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init CDT
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@ -28,14 +28,75 @@
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* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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package org.poly2tri.cdt
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import scala.collection.mutable.ArrayBuffer
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import shapes.{Segment, Point}
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import utils.Util
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/**
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* Sweep-line, Constrained Delauney Triangulation
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* See: Domiter, V. and Žalik, B.(2008)'Sweep-line algorithm for constrained Delaunay triangulation',
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* International Journal of Geographical Information Science,22:4,449 — 462
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*/
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package org.poly2tri.cdt
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class CDT {
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class CDT(segments: ArrayBuffer[Segment]) {
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// The point list
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val points = init
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// The triangle mesh
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val mesh = new Mesh
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// Sweep points; build mesh
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sweep
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// Finalize triangulation
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finalization
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// Initialize and sort point list
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private def init: List[Point] = {
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var xmax, xmin = 0f
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var ymax, ymin = 0f
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val pts = new ArrayBuffer[Point]
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for(i <- 0 until segments.size) {
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val p = segments(i).p
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val q = segments(i).q
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if(p.x > xmax) xmax = p.x
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if(q.x > xmax) xmax = q.x
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if(p.x < xmin) xmin = p.x
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if(q.x < xmin) xmin = q.x
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if(p.y > ymax) ymax = p.x
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if(q.y > ymax) ymax = q.x
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if(p.y < ymin) ymin = p.x
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if(q.y < ymin) ymin = q.x
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pts += shearTransform(p)
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pts += shearTransform(q)
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}
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if(pts.size < 10)
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// Insertion sort is one of the fastest algorithms for sorting arrays containing
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// fewer than ten elements, or for lists that are already mostly sorted.
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Util.insertSort((p1: Point, p2: Point) => p1 > p2)(pts).toList
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else
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// Merge sort: O(n log n)
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Util.msort((p1: Point, p2: Point) => p1 > p2)(pts.toList)
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}
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// Implement sweep-line paradigm
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private def sweep {
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}
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private def finalization {
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}
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// Prevents any two distinct endpoints from lying on a common horizontal line, and avoiding
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// the degenerate case. See Mark de Berg et al, Chapter 6.3
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//val SHEER = 0.0001f
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def shearTransform(point: Point) = Point(point.x, point.y + point.x * 0.0001f)
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}
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@ -31,7 +31,9 @@
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package org.poly2tri.cdt
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import scala.collection.mutable.HashSet
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import shapes.Point
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class Mesh {
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val map = HashSet.empty[Triangle]
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@ -158,7 +158,7 @@ class Triangulator(segments: ArrayBuffer[Segment]) {
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if(s.mPoints.size < 10)
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// Insertion sort is one of the fastest algorithms for sorting arrays containing
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// fewer than ten elements, or for lists that are already mostly sorted.
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k = Util.insertSort(s.mPoints).toList
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k = Util.insertSort((p1: Point, p2: Point) => p1 < p2)(s.mPoints).toList
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else
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k = Util.msort((p1: Point, p2: Point) => p1 < p2)(s.mPoints.toList)
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@ -30,10 +30,18 @@
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*/
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package org.poly2tri.shapes
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object Event extends Enumeration {
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val point, edge = Value
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}
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case class Point(val x: Float, val y: Float) {
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// Pointers to next and previous points in Monontone Mountain
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var next, prev: Point = null
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// The setment this point belongs to
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var segment: Segment = null
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// Point type for CDT
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var eventType: Event.Value = _
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@inline def -(p: Point) = Point(x - p.x, y - p.y)
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@inline def +(p: Point) = Point(x + p.x, y + p.y)
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@ -45,7 +53,10 @@ case class Point(val x: Float, val y: Float) {
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@inline def dot(p: Point) = x * p.x + y * p.y
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@inline def length = Math.sqrt(x * x + y * y).toFloat
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@inline def normalize = this / length
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@inline def <(p: Point) = (x < p.x)
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// Sort along x axis
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@inline def <(p: Point) = (x < p.x)
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// Sort along y axis
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@inline def >(p: Point) = (y < p.y)
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@inline def !(p: Point) = !(p.x == x && p.y == y)
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@inline override def clone = Point(x, y)
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}
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@ -35,11 +35,13 @@ import scala.collection.mutable.{ArrayBuffer}
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// Represents a simple polygon's edge
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class Segment(var p: Point, var q: Point) {
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p.segment = this
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q.segment = this
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// Pointers used for building trapezoidal map
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var above, below: Trapezoid = null
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// Montone mountain points
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val mPoints = new ArrayBuffer[Point]
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// Equation of a line: y = m*x + b
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// Slope of the line (m)
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val slope = (q.y - p.y)/(q.x - p.x)
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@ -50,5 +52,28 @@ class Segment(var p: Point, var q: Point) {
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def > (point: Point) = (Math.floor(point.y) < Math.floor(slope * point.x + b))
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// Determines if this segment lies below the given point
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def < (point: Point) = (Math.floor(point.y) > Math.floor(slope * point.x + b))
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// Assign point type for CDT
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if(p.y > q.y)
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pEdge
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else if (p.y < q.y)
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pPoint
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else
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if(p.x < q.x)
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pPoint
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else if (p.x > q.x)
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pEdge
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else
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throw new Exception("Invalid segment")
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private def pPoint {
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p.eventType = Event.point
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q.eventType = Event.edge
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}
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private def pEdge {
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p.eventType = Event.edge
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q.eventType = Event.point
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}
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}
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@ -19,19 +19,19 @@ object Util {
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else merge(msort(less)(xs take n), msort(less)(xs drop n))
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}
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def insertSort(list:ArrayBuffer[Point]) = {
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def insertSort[A](less: (A, A) => Boolean)(xs: ArrayBuffer[A]): ArrayBuffer[A] = {
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var j = 1
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while(j < list.size){
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val key = list(j)
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while(j < xs.size){
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val key = xs(j)
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var i = j-1
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while(i>=0 && list(i).x > key.x){
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list(i+1) = list(i)
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i=i-1
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while(i >= 0 && less(key, xs(i)) ){
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xs(i+1) = xs(i)
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i -= 1
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}
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list(i+1)=key
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j=j+1
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xs(i+1)=key
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j += 1
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}
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list
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xs
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}
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}
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