http://git-wip-us.apache.org/repos/asf/flex-asjs/blob/7d529524/frameworks/projects/Graphics/src/main/flex/org/apache/flex/core/graphics/utils/MatrixUtil.as
----------------------------------------------------------------------
diff --git
a/frameworks/projects/Graphics/src/main/flex/org/apache/flex/core/graphics/utils/MatrixUtil.as
b/frameworks/projects/Graphics/src/main/flex/org/apache/flex/core/graphics/utils/MatrixUtil.as
deleted file mode 100644
index 04c2c13..0000000
---
a/frameworks/projects/Graphics/src/main/flex/org/apache/flex/core/graphics/utils/MatrixUtil.as
+++ /dev/null
@@ -1,1605 +0,0 @@
-////////////////////////////////////////////////////////////////////////////////
-//
-// Licensed to the Apache Software Foundation (ASF) under one or more
-// contributor license agreements. See the NOTICE file distributed with
-// this work for additional information regarding copyright ownership.
-// The ASF licenses this file to You under the Apache License, Version 2.0
-// (the "License"); you may not use this file except in compliance with
-// the License. You may obtain a copy of the License at
-//
-// http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-//
-////////////////////////////////////////////////////////////////////////////////
-
-package org.apache.flex.core.graphics.utils
-{
-
- import flash.display.DisplayObject;
- import flash.geom.Matrix;
- import flash.geom.Matrix3D;
- import flash.geom.PerspectiveProjection;
- import flash.geom.Point;
- import flash.geom.Rectangle;
- import flash.geom.Utils3D;
- import flash.geom.Vector3D;
- import flash.system.ApplicationDomain;
-
- /**
- * @private
- * The MatrixUtil class is for internal use only.
- * Class for matrix and geometric related math routines.
- */
- public final class MatrixUtil
- {
-
- private static const RADIANS_PER_DEGREES:Number = Math.PI / 180;
- private static var SOLUTION_TOLERANCE:Number = 0.1;
- private static var MIN_MAX_TOLERANCE:Number = 0.1;
-
- private static var staticPoint:Point = new Point();
-
- // For use in getConcatenatedMatrix function
- private static var fakeDollarParent:QName;
- private static var uiComponentClass:Class;
- private static var uiMovieClipClass:Class;
- private static var usesMarshalling:Object;
- private static var lastModuleFactory:Object;
- private static var computedMatrixProperty:QName;
- private static var $transformProperty:QName;
-
-
//--------------------------------------------------------------------------
- //
- // Class methods
- //
-
//--------------------------------------------------------------------------
-
- /**
- * Returns rotation value clamped between -180 and 180
degreeds.
- * This mimicks the Flash player behavior.
- */
- public static function clampRotation(value:Number):Number
- {
- // Flash player doesn't handle values larger than 2^15
- 1 (FP-749).
- if (value > 180 || value < -180)
- {
- value = value % 360;
-
- if (value > 180)
- value = value - 360;
- else if (value < -180)
- value = value + 360;
- }
- return value;
- }
-
- /**
- * Returns a static Point object with the result.
- * If matrix is null, point is untransformed.
- */
- public static function transformPoint(x:Number, y:Number,
m:Matrix):Point
- {
- if (!m)
- {
- staticPoint.x = x;
- staticPoint.y = y;
- return staticPoint;
- }
-
- staticPoint.x = m.a * x + m.c * y + m.tx;
- staticPoint.y = m.b * x + m.d * y + m.ty;
- return staticPoint;
- }
-
- public static function composeMatrix(x:Number = 0,
-
y:Number = 0,
-
scaleX:Number = 1,
-
scaleY:Number = 1,
-
rotation:Number = 0,
-
transformX:Number = 0,
-
transformY:Number = 0):Matrix
- {
- var m:Matrix = new Matrix();
- m.translate(-transformX, -transformY);
- m.scale(scaleX, scaleY);
- if (rotation != 0)
- m.rotate(rotation / 180 * Math.PI);
- m.translate(transformX + x, transformY + y);
- return m;
- }
-
- /**
- * Decompose a matrix into its component scale, rotation, and
translation parts.
- * The Vector of Numbers passed in the components parameter
will be
- * populated by this function with the component parts.
- *
- * @param components Vector which holds the component scale,
rotation
- * and translation values.
- * x = components[0]
- * y = components[1]
- * rotation = components[2]
- * scaleX = components[3]
- * scaleY = components[4]
- *
- * @param matrix The matrix to decompose
- * @param transformX The x value of the transform center
- * @param transformY The y value of the transform center
- */
- public static function
decomposeMatrix(components:Vector.<Number>,
-
matrix:Matrix,
-
transformX:Number = 0,
-
transformY:Number = 0):void
- {
- // else decompose matrix. Don't use MatrixDecompose(),
it can return erronous values
- // when negative scales (and therefore skews) are in
use.
- var Ux:Number;
- var Uy:Number;
- var Vx:Number;
- var Vy:Number;
-
- Ux = matrix.a;
- Uy = matrix.b;
- components[3] = Math.sqrt(Ux*Ux + Uy*Uy);
-
- Vx = matrix.c;
- Vy = matrix.d;
- components[4] = Math.sqrt(Vx*Vx + Vy*Vy );
-
- // sign of the matrix determinant will tell us if the
space is inverted by a 180 degree skew or not.
- var determinant:Number = Ux*Vy - Uy*Vx;
- if (determinant < 0) // if so, choose y-axis scale as
the skewed one. Unfortunately, its impossible to tell if it originally was the
y or x axis that had the negative scale/skew.
- {
- components[4] = -(components[4]);
- Vx = -Vx;
- Vy = -Vy;
- }
-
- components[2] = Math.atan2( Uy, Ux ) /
RADIANS_PER_DEGREES;
-
- if (transformX != 0 || transformY != 0)
- {
- var postTransformCenter:Point =
matrix.transformPoint(new Point(transformX,transformY));
- components[0] = postTransformCenter.x -
transformX;
- components[1] = postTransformCenter.y -
transformY;
- }
- else
- {
- components[0] = matrix.tx;
- components[1] = matrix.ty;
- }
- }
-
- /**
- * @return Returns the union of <code>rect</code> and
- * <code>Rectangle(left, top, right - left, bottom -
top)</code>.
- * Note that if rect is non-null, it will be updated to
reflect the return value.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function rectUnion(left:Number, top:Number,
right:Number, bottom:Number,
-
rect:Rectangle):Rectangle
- {
- if (!rect)
- return new Rectangle(left, top, right - left,
bottom - top);
-
- var minX:Number = Math.min(rect.left, left);
- var minY:Number = Math.min(rect.top, top);
- var maxX:Number = Math.max(rect.right, right);
- var maxY:Number = Math.max(rect.bottom, bottom);
-
- rect.x = minX;
- rect.y = minY;
- rect.width = maxX - minX;
- rect.height = maxY - minY;
- return rect;
- }
-
- /**
- * Calculates the bounding box of a post-transformed ellipse.
- *
- * @param cx The x coordinate of the ellipse's center
- * @param cy The y coordinate of the ellipse's center
- * @param rx The horizontal radius of the ellipse
- * @param ry The vertical radius of the ellipse
- * @param matrix The transformation matrix.
- * @param rect If non-null, rect will be updated to the union
of rect and
- * the segment bounding box.
- * @return Returns the union of the passed in rect with the
- * bounding box of the the post-transformed ellipse.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function getEllipseBoundingBox(cx:Number,
cy:Number,
-
rx:Number, ry:Number,
-
matrix:Matrix,
-
rect:Rectangle = null):Rectangle
- {
- var a:Number = matrix.a;
- var b:Number = matrix.b;
- var c:Number = matrix.c;
- var d:Number = matrix.d;
-
- // Ellipse can be represented by the following
parametric equations:
- //
- // (1) x = cx + rx * cos(t)
- // (2) y = cy + ry * sin(t)
- //
- // After applying transformation with matrix m(a, c, b,
d) we get:
- //
- // (3) x = a * cx + a * cos(t) * rx + c * cy + c *
sin(t) * ry + m.tx
- // (4) y = b * cx + b * cos(t) * rx + d * cy + d *
sin(t) * ry + m.ty
- //
- // In (3) and (4) x and y are functions of a parameter
t. To find the extremums we need
- // to find where dx/dt and dy/dt reach zero:
- //
- // (5) dx/dt = - a * sin(t) * rx + c * cos(t) * ry
- // (6) dy/dt = - b * sin(t) * rx + d * cos(t) * ry
- // (7) dx/dt = 0 <=> sin(t) / cos(t) = (c * ry) / (a *
rx);
- // (8) dy/dt = 0 <=> sin(t) / cos(t) = (d * ry) / (b *
rx);
-
- if (rx == 0 && ry == 0)
- {
- var pt:Point = new Point(cx, cy);
- pt = matrix.transformPoint(pt);
- return rectUnion(pt.x, pt.y, pt.x, pt.y, rect);
- }
-
- var t:Number;
- var t1:Number;
-
- if (a * rx == 0)
- t = Math.PI / 2;
- else
- t = Math.atan((c * ry) / (a * rx));
-
- if (b * rx == 0)
- t1 = Math.PI / 2;
- else
- t1 = Math.atan((d * ry) / (b * rx));
-
- var x1:Number = a * Math.cos(t) * rx + c * Math.sin(t)
* ry;
- var x2:Number = -x1;
- x1 += a * cx + c * cy + matrix.tx;
- x2 += a * cx + c * cy + matrix.tx;
-
- var y1:Number = b * Math.cos(t1) * rx + d *
Math.sin(t1) * ry;
- var y2:Number = -y1;
- y1 += b * cx + d * cy + matrix.ty;
- y2 += b * cx + d * cy + matrix.ty;
-
- return rectUnion(Math.min(x1, x2), Math.min(y1, y2),
Math.max(x1, x2), Math.max(y1, y2), rect);
- }
-
- /**
- * @param x0 x coordinate of the first control point
- * @param y0 y coordinate of the first control point
- * @param x1 x coordinate of the second control point
- * @param y1 y coordinate of the second control point
- * @param x2 x coordinate of the third control point
- * @param y2 y coordinate of the third control point
- * @param sx The pre-transform scale factor for x coordinates.
- * @param sy The pre-transform scale factor for y coordinates.
- * @param matrix The transformation matrix. Can be null for
identity transformation.
- * @param rect If non-null, rect will be updated to the union
of rect and
- * the segment bounding box.
- * @return Returns the union of the post-transformed quadratic
- * bezier segment's axis aligned bounding box and the passed
in rect.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- static public function getQBezierSegmentBBox(x0:Number,
y0:Number,
-
x1:Number, y1:Number,
-
x2:Number, y2:Number,
-
sx:Number, sy:Number,
-
matrix:Matrix,
-
rect:Rectangle):Rectangle
- {
- var pt:Point;
- pt = MatrixUtil.transformPoint(x0 * sx, y0 * sy,
matrix);
- x0 = pt.x;
- y0 = pt.y;
-
- pt = MatrixUtil.transformPoint(x1 * sx, y1 * sy,
matrix);
- x1 = pt.x;
- y1 = pt.y;
-
- pt = MatrixUtil.transformPoint(x2 * sx, y2 * sy,
matrix);
- x2 = pt.x;
- y2 = pt.y;
-
- var minX:Number = Math.min(x0, x2);
- var maxX:Number = Math.max(x0, x2);
-
- var minY:Number = Math.min(y0, y2);
- var maxY:Number = Math.max(y0, y2);
-
- var txDiv:Number = x0 - 2 * x1 + x2;
- if (txDiv != 0)
- {
- var tx:Number = (x0 - x1) / txDiv;
- if (0 <= tx && tx <= 1)
- {
- var x:Number = (1 - tx) * (1 - tx) * x0
+ 2 * tx * (1 - tx) * x1 + tx * tx * x2;
- minX = Math.min(x, minX);
- maxX = Math.max(x, maxX);
- }
- }
-
- var tyDiv:Number = y0 - 2 * y1 + y2;
- if (tyDiv != 0)
- {
- var ty:Number = (y0 - y1) / tyDiv;
- if (0 <= ty && ty <= 1)
- {
- var y:Number = (1 - ty) * (1 - ty) * y0
+ 2 * ty * (1 - ty) * y1 + ty * ty * y2;
- minY = Math.min(y, minY);
- maxY = Math.max(y, maxY);
- }
- }
-
- return rectUnion(minX, minY, maxX, maxY, rect);
- }
-
- /**
- * @param width The width of the bounds to be transformed.
- * @param height The height of the bounds to be transformed.
- * @param matrix The transfomration matrix.
- *
- * @param vec If vec is non-null it will be set to the vector
from the
- * transformed bounds top left to the untransformed bounds top
left
- * in the coordinate space defined by <code>matrix</code>.
- * This is useful if you want to align the transformed bounds
to x,y
- * by modifying the object's position. Moving the object by
- * <code>x + vec.x</code> and <code>y + vec.y</code>
respectively
- * will offset the transformed bounds top left corner by x,y.
- *
- * @return Returns the transformed bounds. Note that the Point
object returned will be reused
- * by other MatrixUtil methods.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function transformSize(width:Number,
height:Number, matrix:Matrix):Point
- {
- const a:Number = matrix.a;
- const b:Number = matrix.b;
- const c:Number = matrix.c;
- const d:Number = matrix.d;
-
- // transform point (0,0)
- var x1:Number = 0;
- var y1:Number = 0;
-
- // transform point (width, 0)
- var x2:Number = width * a;
- var y2:Number = width * b;
-
- // transform point (0, height)
- var x3:Number = height * c;
- var y3:Number = height * d;
-
- // transform point (width, height)
- var x4:Number = x2 + x3;
- var y4:Number = y2 + y3;
-
- var minX:Number = Math.min(Math.min(x1, x2),
Math.min(x3, x4));
- var maxX:Number = Math.max(Math.max(x1, x2),
Math.max(x3, x4));
- var minY:Number = Math.min(Math.min(y1, y2),
Math.min(y3, y4));
- var maxY:Number = Math.max(Math.max(y1, y2),
Math.max(y3, y4));
-
- staticPoint.x = maxX - minX;
- staticPoint.y = maxY - minY;
- return staticPoint;
- }
-
- /**
- * @param width The width of the bounds to be transformed.
- * @param height The height of the bounds to be transformed.
- * @param matrix The transfomration matrix.
- *
- * @param topleft If topLeft is non-null it will be used as
the origin of the bounds
- * rectangle to be transformed. On return, it will be set to
the top left of the rectangle
- * after transformation.
- *
- * @return Returns the transformed width and height. Note that
the Point object returned will be reused
- * by other MatrixUtil methods.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function transformBounds(width:Number,
height:Number, matrix:Matrix, topLeft:Point = null):Point
- {
- const a:Number = matrix.a;
- const b:Number = matrix.b;
- const c:Number = matrix.c;
- const d:Number = matrix.d;
-
- // transform point (0,0)
- var x1:Number = 0;
- var y1:Number = 0;
-
- // transform point (width, 0)
- var x2:Number = width * a;
- var y2:Number = width * b;
-
- // transform point (0, height)
- var x3:Number = height * c;
- var y3:Number = height * d;
-
- // transform point (width, height)
- var x4:Number = x2 + x3;
- var y4:Number = y2 + y3;
-
- var minX:Number = Math.min(Math.min(x1, x2),
Math.min(x3, x4));
- var maxX:Number = Math.max(Math.max(x1, x2),
Math.max(x3, x4));
- var minY:Number = Math.min(Math.min(y1, y2),
Math.min(y3, y4));
- var maxY:Number = Math.max(Math.max(y1, y2),
Math.max(y3, y4));
-
- staticPoint.x = maxX - minX;
- staticPoint.y = maxY - minY;
-
- if (topLeft)
- {
- const tx:Number = matrix.tx;
- const ty:Number = matrix.ty;
- const x:Number = topLeft.x;
- const y:Number = topLeft.y;
-
- topLeft.x = minX + a * x + b * y + tx;
- topLeft.y = minY + c * x + d * y + ty;
- }
- return staticPoint;
- }
-
- /**
- * Returns the axis aligned bounding box <code>bounds</code>
transformed
- * with <code>matrix</code> and then projected with
<code>projection</code>.
- *
- * @param bounds The bounds, in child coordinates, to be
transformed and projected.
- * @param matrix <p>The transformation matrix. Note that the
method will clobber the
- * original matrix values.</p>
- * @param projection The projection.
- * @return Returns the <code>bounds</code> parameter that has
been updated with the
- * transformed and projected bounds.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function projectBounds(bounds:Rectangle,
-
matrix:Matrix3D,
-
projection:PerspectiveProjection):Rectangle
- {
- // Setup the matrix
- var centerX:Number = projection.projectionCenter.x;
- var centerY:Number = projection.projectionCenter.y;
- matrix.appendTranslation(-centerX, -centerY,
projection.focalLength);
- matrix.append(projection.toMatrix3D());
-
- // Project the corner points
- var pt1:Vector3D = new Vector3D(bounds.left,
bounds.top, 0);
- var pt2:Vector3D = new Vector3D(bounds.right,
bounds.top, 0)
- var pt3:Vector3D = new Vector3D(bounds.left,
bounds.bottom, 0);
- var pt4:Vector3D = new Vector3D(bounds.right,
bounds.bottom, 0);
- pt1 = Utils3D.projectVector(matrix, pt1);
- pt2 = Utils3D.projectVector(matrix, pt2);
- pt3 = Utils3D.projectVector(matrix, pt3);
- pt4 = Utils3D.projectVector(matrix, pt4);
-
- // Find the bounding box in 2D
- var maxX:Number = Math.max(Math.max(pt1.x, pt2.x),
Math.max(pt3.x, pt4.x));
- var minX:Number = Math.min(Math.min(pt1.x, pt2.x),
Math.min(pt3.x, pt4.x));
- var maxY:Number = Math.max(Math.max(pt1.y, pt2.y),
Math.max(pt3.y, pt4.y));
- var minY:Number = Math.min(Math.min(pt1.y, pt2.y),
Math.min(pt3.y, pt4.y));
-
- // Add back the projection center
- bounds.x = minX + centerX;
- bounds.y = minY + centerY;
- bounds.width = maxX - minX;
- bounds.height = maxY - minY;
- return bounds;
- }
-
- /**
- * @param matrix
- * @return Returns true when <code>pt ==
matrix.DeltaTransformPoint(pt)</code>
- * for any <code>pt:Point</code> (<code>matrix</code> is
identity matrix,
- * when disregarding the translation part).
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function isDeltaIdentity(matrix:Matrix):Boolean
- {
- return (matrix.a == 1 && matrix.d == 1 &&
- matrix.b == 0 && matrix.c == 0);
- }
-
- /**
- * <code>fitBounds</code> Calculates a size (x,y) for a
bounding box (0,0,x,y)
- * such that the bounding box transformed with
<code>matrix</code> will fit
- * into (0,0,width,height).
- *
- * @param width This is the width of the bounding box that
calculated size
- * needs to fit in.
- *
- * @param height This is the height of the bounding box that
the calculated
- * size needs to fit in.
- *
- * @param matrix This defines the transformations that the
function will take
- * into account when calculating the size. The bounding box
(0,0,x,y) of the
- * calculated size (x,y) transformed with <code>matrix</code>
will fit in the
- * specified <code>width</code> and <code>height</code>.
- *
- * @param explicitWidth Explicit width for the calculated
size. The function
- * will first try to find a solution using this width.
- *
- * @param explicitHeight Preferred height for the calculated
size. The function
- * will first try to find a solution using this height.
- *
- * @param preferredWidth Preferred width for the calculated
size. If possible
- * the function will set the calculated size width to this
value.
- *
- * @param preferredHeight Preferred height for the calculated
size. If possible
- * the function will set the calculated size height to this
value.
- *
- * @param minWidth The minimum allowed value for the
calculated size width.
- *
- * @param minHeight The minimum allowed value for the
calculated size height.
- *
- * @param maxWidth The maximum allowed value for the
calculated size width.
- *
- * @param maxHeight The maximum allowed value for the
calculated size height.
- *
- * @return Returns the size (x,y) such that the bounding box
(0,0,x,y) will
- * fit into (0,0,width,height) after transformation with
<code>matrix</code>.
- * Returns null if there is no possible solution.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function fitBounds(width:Number, height:Number,
matrix:Matrix,
-
explicitWidth:Number, explicitHeight:Number,
-
preferredWidth:Number, preferredHeight:Number,
-
minWidth:Number, minHeight:Number,
-
maxWidth:Number, maxHeight:Number):Point
- {
- if (isNaN(width) && isNaN(height))
- return new Point(preferredWidth,
preferredHeight);
-
- // Allow for precision errors by including tolerance
for certain values.
- const newMinWidth:Number = (minWidth <
MIN_MAX_TOLERANCE) ? 0 : minWidth - MIN_MAX_TOLERANCE;
- const newMinHeight:Number = (minHeight <
MIN_MAX_TOLERANCE) ? 0 : minHeight - MIN_MAX_TOLERANCE;
- const newMaxWidth:Number = maxWidth + MIN_MAX_TOLERANCE;
- const newMaxHeight:Number = maxHeight +
MIN_MAX_TOLERANCE;
-
- var actualSize:Point;
-
- if (!isNaN(width) && !isNaN(height))
- {
- actualSize = calcUBoundsToFitTBounds(width,
height, matrix,
- newMinWidth, newMinHeight,
- newMaxWidth, newMaxHeight);
-
- // If we couldn't fit in both dimensions, try
to fit only one and
- // don't stick out of the other
- if (!actualSize)
- {
- var actualSize1:Point;
- actualSize1 = fitTBoundsWidth(width,
matrix,
- explicitWidth, explicitHeight,
- preferredWidth, preferredHeight,
- newMinWidth, newMinHeight,
- newMaxWidth, newMaxHeight);
-
- // If we fit the width, but not the
height.
- if (actualSize1)
- {
- var fitHeight:Number =
transformSize(actualSize1.x, actualSize1.y, matrix).y;
- if (fitHeight -
SOLUTION_TOLERANCE > height)
- actualSize1 = null;
- }
-
- var actualSize2:Point
- actualSize2 = fitTBoundsHeight(height,
matrix,
- explicitWidth, explicitHeight,
- preferredWidth, preferredHeight,
- newMinWidth, newMinHeight,
- newMaxWidth, newMaxHeight);
-
- // If we fit the height, but not the
width
- if (actualSize2)
- {
- var fitWidth:Number =
transformSize(actualSize2.x, actualSize2.y, matrix).x;
- if (fitWidth -
SOLUTION_TOLERANCE > width)
- actualSize2 = null;
- }
-
- if (actualSize1 && actualSize2)
- {
- // Pick a solution
- actualSize = ((actualSize1.x *
actualSize1.y) > (actualSize2.x * actualSize2.y)) ? actualSize1 : actualSize2;
- }
- else if (actualSize1)
- {
- actualSize = actualSize1;
- }
- else
- {
- actualSize = actualSize2;
- }
- }
- return actualSize;
- }
- else if (!isNaN(width))
- {
- return fitTBoundsWidth(width, matrix,
- explicitWidth, explicitHeight,
- preferredWidth, preferredHeight,
- newMinWidth, newMinHeight,
- newMaxWidth, newMaxHeight);
- }
- else
- {
- return fitTBoundsHeight(height, matrix,
- explicitWidth, explicitHeight,
- preferredWidth, preferredHeight,
- newMinWidth, newMinHeight,
- newMaxWidth, newMaxHeight);
- }
- }
-
- /**
- * @private
- *
- * <code>fitTBoundsWidth</code> Calculates a size (x,y) for a
bounding box (0,0,x,y)
- * such that the bounding box transformed with
<code>matrix</code> will fit
- * into the specified width.
- *
- * @param width This is the width of the bounding box that
calculated size
- * needs to fit in.
- *
- * @param matrix This defines the transformations that the
function will take
- * into account when calculating the size. The bounding box
(0,0,x,y) of the
- * calculated size (x,y) transformed with <code>matrix</code>
will fit in the
- * specified <code>width</code> and <code>height</code>.
- *
- * @param explicitWidth Explicit width for the calculated
size. The function
- * will first try to find a solution using this width.
- *
- * @param explicitHeight Preferred height for the calculated
size. The function
- * will first try to find a solution using this height.
- *
- * @param preferredWidth Preferred width for the calculated
size. If possible
- * the function will set the calculated size width to this
value.
- *
- * @param preferredHeight Preferred height for the calculated
size. If possible
- * the function will set the calculated size height to this
value.
- *
- * @param minWidth The minimum allowed value for the
calculated size width.
- *
- * @param minHeight The minimum allowed value for the
calculated size height.
- *
- * @param maxWidth The maximum allowed value for the
calculated size width.
- *
- * @param maxHeight The maximum allowed value for the
calculated size height.
- *
- * @return Returns the size (x,y) such that the bounding box
(0,0,x,y) will
- * fit into (0,0,width,height) after transformation with
<code>matrix</code>.
- * Returns null if there is no possible solution.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- private static function fitTBoundsWidth(width:Number,
matrix:Matrix,
-
explicitWidth:Number, explicitHeight:Number,
-
preferredWidth:Number, preferredHeight:Number,
-
minWidth:Number, minHeight:Number,
-
maxWidth:Number, maxHeight:Number):Point
- {
- var actualSize:Point;
-
- // cases 1 and 2: only explicit width or explicit
height is specified,
- // so we try to find a solution with that hard
constraint.
- if (!isNaN(explicitWidth) && isNaN(explicitHeight))
- {
- actualSize =
calcUBoundsToFitTBoundsWidth(width, matrix,
- explicitWidth, preferredHeight,
- explicitWidth, minHeight,
- explicitWidth, maxHeight);
-
- if (actualSize)
- return actualSize;
- }
- else if (isNaN(explicitWidth) && !isNaN(explicitHeight))
- {
- actualSize =
calcUBoundsToFitTBoundsWidth(width, matrix,
- preferredWidth, explicitHeight,
- minWidth, explicitHeight,
- maxWidth, explicitHeight);
- if (actualSize)
- return actualSize;
- }
-
- // case 3: default case. When explicitWidth,
explicitHeight are both set
- // or not set, we use the preferred size since
calcUBoundsToFitTBoundsWidth
- // will just pick one.
- actualSize = calcUBoundsToFitTBoundsWidth(width, matrix,
- preferredWidth, preferredHeight,
- minWidth, minHeight,
- maxWidth, maxHeight);
-
- return actualSize;
- }
-
- /**
- * @private
- *
- * <code>fitTBoundsWidth</code> Calculates a size (x,y) for a
bounding box (0,0,x,y)
- * such that the bounding box transformed with
<code>matrix</code> will fit
- * into the specified height.
- *
- * @param height This is the height of the bounding box that
the calculated
- * size needs to fit in.
- *
- * @param matrix This defines the transformations that the
function will take
- * into account when calculating the size. The bounding box
(0,0,x,y) of the
- * calculated size (x,y) transformed with <code>matrix</code>
will fit in the
- * specified <code>width</code> and <code>height</code>.
- *
- * @param explicitWidth Explicit width for the calculated
size. The function
- * will first try to find a solution using this width.
- *
- * @param explicitHeight Preferred height for the calculated
size. The function
- * will first try to find a solution using this height.
- *
- * @param preferredWidth Preferred width for the calculated
size. If possible
- * the function will set the calculated size width to this
value.
- *
- * @param preferredHeight Preferred height for the calculated
size. If possible
- * the function will set the calculated size height to this
value.
- *
- * @param minWidth The minimum allowed value for the
calculated size width.
- *
- * @param minHeight The minimum allowed value for the
calculated size height.
- *
- * @param maxWidth The maximum allowed value for the
calculated size width.
- *
- * @param maxHeight The maximum allowed value for the
calculated size height.
- *
- * @return Returns the size (x,y) such that the bounding box
(0,0,x,y) will
- * fit into (0,0,width,height) after transformation with
<code>matrix</code>.
- * Returns null if there is no possible solution.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- private static function fitTBoundsHeight(height:Number,
matrix:Matrix,
-
explicitWidth:Number, explicitHeight:Number,
-
preferredWidth:Number, preferredHeight:Number,
-
minWidth:Number, minHeight:Number,
-
maxWidth:Number, maxHeight:Number):Point
- {
- var actualSize:Point;
-
- // cases 1 and 2: only explicit width or explicit
height is specified,
- // so we try to find a solution with that hard
constraint.
- if (!isNaN(explicitWidth) && isNaN(explicitHeight))
- {
- actualSize =
calcUBoundsToFitTBoundsHeight(height, matrix,
- explicitWidth, preferredHeight,
- explicitWidth, minHeight,
- explicitWidth, maxHeight);
-
- if (actualSize)
- return actualSize;
- }
- else if (isNaN(explicitWidth) && !isNaN(explicitHeight))
- {
- actualSize =
calcUBoundsToFitTBoundsHeight(height, matrix,
- preferredWidth, explicitHeight,
- minWidth, explicitHeight,
- maxWidth, explicitHeight);
- if (actualSize)
- return actualSize;
- }
-
- // case 3: default case. When explicitWidth,
explicitHeight are both set
- // or not set, we use the preferred size since
calcUBoundsToFitTBoundsWidth
- // will just pick one.
- actualSize = calcUBoundsToFitTBoundsHeight(height,
matrix,
- preferredWidth, preferredHeight,
- minWidth, minHeight,
- maxWidth, maxHeight);
-
- return actualSize;
- }
-
- /**
- * Calculates (x,y) such that the bounding box (0,0,x,y)
transformed
- * with <code>matrix</code> will have bounding box with
- * height equal to <code>h</code>.
- * x and y are restricted by <code>minX</code>,
<code>maxX</code> and
- * <code>minY</code>, <code>maxY</code>.
- *
- * If possible x will be set to <code>preferredX</code> or
- * y will be set to <code>preferredY</code>.
- *
- * When there are multiple solutions, the function picks the
one that
- * minimizes the bounding box area of transformed (0,0,x,y).
- *
- * The functon assumes <code>minX >= 0</code> and <code>minY
>= 0</code>
- * (solution components x and y are non-negative).
- *
- * @return Returns Point(x,y) or null if no solution exists.
- *
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- static public function calcUBoundsToFitTBoundsHeight(h:Number,
-
matrix:Matrix,
-
preferredX:Number,
-
preferredY:Number,
-
minX:Number,
-
minY:Number,
-
maxX:Number,
-
maxY:Number):Point
- {
- // Untransformed bounds size is (x,y). The corners of
the untransformed
- // bounding box are p1(0,0) p2(x,0) p3(0,y) p4(x,y).
- // Matrix is | a c tx |
- // | b d ty |
- //
- // After transfomation with the matrix those four
points are:
- // t1 = (0, 0) =
matrix.deltaTransformPoint(p1)
- // t2 = (ax, bx) =
matrix.deltaTransformPoint(p2)
- // t3 = (cy, dy) =
matrix.deltaTransformPoint(p3)
- // t4 = (ax + cy, cx + dy) =
matrix.deltaTransformPoint(p4)
- //
- // The transformed bounds bounding box dimensions are
(w,h):
- // (1) w = max( t1.x, t2.x, t3.x, t4.x ) - min( t1.x,
t2.x, t3.x, t4.x)
- // (2) h = max( t1.y, t2.y, t3.y, t4.y ) - min( t1.y,
t2.y, t3.y, t4.y)
- //
- // Looking at all the possible cases for min and max
functions above,
- // we can construct and solve simple linear systems for
x and y.
- // For example in the case of
- // t1.x <= t2.x <= t3.x <= t4.x
- // our first equation is
- // (1) w = t4.x - t1.x <==> w = ax + cy
- //
- // To minimize the cases we're looking at we can take
advantage of
- // the limits we have: x >= 0, y >= 0;
- // Taking into account these limits we deduce that:
- // a*c >= 0 gives us (1) w = abs( t4.x - t1.x ) = abs(
ax + cy )
- // a*c < 0 gives us (1) w = abs( t2.x - t3.x ) = abs(
ax - cy )
- // b*d >= 0 gives us (2) h = abs( t4.y - t1.y ) = abs(
bx + dy )
- // b*d < 0 gives us (2) h = abs( t2.y - t3.y ) = abs(
bx - dy )
- //
- // If we do a substitution such that
- // c1 = a*c >= 0 ? c : -c
- // d1 = b*d >= 0 ? d : -d
- // we get the following linear system:
- // (1) w = abs( ax + c1y )
- // (2) h = abs( bx + d1y )
- //
- // Since we're matching height we only care about (2)
-
- var b:Number = matrix.b;
- var d:Number = matrix.d;
-
- // If components are very close to zero, zero them out
to handle the special cases
- if (-1.0e-9 < b && b < +1.0e-9)
- b = 0;
- if (-1.0e-9 < d && d < +1.0e-9)
- d = 0;
-
- if (b == 0 && d == 0)
- return null; // No solution
-
- // Handle special cases first
- if (b == 0 && d == 0)
- return null; // No solution
-
- if (b == 0)
- return new Point( preferredX, h / Math.abs(d)
);
- else if (d == 0)
- return new Point( h / Math.abs(b), preferredY
);
-
- const d1:Number = (b*d >= 0) ? d : -d;
- // Now we have the following linear sytesm:
- // (1) x = preferredX or y = preferredY
- // (2) h = abs( bx + d1y )
-
- var s:Point;
- var x:Number;
- var y:Number;
-
- if (d1 != 0 && preferredX > 0)
- {
- const invD1:Number = 1 / d1;
- preferredX = Math.max(minX, Math.min(maxX,
preferredX));
- x = preferredX;
-
- // Case1:
- // bx + d1y >= 0
- // x = preferredX
- y = (h - b * x) * invD1;
- if (minY <= y && y <= maxY &&
- b * x + d1 * y >= 0 ) // Satisfy Case1
- {
- s = new Point(x, y);
- }
-
- // Case2:
- // bx + d1y < 0
- // x = preferredX
- y = (-h - b * x) * invD1;
- if (minY <= y && y <= maxY &&
- b * x + d1 * y < 0 ) // Satisfy Case2
- {
- // If there is no solution, or the new
solution yields smaller value, pick the new solution.
- if (!s || transformSize(s.x, s.y,
matrix).x > transformSize(x, y, matrix).x)
- s = new Point(x, y);
- }
- }
-
- if (b != 0 && preferredY > 0)
- {
- const invB:Number = 1 / b;
- preferredY = Math.max(minY, Math.min(maxY,
preferredY));
- y = preferredY;
-
- // Case3:
- // bx + d1y >= 0
- // y = preferredY
- x = ( h - d1 * y ) * invB;
- if (minX <= x && x <= maxX &&
- b * x + d1 * y >= 0) // Satisfy Case3
- {
- // If there is no solution, or the new
solution yields smaller value, pick the new solution.
- if (!s || transformSize(s.x, s.y,
matrix).x > transformSize(x, y, matrix).x)
- s = new Point(x, y);
- }
-
- // Case4:
- // bx + d1y < 0
- // y = preferredY
- x = ( -h - d1 * y ) * invB;
- if (minX <= x && x <= maxX &&
- b * x + d1 * y < 0) // Satisfy Case4
- {
- // If there is no solution, or the new
solution yields smaller value, pick the new solution.
- if (!s || transformSize(s.x, s.y,
matrix).x > transformSize(x, y, matrix).x)
- s = new Point(x, y);
- }
- }
-
- // If there's already a solution that matches preferred
dimention, return
- if (s)
- return s;
-
- // Find a solution that matches the width and minimizes
the height:
- const a:Number = matrix.a;
- const c:Number = matrix.c;
- const c1:Number = ( a*c >= 0 ) ? c : -c;
- return solveEquation(b, d1, h, minX, minY, maxX, maxY,
a, c1);
- }
-
- /**
- * Calculates (x,y) such that the bounding box (0,0,x,y)
transformed
- * with <code>matrix</code> will have bounding box with
- * width equal to <code>w</code>.
- * x and y are restricted by <code>minX</code>,
<code>maxX</code> and
- * <code>minY</code>, <code>maxY</code>.
- *
- * If possible x will be set to <code>preferredX</code> or
- * y will be set to <code>preferredY</code>.
- *
- * When there are multiple solutions, the function picks the
one that
- * minimizes the bounding box area of transformed (0,0,x,y).
- *
- * The functon assumes <code>minX >= 0</code> and <code>minY
>= 0</code>
- * (solution components x and y are non-negative).
- *
- * @return Returns Point(x,y) or null if no solution exists.
- *
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- static public function calcUBoundsToFitTBoundsWidth(w:Number,
-
matrix:Matrix,
-
preferredX:Number,
-
preferredY:Number,
-
minX:Number,
-
minY:Number,
-
maxX:Number,
-
maxY:Number):Point
- {
- // Untransformed bounds size is (x,y). The corners of
the untransformed
- // bounding box are p1(0,0) p2(x,0) p3(0,y) p4(x,y).
- // Matrix is | a c tx |
- // | b d ty |
- //
- // After transfomation with the matrix those four
points are:
- // t1 = (0, 0) =
matrix.deltaTransformPoint(p1)
- // t2 = (ax, bx) =
matrix.deltaTransformPoint(p2)
- // t3 = (cy, dy) =
matrix.deltaTransformPoint(p3)
- // t4 = (ax + cy, cx + dy) =
matrix.deltaTransformPoint(p4)
- //
- // The transformed bounds bounding box dimensions are
(w,h):
- // (1) w = max( t1.x, t2.x, t3.x, t4.x ) - min( t1.x,
t2.x, t3.x, t4.x)
- // (2) h = max( t1.y, t2.y, t3.y, t4.y ) - min( t1.y,
t2.y, t3.y, t4.y)
- //
- // Looking at all the possible cases for min and max
functions above,
- // we can construct and solve simple linear systems for
x and y.
- // For example in the case of
- // t1.x <= t2.x <= t3.x <= t4.x
- // our first equation is
- // (1) w = t4.x - t1.x <==> w = ax + cy
- //
- // To minimize the cases we're looking at we can take
advantage of
- // the limits we have: x >= 0, y >= 0;
- // Taking into account these limits we deduce that:
- // a*c >= 0 gives us (1) w = abs( t4.x - t1.x ) = abs(
ax + cy )
- // a*c < 0 gives us (1) w = abs( t2.x - t3.x ) = abs(
ax - cy )
- // b*d >= 0 gives us (2) h = abs( t4.y - t1.y ) = abs(
bx + dy )
- // b*d < 0 gives us (2) h = abs( t2.y - t3.y ) = abs(
bx - dy )
- //
- // If we do a substitution such that
- // c1 = a*c >= 0 ? c : -c
- // d1 = b*d >= 0 ? d : -d
- // we get the following linear system:
- // (1) w = abs( ax + c1y )
- // (2) h = abs( bx + d1y )
- //
- // Since we're matching width we only care about (1)
-
- var a:Number = matrix.a;
- var c:Number = matrix.c;
-
- // If components are very close to zero, zero them out
to handle the special cases
- if (-1.0e-9 < a && a < +1.0e-9)
- a = 0;
- if (-1.0e-9 < c && c < +1.0e-9)
- c = 0;
-
- // Handle special cases first
- if (a == 0 && c == 0)
- return null; // No solution
-
- if (a == 0)
- return new Point( preferredX, w / Math.abs(c)
);
- else if (c == 0)
- return new Point( w / Math.abs(a), preferredY
);
-
- const c1:Number = ( a*c >= 0 ) ? c : -c;
- // Now we have the following linear sytesm:
- // (1) w = abs( ax + c1y )
- // (2) x = preferredX or y = preferredY
-
- var s:Point;
- var x:Number;
- var y:Number;
-
- if (c1 != 0 && preferredX > 0)
- {
- const invC1:Number = 1 / c1;
- preferredX = Math.max(minX, Math.min(maxX,
preferredX));
- x = preferredX;
-
- // Case1:
- // a * x + c1 * y >= 0
- // x = preferredX
- y = (w - a * x) * invC1;
- if (minY <= y && y <= maxY &&
- a * x + c1 * y >= 0 ) // Satisfy Case1
- {
- s = new Point(x, y);
- }
-
- // Case2:
- // a * x + c1 * y < 0
- // x = preferredX
- y = (-w - a * x) * invC1;
- if (minY <= y && y <= maxY &&
- a * x + c1 * y < 0 ) // Satisfy Case2
- {
- // If there is no solution, or the new
solution yields smaller value, pick the new solution.
- if (!s || transformSize(s.x, s.y,
matrix).y > transformSize(x, y, matrix).y)
- s = new Point(x, y);
- }
- }
-
- if (a != 0 && preferredY > 0)
- {
- const invA:Number = 1 / a;
- preferredY = Math.max(minY, Math.min(maxY,
preferredY));
- y = preferredY;
-
- // Case3:
- // a * x + c1 * y >= 0
- // y = preferredY
- x = (w - c1 * y ) * invA;
- if (minX <= x && x <= maxX &&
- a * x + c1 * y >= 0) // Satisfy Case3
- {
- // If there is no solution, or the new
solution yields smaller value, pick the new solution.
- if (!s || transformSize(s.x, s.y,
matrix).y > transformSize(x, y, matrix).y)
- s = new Point(x, y);
- }
-
- // Case4:
- // a * x + c1 * y < 0
- // y = preferredY
- x = (-w - c1 * y ) * invA;
- if (minX <= x && x <= maxX &&
- a * x + c1 * y < 0) // Satisfy Case4
- {
- // If there is no solution, or the new
solution yields smaller value, pick the new solution.
- if (!s || transformSize(s.x, s.y,
matrix).y > transformSize(x, y, matrix).y)
- s = new Point(x, y);
- }
- }
-
- // If there's already a solution that matches preferred
dimention, return
- if (s)
- return s;
-
- // Find a solution that matches the width and minimizes
the height:
- const b:Number = matrix.b;
- const d:Number = matrix.d;
- const d1:Number = (b*d >= 0) ? d : -d;
- return solveEquation(a, c1, w, minX, minY, maxX, maxY,
b, d1);
- }
-
- /**
- * Finds a solution (x,y) for the equation abs(a*x + c*y) = w
such that
- * abs(b*x +d*y) is minimized.
- * If there is infinite number of solutions, x and y are
picked to be
- * as close as possible.
- *
- * Doesn't handle cases where <code>a</code> or <code>c</code>
are zero.
- *
- * @return Returns Point(x,y)
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- static private function solveEquation(a:Number,
-
c:Number,
-
w:Number,
-
minX:Number,
-
minY:Number,
-
maxX:Number,
-
maxY:Number,
-
b:Number,
-
d:Number):Point
- {
- if (a == 0 || c == 0)
- return null; // x and y are not co-dependent
-
- // (1) w = abs( ax + cy )
- // Find the range of solutsion for y and pick:
- var x:Number;
- var y:Number;
- var s:Point;
-
- // Case1: ax + cy >= 0, from (1) above we get:
- // (1) x = (w - cy) / a
- //
- // Lets find the possible range of values for y:
- // We know that
- // (3) minX <= x <= maxX
- //
- // Substitute x with (w - cy)/a in (3):
- // (3) minX - w/a <= -cy/a <= maxX - w/a
- // (3) min( A, B ) <= y <= max( A, B ), where
- // A = (minX - w/a) * (-a/c)
- // B = (maxX - w/a) * (-a/c)
-
- var A:Number = (w - minX * a) / c;
- var B:Number = (w - maxX * a) / c;
- var rangeMinY:Number = Math.max(minY, Math.min(A, B));
- var rangeMaxY:Number = Math.min(maxY, Math.max(A, B));
- const det:Number = (b * c - a * d);
-
- // We have a possible solution for Case1 if the range
for y is valid
- if (rangeMinY <= rangeMaxY)
- {
- // Now that we have a valid range for y, we
need to pick a value within
- // that range.
- //
- // We calculate the value based on a custom
condition.
- //
- // The custom condition that we use could be
anything that defines
- // another equation for x and y. Some examples
are:
- // "make x and y as close as possible": y = w /
( a + c );
- // "minimize abs(bx + dy)": y = b * w / det
- // "preserve aspect ratio": y = w / ( a *
preferredX / preferredY + c );
- if (Math.abs(det) < 1.0e-9)
- {
- // There is infinite number of
solutions, lets pick x == y
- y = w / ( a + c );
- }
- else
- {
- // Minimize abs(bx + dy) - we need to
solve:
- // abs( b * ( w - c * y ) / a + d * y )
= 0
- // which gives us:
- y = b * w / det;
- }
-
- // Now that we have the y value calculated from
the custom condition,
- // we clamp with the range. This gives us a
solution with
- // values as close as possible to satisfy our
custom condition when
- // the condition is a linear function of x and
y (in our case it is).
- y = Math.max(rangeMinY, Math.min(y, rangeMaxY));
-
- x = (w - c * y) / a;
- return new Point(x, y);
- }
-
- // Case2: ax + cy < 0, from (1) above we get:
- // (1) x = (-w - cy) / a
- //
- // Lets find the possible range of values for y:
- // We know that
- // (3) minX <= x <= maxX
- //
- // Substitute x with (-w - cy)/a in (3):
- // (3) minX + w/a <= -cy/a <= maxX + w/a
- // (3) min( A, B ) <= y <= max( A, B ), where
- // A = (minX + w/a) * (-a/c)
- // B = (maxX + w/a) * (-a/c)
-
- A = -(minX * a + w) / c;
- B = -(maxX * a + w) / c;
- rangeMinY = Math.max(minY, Math.min(A, B));
- rangeMaxY = Math.min(maxY, Math.max(A, B));
-
- // We have a possible solution for Case2 if the range
for y is valid
- if (rangeMinY <= rangeMaxY)
- {
- // Now that we have a valid range for y, we
need to pick a value within
- // that range.
- //
- // We calculate the value based on a custom
condition.
- //
- // The custom condition that we use could be
anything that defines
- // another equation for x and y. Some examples
are:
- // "make x and y as close as possible": y = -w
/ ( a + c );
- // "minimize abs(bx + dy)": y = -b * w / det
- // "preserve aspect ratio": y = w / ( a *
preferredX / preferredY + c );
- if (Math.abs(det) < 1.0e-9)
- {
- // There is infinite number of
solutions, lets pick x == y
- y = -w / ( a + c );
- }
- else
- {
- // Minimize abs(bx + dy) - we need to
solve:
- // abs( b * ( -w - c * y ) / a + d * y
) = 0
- // which gives us:
- y = -b * w / det;
- }
-
- // Now that we have the y value calculated from
the custom condition,
- // we clamp with the range. This gives us a
solution with
- // values as close as possible to satisfy our
custom condition when
- // the condition is a linear function of x and
y (in our case it is).
- y = Math.max(rangeMinY, Math.min(y, rangeMaxY));
- x = (-w - c * y) / a;
- return new Point(x, y);
-
- }
- return null; // No solution
- }
-
- /**
- * Calculates (x,y) such that the bounding box (0,0,x,y)
transformed
- * with <code>matrix</code> will have bounding box (0,0,w,h).
- * x and y are restricted by <code>minX</code>,
<code>maxX</code> and
- * <code>minY</code>, <code>maxY</code>.
- *
- * When there is infinite number of solutions, the function
will
- * calculate x and y to be as close as possible.
- *
- * The functon assumes <code>minX >= 0</code> and <code>minY
>= 0</code>
- * (solution components x and y are non-negative).
- *
- * @return Point(x,y) or null if no solution exists.
- *
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- static public function calcUBoundsToFitTBounds(w:Number,
-
h:Number,
-
matrix:Matrix,
-
minX:Number,
-
minY:Number,
-
maxX:Number,
-
maxY:Number):Point
- {
- // Untransformed bounds size is (x,y). The corners of
the untransformed
- // bounding box are p1(0,0) p2(x,0) p3(0,y) p4(x,y).
- // Matrix is | a c tx |
- // | b d ty |
- //
- // After transfomation with the matrix those four
points are:
- // t1 = (0, 0) =
matrix.deltaTransformPoint(p1)
- // t2 = (ax, bx) =
matrix.deltaTransformPoint(p2)
- // t3 = (cy, dy) =
matrix.deltaTransformPoint(p3)
- // t4 = (ax + cy, cx + dy) =
matrix.deltaTransformPoint(p4)
- //
- // The transformed bounds bounding box dimensions are
(w,h):
- // (1) w = max( t1.x, t2.x, t3.x, t4.x ) - min( t1.x,
t2.x, t3.x, t4.x)
- // (2) h = max( t1.y, t2.y, t3.y, t4.y ) - min( t1.y,
t2.y, t3.y, t4.y)
- //
- // Looking at all the possible cases for min and max
functions above,
- // we can construct and solve simple linear systems for
x and y.
- // For example in the case of
- // t1.x <= t2.x <= t3.x <= t4.x
- // our first equation is
- // (1) w = t4.x - t1.x <==> w = ax + cy
- //
- // To minimize the cases we're looking at we can take
advantage of
- // the limits we have: x >= 0, y >= 0;
- // Taking into account these limits we deduce that:
- // a*c >= 0 gives us (1) w = abs( t4.x - t1.x ) = abs(
ax + cy )
- // a*c < 0 gives us (1) w = abs( t2.x - t3.x ) = abs(
ax - cy )
- // b*d >= 0 gives us (2) h = abs( t4.y - t1.y ) = abs(
bx + dy )
- // b*d < 0 gives us (2) h = abs( t2.y - t3.y ) = abs(
bx - dy )
- //
- // If we do a substitution such that
- // c1 = a*c >= 0 ? c : -c
- // d1 = b*d >= 0 ? d : -d
- // we get the following linear system:
- // (1) w = abs( ax + c1y )
- // (2) h = abs( bx + d1y )
- //
-
- var a:Number = matrix.a;
- var b:Number = matrix.b;
- var c:Number = matrix.c;
- var d:Number = matrix.d;
-
- // If components are very close to zero, zero them out
to handle the special cases
- if (-1.0e-9 < a && a < +1.0e-9)
- a = 0;
- if (-1.0e-9 < b && b < +1.0e-9)
- b = 0;
- if (-1.0e-9 < c && c < +1.0e-9)
- c = 0;
- if (-1.0e-9 < d && d < +1.0e-9)
- d = 0;
-
- // Handle special cases.
- if (b == 0 && c == 0)
- {
- // No solution in the following cases since the
matrix collapses
- // all points into a line.
- if (a == 0 || d == 0)
- return null;
-
- // (1) w = abs( ax + cy ) <=> w = abs( ax ) <=>
w = abs(a)x
- // (2) h = abs( bx + dy ) <=> h = abs( dy ) <=>
h = abs(d)y
- return new Point(w / Math.abs(a), h /
Math.abs(d));
- }
-
- if (a == 0 && d == 0)
- {
- // No solution in the following cases since the
matrix collapses
- // all points into a line.
- if (b == 0 || c == 0)
- return null;
-
- // (1) w = abs( ax + cy ) <=> w = abs( cy ) <=>
w = abs(c)y
- // (2) h = abs( bx + dy ) <=> h = abs( bx ) <=>
h = abs(b)x
- return new Point(h / Math.abs(b), w /
Math.abs(c));
- }
-
- // Handle general cases.
- const c1:Number = ( a*c >= 0 ) ? c : -c;
- const d1:Number = ( b*d >= 0 ) ? d : -d;
- // we get the following linear system:
- // (1) w = abs( ax + c1y )
- // (2) h = abs( bx + d1y )
-
- // Calculate the determinant of the system
- const det:Number = a * d1 - b * c1;
- if (Math.abs(det) < 1.0e-9)
- {
- // No solution in these cases since the matrix
- // collapses all points into a line.
- if (c1 == 0 || a == 0 || a == -c1)
- return null;
-
- if (Math.abs(a * h - b * w) > 1.0e-9)
- return null; // No solution in this case
-
- // Determinant is zero, the equations (1) & (2)
are equivalent and
- // we have only one equation:
- // (1) w = abs( ax + c1y )
- //
- // Solve it finding x and y as close as
possible:
- return solveEquation(a, c1, w, minX, minX,
maxX, maxY, b, d1);
- }
-
- // Pre-multiply w & h by the inverse dteterminant
- const invDet:Number = 1 / det;
- w *= invDet;
- h *= invDet;
-
- // Case 1:
- // a * x + c1 * y >= 0
- // b * x + d1 * y >= 0
- var s:Point;
- s = solveSystem(a, c1, b, d1, w, h);
- if (s &&
- minX <= s.x && s.x <= maxX && minY <= s.y &&
s.y <= maxY &&
- a * s.x + c1 * s.x >= 0 &&
- b * s.x + d1 * s.y >= 0)
- return s;
-
- // Case 2:
- // a * x + c1 * y >= 0
- // b * x + d1 * y < 0
- s = solveSystem( a, c1, b, d1, w, -h);
- if (s &&
- minX <= s.x && s.x <= maxX && minY <= s.y &&
s.y <= maxY &&
- a * s.x + c1 * s.x >= 0 &&
- b * s.x + d1 * s.y < 0)
- return s;
-
- // Case 3:
- // a * x + c1 * y < 0
- // b * x + d1 * y >= 0
- s = solveSystem( a, c1, b, d1, -w, h);
- if (s &&
- minX <= s.x && s.x <= maxX && minY <= s.y &&
s.y <= maxY &&
- a * s.x + c1 * s.x < 0 &&
- b * s.x + d1 * s.y >= 0)
- return s;
-
- // Case 4:
- // a * x + c1 * y < 0
- // b * x + d1 * y < 0
- s = solveSystem( a, c1, b, d1, -w, -h);
- if (s &&
- minX <= s.x && s.x <= maxX && minY <= s.y &&
s.y <= maxY &&
- a * s.x + c1 * s.x < 0 &&
- b * s.x + d1 * s.y < 0)
- return s;
-
- return null; // No solution.
- }
-
- /**
- * Determine if two Matrix instances are equal.
- *
- * @return true if the matrices are equal.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function isEqual(m1:Matrix, m2:Matrix):Boolean
- {
- return ((m1 && m2 &&
- m1.a == m2.a &&
- m1.b == m2.b &&
- m1.c == m2.c &&
- m1.d == m2.d &&
- m1.tx == m2.tx &&
- m1.ty == m2.ty) ||
- (!m1 && !m2));
- }
-
- /**
- * Determine if two Matrix3D instances are equal.
- *
- * @return true if the matrices are equal.
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- public static function isEqual3D(m1:Matrix3D,
m2:Matrix3D):Boolean
- {
- if (m1 && m2 && m1.rawData.length == m2.rawData.length)
- {
- var r1:Vector.<Number> = m1.rawData;
- var r2:Vector.<Number> = m2.rawData;
-
- return (r1[0] == r2[0] &&
- r1[1] == r2[1] &&
- r1[2] == r2[2] &&
- r1[3] == r2[3] &&
- r1[4] == r2[4] &&
- r1[5] == r2[5] &&
- r1[6] == r2[6] &&
- r1[7] == r2[7] &&
- r1[8] == r2[8] &&
- r1[9] == r2[9] &&
- r1[10] == r2[10] &&
- r1[11] == r2[11] &&
- r1[12] == r2[12] &&
- r1[13] == r2[13] &&
- r1[14] == r2[14] &&
- r1[15] == r2[15]);
- }
-
- return (!m1 && !m2);
- }
-
- /**
- * Calculates (x,y) such as to satisfy the linear system:
- * | a * x + c * y = m
- * | b * x + d * y = n
- *
- * @param mOverDet <code>mOverDet must be equal to m / (a*d -
b*c)</code>
- * @param nOverDet <code>mOverDet must be equal to n / (a*d -
b*c)</code>
- *
- * @return returns Point(x,y)
- *
- *
- * @langversion 3.0
- * @playerversion Flash 9
- * @playerversion AIR 1.1
- * @productversion Flex 3
- */
- static private function solveSystem(a:Number,
-
c:Number,
-
b:Number,
-
d:Number,
-
mOverDet:Number,
-
nOverDet:Number):Point
- {
- return new Point(d * mOverDet - c * nOverDet,
- a * nOverDet - b * mOverDet);
- }
-
- }
-
-}
-
