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/* _____ _ __ ________ ___ *\
** / ___/(_) |/ / ___/ |__ \ Simple Mechanics Simulator 2 **
** \__ \/ / /|_/ /\__ \ __/ / copyright (c) 2011 Jakob Odersky **
** ___/ / / / / /___/ / / __/ **
** /____/_/_/ /_//____/ /____/ **
\* */
package sims.dynamics
import scala.math._
import sims.collision.ConvexPolygon
import sims.math._
/**A regular polygon with <code>n</code> sides whose excircle has a radius <code>radius</code>.
* @define shape regular polygon
*
* @param n number 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) extends ConvexPolygon with Shape {
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 <- (0 until n).toArray) yield (Vector2D(0, radius) rotate (2 * Pi * i / n))) map (_ rotate rotation)
def vertices = for (h <- halfDiags) yield position + h
val area = n * h * b / 2
/**Moment of inertia of one of the constituting triangles about the center of this polygon.*/
private val Ic: Double = density * b * (3 * b + 16) * pow(h, 4) / 54
val inertia = n * Ic
}
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