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/*
* 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)
}
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