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# Mathematics Sketch

ActionScriptを使って数学の勉強。
ベクトルの内積を使うと線と点の一番近い点を簡単に求める事ができる。
１）線のベクトルを正規化（大きさが1のベクトル）にする
２）点のベクトルと正規化したベクトルの内積を求める
３）正規化ベクトルを内積倍すると点の位置になる
by euakast 15 Feb 2011

## Tags

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/**
* Copyright euakast ( http://wonderfl.net/user/euakast )
*/

package
{
import com.bit101.components.*;
import flash.display.Sprite;
import flash.events.Event;
import flash.events.MouseEvent;

public class MathematicsSketch extends Sprite
{
private var _center:Vec2d;
private var _container:Sprite;

private var _rotateSpeed:Number;

private var _point:PointSprite;
private var _pointVec:Vec2d;

private var _lineStartPoint:Vec2d;
private var _lineEndPoint:Vec2d;

private var _circleLabel:Label;

public function MathematicsSketch()
{
if (stage) init();
}

private function init(e:Event = null):void
{
_center = new Vec2d(stage.stageWidth * 0.5, stage.stageHeight * 0.5);
_rotateSpeed = 0.01;
_pointVec = new Vec2d(150, 0);
_lineStartPoint = new Vec2d( -_center.x, -_center.y);
_lineEndPoint = new Vec2d(_center.x, _center.y);

_container = new Sprite();
_container.x = _center.x;
_container.y = _center.y;

_point = new PointSprite(_pointVec.x, _pointVec.y);

drawInterface();

}

private function enterFrameHandler(e:Event):void
{
// UPDATE
_lineStartPoint.rotate(_rotateSpeed);
_lineEndPoint.rotate(_rotateSpeed);
_pointVec.x = _point.x;
_pointVec.y = _point.y;

var norm:Vec2d = _lineEndPoint.sub(_lineStartPoint).normalized();
var connectVec:Vec2d = norm.scale(_pointVec.dot(norm));

// CLEAR
_container.graphics.clear();
_container.graphics.lineStyle(1.0);

// DRAW LINE
_container.graphics.lineStyle(2.0);
_container.graphics.moveTo(_lineStartPoint.x, _lineStartPoint.y);
_container.graphics.lineTo(_lineEndPoint.x, _lineEndPoint.y);

// DRAW CIRCLE
var circleVec:Vec2d = _pointVec.sub(connectVec);
circleVec = circleVec.scale(0.5);
_container.graphics.lineStyle(1.0, 0x0000FF);
_container.graphics.drawCircle(_pointVec.x - circleVec.x, _pointVec.y - circleVec.y, circleVec.length);
_circleLabel.text = "Circle Radius = " + circleVec.length * 0.5;

// DRAW CONNECT LINE
_container.graphics.lineStyle(1.0, 0xFF0000);
_container.graphics.moveTo(_point.x, _point.y);
_container.graphics.lineTo(connectVec.x, connectVec.y);

// DRAW CONNECT POINT
_container.graphics.beginFill(0xFF0000);
_container.graphics.drawCircle(connectVec.x, connectVec.y, 4);
_container.graphics.endFill();
}

private function drawInterface():void
{
var vBox:VBox = new VBox(this, 10, 10);
vBox.spacing = 0;
var fps:FPSMeter = new FPSMeter(vBox);
var rotateSpeedSlider:HUISlider = new HUISlider(vBox, 0, 0, "Rotate Speed", function():void {
_rotateSpeed = rotateSpeedSlider.value * 0.1;
});
rotateSpeedSlider.minimum = 0;
rotateSpeedSlider.maximum = 1.0;
rotateSpeedSlider.value = 0.1;

_circleLabel = new Label(vBox, 0, 0);
}
}

}

import flash.events.MouseEvent;
class PointSprite extends flash.display.Sprite {
public function PointSprite(x:Number, y:Number) {
this.x = x;
this.y = y;
buttonMode = true;
draw();
}
private function draw():void {
graphics.beginFill(0x0);
graphics.drawCircle(0, 0, 4);
graphics.endFill();
}
private function mouseDownHandler(e:MouseEvent):void {
startDrag();
}
private function mouseUpHandler(e:MouseEvent):void {
stage.removeEventListener(MouseEvent.MOUSE_UP, mouseUpHandler);
stopDrag();
}
}

class Vec2d {
public var x:Number, y:Number;
public function Vec2d(ax:Number = 0.0, ay:Number = 0.0) { x = ax; y = ay; }
public function clone():Vec2d { return new Vec2d(x, y); }
public function set(ax:Number, ay:Number):void { x = ax; y = ay; }
public function get length():Number { return Math.sqrt(x * x + y * y); }
public function set length(value:Number):void { var a:Number = angle; x = Math.cos(a) * value; y = Math.sin(a) * value; }
public function get lengthSqrt():Number { return x * x + y * y; }
public function get angle():Number { return Math.atan2(y, x); }
public function normalize():void { var invS:Number = 1 / length; x *= invS; y *= invS; }
public function normalized():Vec2d { var invS:Number = 1 / length; return new Vec2d(x * invS, y * invS); }
public function add(rhs:Vec2d):Vec2d { return new Vec2d(x + rhs.x, y + rhs.y); }
public function sub(rhs:Vec2d):Vec2d { return new Vec2d(x - rhs.x, y - rhs.y); }
public function mul(rhs:Vec2d):Vec2d { return new Vec2d(x * rhs.x, y * rhs.y); }
public function div(rhs:Vec2d):Vec2d { return new Vec2d(x / rhs.x, y / rhs.y); }
public function dot(rhs:Vec2d):Number { return x * rhs.x + y * rhs.y; }
public function cross(rhs:Vec2d):Number { return x * rhs.y - y * rhs.x; }
public function scale(s:Number):Vec2d { return new Vec2d(x * s, y * s); }
public function distance(rhs:Vec2d):Number { var dx:Number = x - rhs.x; var dy:Number = y - rhs.y; return Math.sqrt(dx * dx + dy * dy); }
public function distanceSqrd(rhs:Vec2d):Number { var dx:Number = x - rhs.x; var dy:Number = y - rhs.y; return dx * dx + dy * dy; }
public function rotate(angle:Number):void { var cosa:Number = Math.cos(angle); var sina:Number = Math.sin(angle); var rx:Number = x * cosa - y * sina; y = x * sina + y * cosa; x = rx; }
public function truncate(max:Number):void { this.length = Math.min(max, this.length); }
}