// forked from AndreMichelle's Closest Point Bezier Curve package { import flash.events.MouseEvent; import flash.display.Sprite; import flash.events.Event; import flash.geom.Point; import flash.text.TextField; import flash.text.TextFieldAutoSize; import flash.text.TextFormat; /** * <<< DIRTY GEOMETRY >>> * * Computes the closest point to a bezier curve * * @author Andre Michelle */ [SWF(width='465',height='490',frameRate='50',backgroundColor='0x202020')] public class BezierClosestPoint extends Sprite { private const point: Point = new Point(); private const pointA: AnchorPoint = new AnchorPoint(); private const pointB: AnchorPoint = new AnchorPoint(); private const pointC: AnchorPoint = new AnchorPoint(); private const pointD: AnchorPoint = new AnchorPoint(); private const EPSILON: Number = 1e-8; private const R: Vector.<Number> = new Vector.<Number>( 3, true ); private const textField: TextField = new TextField(); private var dragAnchor: AnchorPoint; public function BezierClosestPoint() { pointA.x = 140.0; pointA.y = 140.0; addChild( pointA ); pointB.x = 300; pointB.y = 300; addChild( pointB ); pointC.x = 200; pointC.y = 320; addChild( pointC ); pointD.x = 120; pointD.y = 300; addChild( pointD ); textField.mouseEnabled = false; textField.selectable = false; textField.autoSize = TextFieldAutoSize.LEFT; textField.defaultTextFormat = new TextFormat( 'Arial', 10, 0x999999 ); addChild( textField ); addEventListener( Event.ENTER_FRAME, enterFrame ); addEventListener( MouseEvent.MOUSE_DOWN, mouseDown ); addEventListener( MouseEvent.MOUSE_UP, mouseUp ); } private function mouseDown( event: MouseEvent ): void { dragAnchor = event.target as AnchorPoint; } private function mouseUp( event: MouseEvent ): void { dragAnchor = null; } private function enterFrame( event: Event ): void { if( dragAnchor == pointA ) { pointA.x = mouseX; pointA.y = mouseY; } else if( dragAnchor == pointB ) { pointB.x = mouseX; pointB.y = mouseY; } else if( dragAnchor == pointC ) { pointC.x = mouseX; pointC.y = mouseY; } else if( dragAnchor == pointD ) { pointD.x = mouseX; pointD.y = mouseY; } var x0: Number = pointA.x; var y0: Number = pointA.y; var x1: Number = pointC.x; var y1: Number = pointC.y; var x2: Number = pointB.x; var y2: Number = pointB.y; graphics.clear(); graphics.lineStyle( 0, 0xFF9900 ); graphics.moveTo( x0, y0 ); graphics.curveTo( x1, y1, x2, y2 ); point.x = pointD.x; point.y = pointD.y; var distance: Number = getClosestPoint( x0, y0, x1, y1, x2, y2, point ); textField.text = 'Distance to bezier: ' + distance.toFixed( 2 ); graphics.lineStyle( 0, 0x777777 ); graphics.moveTo( pointD.x, pointD.y ); graphics.lineTo( point.x, point.y ); } private function getClosestPoint( x0: Number, y0: Number, x1: Number, y1: Number, x2: Number, y2: Number, point: Point ): Number { var ax: Number; var ay: Number; var dx: Number; var dy: Number; var px: Number = point.x; var py: Number = point.y; var dd: Number = Number.MAX_VALUE; var t: Number; var i: int = 0; var n: int = getClosestT( x0, y0, x1, y1, x2, y2, px, py ); for( ; i < n ; ++i ) { t = R[i]; if( t <= 0.0 ) { ax = x0; ay = y0; } else if( t >= 1.0 ) { ax = x2; ay = y2; } else { ax = eval( x0, x1, x2, t ); ay = eval( y0, y1, y2, t ); } dx = px - ax; dy = py - ay; if( dx * dx + dy * dy < dd ) { point.x = ax; point.y = ay; dd = dx * dx + dy * dy; } } return Math.sqrt( dd ); } private function eval( v0: Number, v1: Number, v2: Number, t: Number ): Number { var t1: Number = 1.0 - t; return v0 * t1 * t1 + v1 * 2.0 * t1 * t + v2 * t * t; } private function getClosestT( x0: Number, y0: Number, x1: Number, y1: Number, x2: Number, y2: Number, px: Number, py: Number ): int { var dx: Number = x0 - px; var dy: Number = y0 - py; var ex: Number = x0 - 2.0 * x1 + x2; var ey: Number = y0 - 2.0 * y1 + y2; var fx: Number = 2.0 * x1 - 2.0 * x0; var fy: Number = 2.0 * y1 - 2.0 * y0; var d: Number = 2.0 * ( ex * ex + ey * ey ); var a: Number; var b: Number; var u: Number; var v: Number; var w: Number; var p: Number; var q: Number; var r: Number; var x: Number; if( 0.0 == d ) { b = ( fx * fx + fy * fy ) + 2.0 * ( dx * ex + dy * ey ); if( b < 0.0 ) { if( -b > EPSILON ) return 0; } else if( b < EPSILON ) return 0; R[ 0 ] = -( fx * dx + fy * dy ) / b; return 1; } else { var dInv: Number = 1.0 / d; a = 3.0 * ( fx * ex + fy * ey ) * dInv; b = ( ( fx * fx + fy * fy ) + 2.0 * ( dx * ex + dy * ey ) ) * dInv; p = -a * a * 0.33333333333 + b; q = a * a * a * 0.074074074074074 - a * b * 0.33333333333 + ( fx * dx + fy * dy ) * dInv; r = q * q * 0.25 + p * p * p * 0.037037037037037; if( r >= 0.0 ) { r = Math.sqrt( r ); x = sqrt3( -q * 0.5 + r ) + sqrt3( -q * 0.5 - r ) - a * 0.33333333333; } else { x = 2.0 * Math.sqrt( -p * 0.33333333333 ) * Math.cos( Math.atan2( Math.sqrt( -r ), -q * 0.5 ) * 0.33333333333 ) - a * 0.33333333333; } u = x + a; v = x * x + a * x + b; w = u * u - 4.0 * v; if( w < 0.0 ) { R[ 0 ] = x; return 1; } if( w > 0.0 ) { w = Math.sqrt( w ); R[ 0 ] = x; R[ 1 ] = -( u + w ) * 0.5; R[ 2 ] = ( w - u ) * 0.5; return 3; } R[ 0 ] = x; R[ 1 ] = -u * 0.5; return 2; } } private function sqrt3( x: Number ): Number { if( x > 0.0 ) return Math.pow( x, 0.33333333333 ); else if( x < 0.0 ) return -Math.pow( -x, 0.33333333333 ); return 0.0; } } } import flash.display.Sprite; class AnchorPoint extends Sprite { public function AnchorPoint() { graphics.beginFill( 0xFFFFFF, 0.1 ); graphics.drawCircle( 0.0, 0.0, 8.0 ); graphics.endFill(); graphics.beginFill( 0xFFFFFF, 0.8 ); graphics.drawCircle( 0.0, 0.0, 2.0 ); graphics.endFill(); } }