内接円付きドロネー図（分割）
画面を適当にクリックすると3クリック以降、ポイントと線がひかれます。
線は交差すること無くひかれていきます
参照：
ドロネー図
http://ja.wikipedia.org/wiki/ドロネー図
ドロネー図の作図方法
http://homepage3.nifty.com/endou/tips/04/tips33.htm
外接円
http://wonderfl.net/code/ad8b6c5010abdb44d3e34d3a7cd06a200b35175d
.fla2「YuruYurer」（195P）
http://www.amazon.co.jp/dp/4862670717
内接円を求める
http://homepage1.nifty.com/MADIA/delphi/delphi_bbs/200706/200706_07060041.html
ヘロンの公式
http://ja.wikipedia.org/wiki/ヘロンの公式
/**
* Copyright fumix ( http://wonderfl.net/user/fumix )
* MIT License ( http://www.opensource.org/licenses/mit-license.php )
* Downloaded from: http://wonderfl.net/c/yhBp
*/
// forked from fumix's ドロネー図（分割）
/**
画面を適当にクリックすると3クリック以降、ポイントと線がひかれます。
線は交差すること無くひかれていきます
参照：
ドロネー図
http://ja.wikipedia.org/wiki/ドロネー図
ドロネー図の作図方法
http://homepage3.nifty.com/endou/tips/04/tips33.htm
外接円
http://wonderfl.net/code/ad8b6c5010abdb44d3e34d3a7cd06a200b35175d
.fla2「YuruYurer」（195P）
http://www.amazon.co.jp/dp/4862670717
内接円を求める
http://homepage1.nifty.com/MADIA/delphi/delphi_bbs/200706/200706_07060041.html
ヘロンの公式
http://ja.wikipedia.org/wiki/ヘロンの公式
*/
package {
import flash.display.Graphics;
import flash.display.Sprite;
import flash.display.StageQuality;
import flash.display.StageScaleMode;
import flash.events.Event;
import flash.events.MouseEvent;
import flash.geom.Point;
[SWF(width = 465, height = 465, backgroundColor = 0x0, frameRate = 60)]
public class Delaunay extends Sprite {
//----------------------------------------
//VARIABLES
//点群
private var _points : Array;
//三角形の集まり
private var _triangles : Array;
//キャンバス
private var _canvas : Sprite;
/*
* コンストラクタ
*/
public function Delaunay() {
//初期化
addEventListener(Event.ADDED_TO_STAGE, _initialize);
}
/*
* 初期化
*/
private function _initialize(event : Event) : void {
removeEventListener(Event.ADDED_TO_STAGE, _initialize);
stage.scaleMode = StageScaleMode.NO_SCALE;
stage.quality = StageQuality.LOW;
var stageWidth : Number = stage.stageWidth;
var stageHeight : Number = stage.stageHeight;
//ドロー用
_canvas = addChild(new Sprite()) as Sprite;
_points = new Array();
_triangles = new Array();
//_points生成
//ステージの大きさの三角形2つを用意
_points.push(new Node(0, 0, 0));
_points.push(new Node(1, stageWidth, 0));
_points.push(new Node(2, stageWidth, stageHeight));
_points.push(new Node(3, 0, stageHeight));
_triangles.push(new Triangle(_points[0], _points[1], _points[2]));
_triangles.push(new Triangle(_points[0], _points[2], _points[3]));
addEventListener(Event.ENTER_FRAME, _updateHandler);
stage.addEventListener(MouseEvent.MOUSE_UP, _stageMouseUpHandler);
}
/*
* アップデート
*/
private function _updateHandler(event : Event) : void {
_interaction();
_draw();
}
/*
* インタラクション
*/
private function _interaction() : void {
//一時保持の三角形群
var localTriangles : Array = new Array();
//辺
var edges : Array;
//多角形
var polygon : Array;
//ポイント群ループ
for (var k : int = 4;k < _points.length;k++) {
var node : Node = _points[k];
localTriangles = new Array();
edges = new Array();
for (var i : String in _triangles) {
//点が外接円
var tri : Triangle = _triangles[i];
if(inOuterCircle(node.point.x, node.point.y, tri)) {
edges.push(new Edge(tri.node0, tri.node1));
edges.push(new Edge(tri.node1, tri.node2));
edges.push(new Edge(tri.node2, tri.node0));
} else {
localTriangles.push(tri);
}
}
//edgesからpolygonを作る（重複辺の削除
polygon = new Array();
for (i in edges) {
var edge0 : Edge = edges[i];
//重複チェック
var flg : Boolean = false;
for (var j : String in polygon) {
var edge1 : Edge = polygon[j];
if(judgeEdges(edge0, edge1)) {
flg = true;
polygon.splice(j, 1);
break;
}
}
//データが存在しない場合は追加
if(!flg) polygon.push(edges[i]);
}
//polygonから三角形を作って挿入
for (i in polygon) {
var tri1 : Triangle = new Triangle(polygon[i].node0, polygon[i].node1, node);
localTriangles.push(tri1);
}
if(localTriangles.length > 1) _triangles = localTriangles;
}
}
/*
* 同じ辺かどうかの判定
*/
private function judgeEdges(edge : Edge, edge0 : Edge) : Boolean {
if(edge.node0.id == edge0.node0.id && edge.node1.id == edge0.node1.id) {
return true;
}
if(edge.node1.id == edge0.node0.id && edge.node0.id == edge0.node1.id) {
return true;
}
return false;
}
/*
* 描画
*/
private function _draw() : void {
var g : Graphics = _canvas.graphics;
var offset : Number = 0;
g.clear();
g.lineStyle(1, 0xffffff);
//三角形群のループ
for (var i : int = 0;i < _triangles.length;i++) {
var tri : Triangle = _triangles[i];
//四隅のポイントを含む三角形は描画しない
if(!(tri.node0.id == 0 || tri.node1.id == 0 || tri.node2.id == 0 || tri.node0.id == 1 || tri.node1.id == 1 || tri.node2.id == 1 || tri.node0.id == 2 || tri.node1.id == 2 || tri.node2.id == 2 || tri.node0.id == 3 || tri.node1.id == 3 || tri.node2.id == 3)
) {
g.moveTo(tri.node0.point.x + offset, tri.node0.point.y + offset);
g.lineTo(tri.node1.point.x + offset, tri.node1.point.y + offset);
g.lineTo(tri.node2.point.x + offset, tri.node2.point.y + offset);
g.lineTo(tri.node0.point.x + offset, tri.node0.point.y + offset);
g.beginFill(0xFF0000);
g.drawCircle(tri.node0.point.x + offset, tri.node0.point.y + offset, 3);
g.drawCircle(tri.node1.point.x + offset, tri.node1.point.y + offset, 3);
g.drawCircle(tri.node2.point.x + offset, tri.node2.point.y + offset, 3);
g.endFill();
//内接円の描画
var innerCirclePoint : Point = addInnerCircle(tri);
g.drawCircle(innerCirclePoint.x, innerCirclePoint.y, addInnerCircleRadius(tri));
}
}
}
/*
* 外接円の内か外か
*/
static function inOuterCircle(x : Number,y : Number,tri : Triangle) : Boolean {
var node0 : Node = tri.node0;
var node1 : Node = tri.node1;
var node2 : Node = tri.node2;
var d : Number = (node0.point.x * node0.point.x + node0.point.y * node0.point.y - x * x - y * y) * ((node1.point.x - x) * (node2.point.y - y) - (node2.point.x - x) * (node1.point.y - y)) + (node1.point.x * node1.point.x + node1.point.y * node1.point.y - x * x - y * y) * ((node2.point.x - x) * (node0.point.y - y) - (node2.point.y - y) * (node0.point.x - x)) + (node2.point.x * node2.point.x + node2.point.y * node2.point.y - x * x - y * y) * ((node0.point.x - x) * (node1.point.y - y) - (node0.point.y - y) * (node1.point.x - x));
return ( (node1.point.x - node0.point.x) * (node2.point.y - node0.point.y) - (node1.point.y - node0.point.y) * (node2.point.x - node0.point.x) > 0 ) ? d > 0 : d <= 0;
}
/*
* マウスクリック時
*/
private function _stageMouseUpHandler(event : MouseEvent) : void {
_points.push(new Node(_points.length, mouseX, mouseY));
}
/*
* 内接円の中心
*/
static function addInnerCircle(tri : Triangle) : Point {
var x1 : Number = tri.node0.point.x;
var y1 : Number = tri.node0.point.y;
var x2 : Number = tri.node1.point.x;
var y2 : Number = tri.node1.point.y;
var x3 : Number = tri.node2.point.x;
var y3 : Number = tri.node2.point.y;
var a : Number = Math.sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
var b : Number = Math.sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1));
var c : Number = Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
var px : Number = (1 / (a + b + c)) * (a * x1 + b * x2 + c * x3);
var py : Number = (1 / (a + b + c)) * (a * y1 + b * y2 + c * y3);
return new Point(px, py);
}
/*
* 内接円の半径
*/
static function addInnerCircleRadius(tri : Triangle) : Number {
var x1 : Number = tri.node0.point.x;
var y1 : Number = tri.node0.point.y;
var x2 : Number = tri.node1.point.x;
var y2 : Number = tri.node1.point.y;
var x3 : Number = tri.node2.point.x;
var y3 : Number = tri.node2.point.y;
var a : Number = Math.sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
var b : Number = Math.sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1));
var c : Number = Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
var s : Number = (a + b + c) * 0.5;
var ss : Number = Math.sqrt(s * (s - a) * (s - b) * (s - c));
var r : Number = 2 * ss / (a + b + c);
return r;
}
}
}
class Triangle {
private var _node0 : Node;
private var _node1 : Node;
private var _node2 : Node;
public function Triangle(node0:Node,node1:Node,node2:Node):void {
_node0 = node0;
_node1 = node1;
_node2 = node2;
}
public function get node0() : Node {
return _node0;
}
public function get node1() : Node {
return _node1;
}
public function get node2() : Node {
return _node2;
}
}
import flash.geom.Point;
class Node {
private var _id : int;
private var _point : Point;
public function Node(id:int,x:Number,y:Number) {
_id = id;
_point = new Point(x,y);
}
public function get id() : int {
return _id;
}
public function get point() : Point {
return _point;
}
}
class Edge {
private var _node0 : Node;
private var _node1 : Node;
public function Edge(node0:Node,node1:Node):void {
_node0 = node0;
_node1 = node1;
}
public function get node0() : Node {
return _node0;
}
public function get node1() : Node {
return _node1;
}
}