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/*
* Simple Mechanics Simulator (SiMS)
* copyright (c) 2009 Jakob Odersky
* made available under the MIT License
*/
package sims.geometry
/**Ein Segment wird durch seine beiden Extrempunkte gegeben.
* @param vertex1 Ortsvektor des 1. Extrempunkts
* @param vertex2 Ortsvektor des 2. Extrempunkts*/
case class Segment(vertex1: Vector2D, vertex2: Vector2D){
require(vertex1 != vertex2, "A segment must have 2 distinct vertices!")
/**Laenge dieses Segments.*/
val length = (vertex2 - vertex1).length
/**Vektor von EP1 zu EP2.*/
val d = vertex2 - vertex1
/**Einheitsrichtungsvektor.*/
val d0 = d.unit
/**Normalenvektor. Richtung: 90 Grad rechts zu d.*/
val n = d.rightNormal
/**Normaleneinheitsvektor. Richtung: 90 Grad rechts zu d.*/
val n0 = n.unit
/**Kleinster Abstand zwischen diesem Segment und dem Punkt <code>p</code>.*/
def distance(point: Vector2D): Double = {
val v = point - vertex1 //Vektor von EP1 zu 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) //Punkt ist naeher zu der Geraden zwischen EP1 und EP2
(v project n0).length
else if (alpha < 0) //Punkt ist naeher zu EP1
(point - vertex1).length
else if (alpha > 0) //Punkt ist naeher zu EP2
(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
}
}
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