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Diffstat (limited to 'src/main/scala/sims/math/vector.scala')
| -rw-r--r-- | src/main/scala/sims/math/vector.scala | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/src/main/scala/sims/math/vector.scala b/src/main/scala/sims/math/vector.scala new file mode 100644 index 0000000..8e7c716 --- /dev/null +++ b/src/main/scala/sims/math/vector.scala @@ -0,0 +1,127 @@ +/* _____ _ __ ________ ___ *\ +** / ___/(_) |/ / ___/ |__ \ Simple Mechanics Simulator 2 ** +** \__ \/ / /|_/ /\__ \ __/ / copyright (c) 2011 Jakob Odersky ** +** ___/ / / / / /___/ / / __/ ** +** /____/_/_/ /_//____/ /____/ ** +\* */ + +package sims.math + +import scala.math._ + +/** A 2D vector. + * @param x 1st component + * @param y 2nd component */ +case class Vector2D(x: Double, y: Double) { + + /** Components of this vector. */ + lazy val components = List(x, y) + + /** Vector addition. */ + def +(v: Vector2D): Vector2D = new Vector2D(x + v.x, y + v.y) + + /** Scalar multiplication. */ + def *(n: Double): Vector2D = new Vector2D(x * n, y * n) + + /** Inverse of this vector. */ + lazy val unary_- = this * (-1) + + /** Add inverse of another vector. */ + def -(v: Vector2D) = this + -v + + /** Multiply by inverse of scalar. */ + def /(n: Double) = this * (1 / n) + + /** 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 + + /** Cross product with an imaginary vector parallel to the x3-axis. + * Its magnitude is given by |p| and its direction sign(p). */ + def cross(p: PseudoVector3D): Vector2D = rightNormal * p.x3 + + /** Magnitude of this vector. */ + lazy val length: Double = math.sqrt(lengthSquare) + + lazy val lengthSquare: Double = x * x + y * y + + /** Unit vector. */ + lazy val unit: UnitVector2D = + if (!(x == 0.0 && y == 0.0)) new UnitVector2D(x / length, y / length) + else throw new UnsupportedOperationException("Null vector does not have a unit vector.") + + /** Returns the projection of this vector onto the vector `v`. */ + def project(v: Vector2D): Vector2D = { + if (v != Vector2D.Null) + v * ((this dot v) / (v.lengthSquare)) + else + Vector2D.Null + } + + /** Returns the projection of this vector onto the unit vector `v`. */ + def project(v: UnitVector2D): Vector2D = { + if (v != Vector2D.Null) + v * (this dot v) + else + Vector2D.Null + } + + /** Returns this vector rotated by `angle` radians. */ + def rotate(angle: Double): Vector2D = { + Vector2D(cos(angle) * x - sin(angle) * y, + cos(angle) * y + sin(angle) * x) + } + + /** Left normal vector. (-y, x) */ + lazy val leftNormal: Vector2D = Vector2D(-y, x) + + /** Right normal vector. (y, -x) */ + lazy val rightNormal: Vector2D = Vector2D(y, -x) + + /** Checks if this vector is the null vector. */ + def isNull: Boolean = this == Vector2D.Null + + /** Colinearity check. */ + def ~(v: Vector2D): Boolean = x * v.y - v.x * y == 0 + + + def leftOf(v: Vector2D): Boolean = (this dot v.leftNormal) > 0 + def rightOf(v: Vector2D): Boolean = (this dot v.rightNormal) > 0 + def directionOf(v: Vector2D): Boolean = (this dot v) > 0 + +} + +object Vector2D { + + /**Null vector.*/ + val Null = Vector2D(0,0) + + /**Horizontal unit vector. (1,0)*/ + val i = new UnitVector2D(1,0) + + /**Vertical unit vector. (0,1)*/ + val j = new UnitVector2D(0,1) + +} + +/** A two dimensional vector considered having a magnitude of one. + * Unit vectors are used internally for increasing performance + * (i.e. the length of a unit vector is always one, the unit vector of + * a unit vector is always itself). */ +class UnitVector2D(x: Double, y: Double) extends Vector2D(x, y) { + + def isValid = x * x + y * y == 1 + + override lazy val unit = this + + override lazy val length = 1.0 + + override lazy val lengthSquare = 1.0 + + override lazy val leftNormal = new UnitVector2D(-y, x) + + override lazy val rightNormal = new UnitVector2D(y, -x) + +}
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