamics/joints/Joint.scala b/src/main/scala/sims/dynamics/joints/Joint.scala new file mode 100644 index 0000000..652df97 --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/Joint.scala @@ -0,0 +1,27 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics.joints + +import sims.geometry._ +import sims.dynamics._ + +/**Joints constrain the movement of two bodies. + * Their implementation was inspired by Erin Catto's box2d.*/ +abstract class Joint extends Constraint{ + + /**First body of the joint.*/ + val node1: Body + + /**Second body of the joint.*/ + val node2: Body + + /**Corrects the velocities of this joint's associated bodies.*/ + def correctVelocity(h: Double): Unit + + /**Corrects the positions of this joint's associated bodies.*/ + def correctPosition(h: Double): Unit +}
\ No newline at end of file diff --git a/src/main/scala/sims/dynamics/joints/RevoluteJoint.scala b/src/main/scala/sims/dynamics/joints/RevoluteJoint.scala new file mode 100644 index 0000000..bf6f05e --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/RevoluteJoint.scala @@ -0,0 +1,57 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics.joints + +import sims.geometry._ +import sims.math._ +import sims.dynamics._ +import math._ + +/**A revolute joint that connects two bodies at a singe point. Inspired from JBox2D. + * <b>Warning:</b> there are still several bugs with revolute joints, if they are between two free + * bodies and not connected at their respective COMs.*/ +case class RevoluteJoint(node1: Body, node2: Body, anchor: Vector2D) extends Joint{ + private val a1 = anchor - node1.pos + private val a2 = anchor - node2.pos + private val initRotation1 = node1.rotation + private val initRotation2 = node2.rotation + def connection1 = (a1 rotate (node1.rotation - initRotation1)) + node1.pos + def connection2 = (a2 rotate (node2.rotation - initRotation2)) + node2.pos + + def x = connection2 - connection1 + def v = node2.velocityOfPoint(connection2) - node1.velocityOfPoint(connection1) + + /* x = connection2 - connection1 + * C = x + * Cdot = v = v2 - v1 = v2 + (w2 cross r2) - v1 - (w1 cross r1) + * J = [-I -r1_skew I r2_skew ] ????? + */ + def correctVelocity(h: Double) = { + val m1 = node1.mass + val m2 = node2.mass + val I1 = node1.I + val I2 = node2.I + val r1 = connection1 - node1.pos + val r2 = connection2 - node2.pos + + val K1 = new Matrix22(1/m1 + 1/m2, 0, + 0, 1/m1 + 1/m2) + val K2 = new Matrix22(1/I1 * r1.x * r1.x, -1/I1 * r1.x * r1.y, + -1/I1 * r1.x * r1.y, 1/I1 * r1.x * r1.x) + val K3 = new Matrix22(1/I2 * r2.x * r2.x, -1/I2 * r2.x * r2.y, + -1/I2 * r2.x * r2.y, 1/I2 * r2.x * r2.x) + val pivotMass = (K1 + K2 + K3).invert + val cdot = v + val p = pivotMass * cdot + node1.applyImpulse(p, connection1) + node2.applyImpulse(-p, connection2) + } + + def correctPosition(h: Double) = { + + } +} diff --git a/src/main/scala/sims/dynamics/joints/SpringJoint.scala b/src/main/scala/sims/dynamics/joints/SpringJoint.scala new file mode 100644 index 0000000..10d5afb --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/SpringJoint.scala @@ -0,0 +1,85 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics.joints + +import sims.dynamics._ +import sims.geometry._ + +/**A spring obeying Hooke's law. + * @param node1 first associated body + * @param anchor1 first connection point + * @param node2 second associated body + * @param anchor2 second connection point + * @param springConstant spring constant + * @param initialLength initial length + */ +case class SpringJoint(node1: Body, anchor1: Vector2D, node2: Body, anchor2: Vector2D, springConstant: Double, initialLength: Double) extends Joint with ForceJoint{ + + def this(node1: Body, anchor1: Vector2D, node2: Body, anchor2: Vector2D, springConstant: Double) = { + this(node1: Body, anchor1, node2: Body, anchor2, springConstant: Double, (anchor2 - anchor1).length) + } + + def this(node1: Body, node2: Body, springConstant: Double, initialLength: Double) = { + this(node1: Body, node1.pos, node2: Body, node2.pos, springConstant: Double, initialLength: Double) + } + def this(node1: Body, node2: Body, springConstant: Double) = { + this(node1: Body, node1.pos, node2: Body, node2.pos, springConstant: Double, (node2.pos - node1.pos).length) + } + + private val a1 = anchor1 - node1.pos + private val a2 = anchor2 - node2.pos + private val initRotation1 = node1.rotation + private val initRotation2 = node2.rotation + + /**Returns the connection point on body one (in world coordinates).*/ + def connection1 = (a1 rotate (node1.rotation - initRotation1)) + node1.pos + + /**Returns the connection point on body two (in world coordinates).*/ + def connection2 = (a2 rotate (node2.rotation - initRotation2)) + node2.pos + + /**Damping.*/ + var damping = 0.0 + + /**Relative position of the connection points.*/ + def x = connection2 - connection1 + + /**Relative velocity of the connection points.*/ + def v = node2.velocityOfPoint(connection2) - node1.velocityOfPoint(connection1) + + /**Returns the spring force.*/ + def force = (x.length - initialLength) * springConstant + + /**Applies the spring force to the connection points.*/ + def applyForce() = { + node1.applyForce(x.unit * force - (v * damping) project x, connection1) + node2.applyForce(-x.unit * force - (v * damping) project x, connection2) + //println("this should not happen") + } + + def correctVelocity(h: Double) = { + /* + val x = this.x + val v = this.v + val r1 = (connection1 - node1.pos) + val r2 = (connection2 - node2.pos) + val cr1 = r1 cross x.unit + val cr2 = r2 cross x.unit + val Cdot = x.unit dot v + val invMass = 1/node1.mass + 1/node1.I * cr1 * cr1 + 1/node2.mass + 1/node2.I * cr2 * cr2 //=J M^-1 JT + val m = if (invMass == 0.0) 0.0 else 1/invMass + val lambda = math.min(math.max(-this.force * h, (-m * Cdot)), this.force * h) + println (force * h, -m * Cdot) + val impulse = x.unit * lambda + node1.applyImpulse(-impulse, connection1) + node2.applyImpulse(impulse, connection2) + */ + } + + def correctPosition(h: Double) = { + + } +} diff --git a/src/main/scala/sims/dynamics/joints/test/PrismaticJoint.scala b/src/main/scala/sims/dynamics/joints/test/PrismaticJoint.scala new file mode 100644 index 0000000..040647d --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/test/PrismaticJoint.scala @@ -0,0 +1,84 @@ +package sims.dynamics.joints.test + +import sims.dynamics._ +import sims.dynamics.joints._ +import sims.geometry._ + +case class PrismaticJoint(node1: Body, anchor1: Vector2D, node2: Body, anchor2: Vector2D) extends Joint{ + def this(node1: Body, node2: Body) = this(node1, node1.pos, node2, node2.pos) + + val angle = node2.rotation - node1.rotation + + private val a1 = anchor1 - node1.pos + private val a2 = anchor2 - node2.pos + private val initRotation1 = node1.rotation + private val initRotation2 = node2.rotation + + def connection1 = (a1 rotate (node1.rotation - initRotation1)) + node1.pos + def connection2 = (a2 rotate (node2.rotation - initRotation2)) + node2.pos + + def x = connection2 - connection1 + + def v = node2.velocityOfPoint(connection2) - node1.velocityOfPoint(connection1) + + + def correctVelocity(h: Double) = { + correctLinear(h) + //correctAngular(h) + } + + def correctLinear(h: Double) = { + val x = this.x.unit + val n0 = x.leftNormal + val v = this.v + val r1 = (connection1 - node1.pos) + val r2 = (connection2 - node2.pos) + val cr1 = r1 cross n0 + val cr2 = r2 cross n0 + val Cdot = n0 dot v + val invMass = 1/node1.mass + 1/node1.I * cr1 * cr1 + 1/node2.mass + 1/node2.I * cr2 * cr2 + val m = if (invMass == 0.0) 0.0 else 1/invMass + val impulse = -n0 * m * Cdot + node1.applyImpulse(-impulse, connection1) + node2.applyImpulse(impulse, connection2) + } + + //J=[-1,1] + + def correctAngular(h: Double) = { + val w = node2.angularVelocity - node1.angularVelocity + val Cdot = w + val invMass = node1.I + node2.I + val m = 1 / invMass + val lambda = m * Cdot + node1.angularVelocity += lambda / node1.I + node2.angularVelocity += -lambda / node2.I + } + + def correctPosition(h: Double) = { + /* + val x = this.x.unit + val n0 = x.leftNormal + val v = this.v + val r1 = (connection1 - node1.pos) + val r2 = (connection2 - node2.pos) + val cr1 = r1 cross n0 + val cr2 = r2 cross n0 + val C = n0 dot x + val invMass = 1/node1.mass + 1/node1.I * cr1 * cr1 + 1/node2.mass + 1/node2.I * cr2 * cr2 + val m = if (invMass == 0.0) 0.0 else 1/invMass + val impulse = -n0 * m * C + node1.pos += -impulse + node1.rotation += -impulse cross r1 + node2.pos += impulse + node2.rotation += impulse cross r2 + + val relOmega = node2.angularVelocity - node2.angularVelocity + val invMassOmega = node1.I + node2.I + val mOmega = if (invMassOmega == 0.0) 0.0 else 1/invMassOmega + val Crot = node2.rotation - node2.rotation + angle + node1.rotation += mOmega * Crot + node2.rotation += -mOmega * Crot + */ + } +} diff --git a/src/main/scala/sims/dynamics/joints/test/UnitCircleJoint.scala b/src/main/scala/sims/dynamics/joints/test/UnitCircleJoint.scala new file mode 100644 index 0000000..09e72d9 --- /dev/null +++ b/src/main/scala/sims/dynamics/joints/test/UnitCircleJoint.scala @@ -0,0 +1,46 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.dynamics.joints.test + +import sims.dynamics._ +import sims.dynamics.joints._ +import sims.geometry._ + +class UnitCircleJoint(body: Body, anchor: Vector2D) extends Joint{ + + val node1 = body + val node2 = body + + private val a = anchor - body.pos + private val initRotation = body.rotation + def connection = (a rotate (body.rotation - initRotation)) + body.pos + def x = connection + def v = body.velocityOfPoint(connection) + + /* + * C = ||x|| - 1 + * Cdot = x/||x|| dot v = u dot v + * J = [u (r cross u)] + */ + def correctVelocity(h: Double) = { + val r = connection - body.pos + val u = x.unit + val cr = r cross u + val mc = 1.0/(1/body.mass + 1/body.I * cr * cr) + val lambda = -mc * (u dot v) + val Pc = u * lambda + + val vupdate = u * lambda / body.mass + val wupdate = (r cross u) * lambda / body.I + + println("dv = " + vupdate + " dw = " + wupdate) + body.linearVelocity = body.linearVelocity + u * lambda / body.mass + body.angularVelocity = body.angularVelocity + (r cross u) * lambda / body.I + } + + def correctPosition(h: Double) = {} +} diff --git a/src/main/scala/sims/geometry/ConvexPolygon.scala b/src/main/scala/sims/geometry/ConvexPolygon.scala new file mode 100644 index 0000000..bfd17a1 --- /dev/null +++ b/src/main/scala/sims/geometry/ConvexPolygon.scala @@ -0,0 +1,56 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.geometry + +import sims.collision._ +import sims.geometry._ + +/**Common properties of all convex polygons.*/ +trait ConvexPolygon { + + /**Returns positions of all vertices of this Polygon. Vertices are ordered counter-clockwise. + * @return position vectors of the vertices*/ + def vertices: Seq[Vector2D] + + /**Returns all sides of this polygon. The sides are ordered counter-clockwise, the first vertex of the side + * giving the side index.*/ + def sides = (for (i <- 0 until vertices.length) yield (new Segment(vertices(i), vertices((i + 1) % vertices.length)))).toArray + + /**Returns the projection of this polygon onto the line given by the directional vector <code>axis</code>. + * @param axis directional vector of the line + * @return projection of this polygon*/ + def project(axis: Vector2D) = { + val points = for (v <- vertices) yield {v project axis} + val bounds = for (p <- points) yield {if (axis.x != 0) p.x / axis.x else p.y / axis.y} + Projection(axis, + (bounds(0) /: bounds)(math.min(_,_)), + (bounds(0) /: bounds)(math.max(_,_))) + } + + /**Returns this polygon's axis aligned bounding box. + * @see collision.AABB*/ + def AABB = { + val xs = vertices map (_.x) + val ys = vertices map (_.y) + new AABB(Vector2D(xs.min, ys.min), + Vector2D(xs.max, ys.max)) + } + + /**Checks if the point <code>point</code> is contained in this polygon. + * <p> + * A ray is created, originating from the point and following an arbitrary direction (X-Axis was chosen). + * The number of intersections between the ray and this polygon's sides (including vertices) is counted. + * The amount of intersections with vertices is substracted form the previuos number. + * If the latter number is odd, the point is contained in the polygon.*/ + def contains(point: Vector2D) = { + val r = new Ray(point, Vector2D.i) + var intersections = 0 + for (s <- sides; if (r intersects s)) intersections += 1 + for (v <- vertices; if (r contains v)) intersections -= 1 + intersections % 2 != 0 + } +} diff --git a/src/main/scala/sims/geometry/Projection.scala b/src/main/scala/sims/geometry/Projection.scala new file mode 100644 index 0000000..9957c73 --- /dev/null +++ b/src/main/scala/sims/geometry/Projection.scala @@ -0,0 +1,35 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.geometry + +import sims.math._ + +/**Projection on an axis. + * <p> + * Projections are commonly used in SiMS for collision detection. + * @param axis directional vector of the axis of the projection + * @param lower lower value of the projection + * @param upper upper value of the projection*/ +case class Projection(axis: Vector2D, + lower: Double, + upper: Double) { + require(axis != Vector2D.Null, "A projection's axis cannot be given by a null vector!") + + /**Checks this projection for overlap with another projection <code>other</code>. + * @throws IllegalArgumentExcepion if both projections axes aren't the same*/ + def overlaps(other: Projection): Boolean = { + require(axis == other.axis, "Cannot compare two projections on different axes!") + !((other.lower - this.upper) > 0 || (this.lower - other.upper) > 0) + } + + /**Returns the overlap between this projection and another projection <code>other</code>. + * @throws IllegalArgumentExcepion if both projections axes aren't the same*/ + def overlap(other: Projection): Double = { + require(axis == other.axis, "Cannot compare two projections on different axes!") + (math.max(lower, other.lower) - math.min(upper, other.upper)).abs + } +} diff --git a/src/main/scala/sims/geometry/Ray.scala b/src/main/scala/sims/geometry/Ray.scala new file mode 100644 index 0000000..1cca8d5 --- /dev/null +++ b/src/main/scala/sims/geometry/Ray.scala @@ -0,0 +1,49 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.geometry + +import sims.math._ +import scala.math._ + +/**A ray. + * @param point a point on the ray + * @param direction this ray's directional vector + * @throws IllegalArgumentException if the directional vector is the null vector*/ +case class Ray(point: Vector2D, direction: Vector2D) { + + require(direction != Vector2D.Null, "A ray's direction cannot be given by a null vector!") + + /**Checks this ray and the given segment for intersection. + * @param s the segment to test for intersection*/ + def intersects(s: Segment) = { + val p1 = point + val p2 = point + direction + val p3 = s.vertex1 + val p4 = s.vertex2 + val d = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y) + val na = (p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x) + val nb = (p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x) + if (d == 0 && na == 0 && nb == 0) + true //lines are coincident + else if (d == 0) + false //parallel + else { + val ua = na / d + val ub = nb / d + (ub >= 0) && (ub <= 1) && (ua >= 0) + } + } + + /**Checks if this ray contains the point <code>p</code>.*/ + def contains(p: Vector2D) = { + val v = p - point + p == point || + Matrix22(direction, v).det == 0 && + signum(direction.x) == signum(v.x) && + signum(direction.y) == signum(v.y) + } +} diff --git a/src/main/scala/sims/geometry/Segment.scala b/src/main/scala/sims/geometry/Segment.scala new file mode 100644 index 0000000..4aaec21 --- /dev/null +++ b/src/main/scala/sims/geometry/Segment.scala @@ -0,0 +1,72 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.geometry + +/**A segment is given by its vertices. + * @param vertex1 position vector of the first vertex + * @param vertex2 position vector of the second vertex + * @throws IllegalArgumentException if both vertices are equal + */ +case class Segment(vertex1: Vector2D, vertex2: Vector2D){ + require(vertex1 != vertex2, "A segment must have 2 distinct vertices!") + + /**Length of this segment.*/ + val length = (vertex2 - vertex1).length + + /**Vector from <code>vertex1</code> to <code>vertex2</code>.*/ + val d = vertex2 - vertex1 + + /**Unit directional vector.*/ + val d0 = d.unit + + /**Right normal vector.*/ + val n = d.rightNormal + + /**Right normal unit vector.*/ + val n0 = n.unit + + /**Smallest distance between this segment and the point <code>point</code>.*/ + def distance(point: Vector2D): Double = { + val v = point - vertex1 //vector from vertex1 to point + val projection = v project d + val alpha = if (d.x != 0) d.x / projection.x else d.y / projection.y + if (alpha >= 0 && projection.length <= length) //point is closer to line between vertex1 and vertex2 + (v project n0).length + else if (alpha < 0) //point is closer to vertex1 + (point - vertex1).length + else if (alpha > 0) //point is closer to vertex2 + (point - vertex2).length + else + throw new IllegalArgumentException("Error occured trying to compute distance between segment and point.") + } + + def clipToSegment(s: Segment): Option[Vector2D] = { + + val distance1 = (vertex1 - s.vertex1) dot s.n0 + val distance2 = (vertex2 - s.vertex1) dot s.n0 + + if (distance1 * distance2 < 0) { //auf anderen Seiten + /* Geradengleichungen + * ================== + * Segment1: s1: x = a + alpha * r | alpha in [0,1] + * Segment2: s2: x = b + beta * s | beta in [0,1] + * + * alpha = [s2(a1-b1)-s1(a2-b2)] / [r2s1-r1s2] + * beta = [r2(b1-a1)-r1(b2-a2)] / [r1s2-r2s1] + * = [r1(b2-a2)]-r2(b1-a1) / [r2s1-r1s2] + * s1: vertex1 + alpha * d + * s2: s.vertex1 + beta * s.d + */ + val denom: Double = d.y * s.d.x - d.x * s.d.y + val alpha: Double = (s.d.y * (vertex1.x - s.vertex1.x) - s.d.x * (vertex1.y - s.vertex1.y)) / denom + val beta: Double = (d.x * (s.vertex1.y - vertex1.y) - d.y * (s.vertex1.x - vertex1.x)) / denom + if (0.0 <= alpha && alpha <= 1.0 && 0.0 <= beta && beta <= 1.0) Some(vertex1 + d * alpha) + else None + } + else None + } +} diff --git a/src/main/scala/sims/geometry/Vector2D.scala b/src/main/scala/sims/geometry/Vector2D.scala new file mode 100644 index 0000000..8d5205f --- /dev/null +++ b/src/main/scala/sims/geometry/Vector2D.scala @@ -0,0 +1,83 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.geometry + +import scala.math._ + +/**A 2D vector. + * @param x 1st component + * @param y 2nd component*/ +case class Vector2D(x: Double, y: Double) { + + /**Vector addition.*/ + def +(v: Vector2D): Vector2D = Vector2D(x + v.x, y + v.y) + + /**Vector substraction.*/ + def -(v: Vector2D): Vector2D = this + (v * -1) + + /**Scalar multiplication.*/ + def *(n: Double): Vector2D = Vector2D(x * n, y * n) + + /**Scalar division.*/ + def /(n: Double): Vector2D = this * (1/n) + + /**Unary minus.*/ + def unary_- : Vector2D = Vector2D(-x, -y) + + /**Dot product.*/ + def dot(v: Vector2D): Double = x * v.x + y * v.y + + /**Cross product. Length only because in 2D. The direction would be given by the x3-axis.*/ + def cross(v: Vector2D): Double = x * v.y - y * v.x + + /**Norm or length of this vector.*/ + val length: Double = math.sqrt(x * x + y * y) + + /**Unit vector.*/ + def unit: Vector2D = if (!(x == 0.0 && y == 0.0)) Vector2D(x / length, y / length) + else throw new IllegalArgumentException("Null vector does not have a unit vector.") + + /**Returns the projection of this vector onto the vector <code>v</code>.*/ + def project(v: Vector2D): Vector2D = { + if (v != Vector2D.Null) + v * ((this dot v) / (v dot v)) + else + Vector2D.Null + } + + /**Returns a rotation of this vector by <code>angle</code> radian.*/ + def rotate(angle: Double): Vector2D = { + Vector2D(cos(angle) * x - sin(angle) * y, + cos(angle) * y + sin(angle) * x) + } + + /**Left normal vector. (-y, x)*/ + def leftNormal: Vector2D = Vector2D(-y, x) + + /**Right normal vector. (y, -x)*/ + def rightNormal: Vector2D = Vector2D(y, -x) + + /**Checks if this vector is the null vector.*/ + def isNull: Boolean = this == Vector2D.Null + + /**Returns a list of this vector's components.*/ + def components = List(x, y) +} + +/**Contains special vectors.*/ +object Vector2D { + + /**Null vector.*/ + val Null = Vector2D(0,0) + + /**Horizontal unit vector. (1,0)*/ + val i = Vector2D(1,0) + + /**Vertical unit vector. (0,1)*/ + val j = Vector2D(0,1) +} + diff --git a/src/main/scala/sims/materials/Material.scala b/src/main/scala/sims/materials/Material.scala new file mode 100644 index 0000000..b05e082 --- /dev/null +++ b/src/main/scala/sims/materials/Material.scala @@ -0,0 +1,7 @@ +package sims.materials + +trait Material { + val density: Double + val restitution: Double + val friction: Double +} diff --git a/src/main/scala/sims/materials/Rubber.scala b/src/main/scala/sims/materials/Rubber.scala new file mode 100644 index 0000000..b408d2d --- /dev/null +++ b/src/main/scala/sims/materials/Rubber.scala @@ -0,0 +1,5 @@ +package sims.materials + +object Rubber { + +} diff --git a/src/main/scala/sims/materials/Steel.scala b/src/main/scala/sims/materials/Steel.scala new file mode 100644 index 0000000..1d14563 --- /dev/null +++ b/src/main/scala/sims/materials/Steel.scala @@ -0,0 +1,5 @@ +package sims.materials + +object Steel { + +}
\ No newline at end of file diff --git a/src/main/scala/sims/math/Matrix22.scala b/src/main/scala/sims/math/Matrix22.scala new file mode 100644 index 0000000..54d24c7 --- /dev/null +++ b/src/main/scala/sims/math/Matrix22.scala @@ -0,0 +1,55 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.math + +import sims.geometry._ + +/**A 2x2 matrix. + * @param c11 component 1,1 + * @param c12 component 1,2 + * @param c21 component 2,1 + * @param c22 component 2,2 + */ +case class Matrix22(c11: Double, c12: Double, c21: Double, c22: Double) { + + /**A 2x2 matrix can be created with two 2D vectors. In this case, each column is represented by a vector. + * @param c1 first column + * @param c2 second column*/ + def this(c1: Vector2D, c2: Vector2D) = this(c1.x, c2.x, c1.y, c2.y) + + /**Determinant of this matrix.*/ + def det = c11 * c22 - c21 * c12 + + /**Addition.*/ + def +(m: Matrix22) = + new Matrix22(c11 + m.c11, c12 + m.c12, + c21 + m.c21, c22 + m.c22) + + /**Scalar multiplication.*/ + def *(n: Double) = + new Matrix22(c11 * n, c12 * n, + c21 * n, c22 * n) + + /**Matrix multiplication.*/ + def *(m: Matrix22) = + new Matrix22(c11 * m.c11 + c12 * m.c21, c11 * m.c12 + c12 * m.c22, + c21 * m.c11 + c22 * m.c21, c21 * m.c12 + c22 * m.c22) + + /**Multiplikation with a 2D vector.*/ + def *(v: Vector2D) = + new Vector2D(c11 * v.x + c12 * v.y, + c21 * v.x + c22 * v.y) + + /**Inverse.*/ + def invert = + new Matrix22(c22 / det, -c12 / det, + -c21 / det, c11 / det) + } + +object Matrix22 { + def apply(c1: Vector2D, c2: Vector2D) = new Matrix22(c1.x, c2.x, c1.y, c2.y) +} diff --git a/src/main/scala/sims/prefabs/Net.scala b/src/main/scala/sims/prefabs/Net.scala new file mode 100644 index 0000000..d3f4d57 --- /dev/null +++ b/src/main/scala/sims/prefabs/Net.scala @@ -0,0 +1,47 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.prefabs + +import sims.geometry._ +import sims.dynamics._ +import sims.dynamics.joints._ + +class Net(width: Int, height: Int, initPos: Vector2D) extends Prefab { + val nodeDistance: Double = 0.2 + val nodeRadius: Double = 0.05 + val nodeDensity: Double = 4 + + val springConstant: Double = 50 + val springDamping: Double = 0 + + private val connectors: Array[Array[Body]] = + makeConnectors(width, height) + + override val bodies: List[Body] = for (row <- connectors.toList; elem <- row) yield elem + override val joints = connect(connectors) + + private def makeConnectors(w: Int, h: Int): Array[Array[Body]] = { + for(i <- (0 until w).toArray[Int]) yield + for(j <- (0 until h).toArray[Int]) yield + new Body(new Circle(nodeRadius, nodeDensity) {pos = Vector2D(nodeDistance * i, nodeDistance * j) + initPos}) + } + + private def connect(connectors: Array[Array[Body]]): List[DistanceJoint] = { + var r: List[DistanceJoint] = Nil + for(i <- 0 to connectors.length - 1; j <- 0 to connectors(i).length - 1) { + if (i > 0) + r = connect(connectors(i-1)(j),connectors(i)(j)) :: r + if (j > 0) + r = connect(connectors(i)(j-1),connectors(i)(j)) :: r + } + r + } + + private def connect(s1: Body, s2: Body): DistanceJoint = + new DistanceJoint(s1, s1.pos, s2, s2.pos) + +}
\ No newline at end of file diff --git a/src/main/scala/sims/prefabs/Prefab.scala b/src/main/scala/sims/prefabs/Prefab.scala new file mode 100644 index 0000000..84bb3b7 --- /dev/null +++ b/src/main/scala/sims/prefabs/Prefab.scala @@ -0,0 +1,15 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.prefabs + +import sims.dynamics._ +import sims.dynamics.joints._ + +trait Prefab { + val bodies: Iterable[Body] = Nil + val joints: Iterable[Joint] = Nil +} diff --git a/src/main/scala/sims/prefabs/Pylon.scala b/src/main/scala/sims/prefabs/Pylon.scala new file mode 100644 index 0000000..7f3211f --- /dev/null +++ b/src/main/scala/sims/prefabs/Pylon.scala @@ -0,0 +1,47 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.prefabs + +import sims.geometry._ +import sims.dynamics._ +import sims.dynamics.joints._ + +class Pylon extends Prefab{ + val position: Vector2D = Vector2D(2,1) + val nodeDensity: Double = 100 + val beamHeight: Double = 1 + val beamWidth: Double = 0.5 + val beamNumber: Int = 10 + + private val nodeRow1 = (for (i <- 0 to beamNumber) yield (new Circle(0.01, nodeDensity) { + pos = position + Vector2D(0, i * beamHeight)}).asBody).toList + private val nodeRow2 = (for (i <- 0 to beamNumber) yield (new Circle(0.01, nodeDensity) { + pos = position + Vector2D(beamWidth, i * beamHeight)}).asBody).toList + + private val beamRow1 = (for (i <- 0 until nodeRow1.length - 1) yield + new DistanceJoint(nodeRow1(i), nodeRow1(i).pos, nodeRow1(i+1), nodeRow1(i + 1).pos)).toList + private val beamRow2 = (for (i <- 0 until nodeRow1.length - 1) yield + new DistanceJoint(nodeRow2(i), nodeRow2(i).pos, nodeRow2(i+1), nodeRow2(i + 1).pos)).toList + + private val latBeams = (for (i <- 0 to beamNumber) yield + new DistanceJoint(nodeRow1(i), nodeRow2(i))).toList + private val diagBeams1 = (for (i <- 0 until beamNumber) yield + new DistanceJoint(nodeRow1(i), nodeRow2(i + 1))).toList + private val diagBeams2 = (for (i <- 0 until beamNumber) yield + new DistanceJoint(nodeRow2(i), nodeRow1(i + 1))).toList + + + + + lazy val nodes = nodeRow1 ++ nodeRow2 + lazy val beams = beamRow1 ++ beamRow2 ++ latBeams ++ diagBeams1 ++ diagBeams2 + + override val bodies = nodes + override val joints = beams + + +} diff --git a/src/main/scala/sims/prefabs/Ragdoll.scala b/src/main/scala/sims/prefabs/Ragdoll.scala new file mode 100644 index 0000000..00e4b8d --- /dev/null +++ b/src/main/scala/sims/prefabs/Ragdoll.scala @@ -0,0 +1,43 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.prefabs + +import sims.dynamics._ +import sims.dynamics.joints._ +import sims.geometry._ + +class Ragdoll(position: Vector2D) extends Prefab { + val headTorso = new Body(new Circle(0.1, 1) {pos = position}, + new Rectangle(0.09, 0.35, 1) {pos = position + Vector2D(0, -0.45)}) + val thigh1 = (new Rectangle(0.075, 0.17, 1) {pos = position + Vector2D(0, -0.97)}).asBody + val thigh2 = (new Rectangle(0.075, 0.17, 1) {pos = position + Vector2D(0, -0.97)}).asBody + val tibia1 = (new Rectangle(0.075, 0.25, 1) {pos = position + Vector2D(0, -1.39)}).asBody + val tibia2 = (new Rectangle(0.075, 0.25, 1) {pos = position + Vector2D(0, -1.39)}).asBody + val foot1 = (new Circle(0.08, 1) {pos = position + Vector2D(0, -1.72)}).asBody + val foot2 = (new Circle(0.08, 1) {pos = position + Vector2D(0, -1.72)}).asBody + val upperArm1 = (new Rectangle(0.17, 0.06, 1) {pos = position + Vector2D(0.17, -0.16)}).asBody + val upperArm2 = (new Rectangle(0.17, 0.06, 1) {pos = position + Vector2D(-0.17, -0.16)}).asBody + val forearm1 = (new Rectangle(0.15, 0.06, 1) {pos = position + Vector2D(0.49, -0.16)}).asBody + val forearm2 = (new Rectangle(0.15, 0.06, 1) {pos = position + Vector2D(-0.49, -0.16)}).asBody + val hand1 = (new Circle(0.07, 1) {pos = position + Vector2D(0.71, -0.16)}).asBody + val hand2 = (new Circle(0.07, 1) {pos = position + Vector2D(-0.71, -0.16)}).asBody + + override val bodies = List(headTorso, + thigh1, thigh2, + tibia1, tibia2, + foot1, foot2, + upperArm1, upperArm2, + forearm1, forearm2, + hand1, hand2) + private val shapes = bodies.flatMap(_.shapes) + for (s <- shapes) s.transientShapes ++= shapes + + val shoulder1 = RevoluteJoint(headTorso, upperArm1, position + Vector2D(0, -0.16)) + val shoulder2 = RevoluteJoint(headTorso, upperArm2, position + Vector2D(0, -0.16)) + override val joints = Nil //List(shoulder1, shoulder2) + +} diff --git a/src/main/scala/sims/util/Polar.scala b/src/main/scala/sims/util/Polar.scala new file mode 100644 index 0000000..494c984 --- /dev/null +++ b/src/main/scala/sims/util/Polar.scala @@ -0,0 +1,17 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.util + +import sims.geometry._ +import scala.math._ + +/**Polar coordinates.*/ +case class Polar(distance: Double, angle: Double) { + + /**Returns the vector representation of these polar coordinates.*/ + def toCarthesian = Vector2D(distance * sin(angle), distance * cos(angle)) +} diff --git a/src/main/scala/sims/util/Positioning.scala b/src/main/scala/sims/util/Positioning.scala new file mode 100644 index 0000000..cf72276 --- /dev/null +++ b/src/main/scala/sims/util/Positioning.scala @@ -0,0 +1,24 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.util + +import sims.geometry._ +import sims.dynamics._ + +/**Utility functions for comfortable positioning of bodies.*/ +object Positioning { + + implicit def int2RelativeVector(x: Int): RelativeVector = new RelativeVector(x, 0) + implicit def double2RelativeVector(x: Double): RelativeVector = new RelativeVector(x, 0) + implicit def vector2RelativeVector(v: Vector2D): RelativeVector = new RelativeVector(v.x, v.y) + implicit def polar2Carthesian(p: Polar): Vector2D = p.toCarthesian + implicit def polar2RelativeVector(p: Polar): RelativeVector = vector2RelativeVector(p.toCarthesian) + + def position(s: Shape)(a: Vector2D) = { + s.pos = a + } +} diff --git a/src/main/scala/sims/util/RelativeVector.scala b/src/main/scala/sims/util/RelativeVector.scala new file mode 100644 index 0000000..374f92c --- /dev/null +++ b/src/main/scala/sims/util/RelativeVector.scala @@ -0,0 +1,24 @@ +/* + * Simple Mechanics Simulator (SiMS) + * copyright (c) 2009 Jakob Odersky + * made available under the MIT License +*/ + +package sims.util + +import sims.geometry._ +import sims.dynamics._ + +class RelativeVector(val x: Double, val y: Double) { + def above(point: Vector2D): Vector2D = point + Vector2D(0, x) + def below(point: Vector2D): Vector2D = point - Vector2D(0, x) + def left(point: Vector2D): Vector2D = point - Vector2D(x, 0) + def right(point: Vector2D): Vector2D = point + Vector2D(x, 0) + def from(point: Vector2D): Vector2D = point + Vector2D(x, y) + + def above(s: Shape): Vector2D = this.above(s.pos) + def below(s: Shape): Vector2D = this.below(s.pos) + def left(s: Shape): Vector2D = this.left(s.pos) + def right(s: Shape): Vector2D = this.right(s.pos) + def from(s: Shape): Vector2D = this.from(s.pos) +} |