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- // Copyright 2008 The Closure Library Authors. All Rights Reserved.
- //
- // Licensed 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.
- /**
- * @fileoverview Provides an object representation of an AffineTransform and
- * methods for working with it.
- */
- goog.provide('goog.math.AffineTransform');
- /**
- * Creates a 2D affine transform. An affine transform performs a linear
- * mapping from 2D coordinates to other 2D coordinates that preserves the
- * "straightness" and "parallelness" of lines.
- *
- * Such a coordinate transformation can be represented by a 3 row by 3 column
- * matrix with an implied last row of [ 0 0 1 ]. This matrix transforms source
- * coordinates (x,y) into destination coordinates (x',y') by considering them
- * to be a column vector and multiplying the coordinate vector by the matrix
- * according to the following process:
- * <pre>
- * [ x'] [ m00 m01 m02 ] [ x ] [ m00x + m01y + m02 ]
- * [ y'] = [ m10 m11 m12 ] [ y ] = [ m10x + m11y + m12 ]
- * [ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ]
- * </pre>
- *
- * This class is optimized for speed and minimizes calculations based on its
- * knowledge of the underlying matrix (as opposed to say simply performing
- * matrix multiplication).
- *
- * @param {number=} opt_m00 The m00 coordinate of the transform.
- * @param {number=} opt_m10 The m10 coordinate of the transform.
- * @param {number=} opt_m01 The m01 coordinate of the transform.
- * @param {number=} opt_m11 The m11 coordinate of the transform.
- * @param {number=} opt_m02 The m02 coordinate of the transform.
- * @param {number=} opt_m12 The m12 coordinate of the transform.
- * @struct
- * @constructor
- * @final
- */
- goog.math.AffineTransform = function(
- opt_m00, opt_m10, opt_m01, opt_m11, opt_m02, opt_m12) {
- if (arguments.length == 6) {
- this.setTransform(
- /** @type {number} */ (opt_m00),
- /** @type {number} */ (opt_m10),
- /** @type {number} */ (opt_m01),
- /** @type {number} */ (opt_m11),
- /** @type {number} */ (opt_m02),
- /** @type {number} */ (opt_m12));
- } else if (arguments.length != 0) {
- throw Error('Insufficient matrix parameters');
- } else {
- this.m00_ = this.m11_ = 1;
- this.m10_ = this.m01_ = this.m02_ = this.m12_ = 0;
- }
- };
- /**
- * @return {boolean} Whether this transform is the identity transform.
- */
- goog.math.AffineTransform.prototype.isIdentity = function() {
- return this.m00_ == 1 && this.m10_ == 0 && this.m01_ == 0 && this.m11_ == 1 &&
- this.m02_ == 0 && this.m12_ == 0;
- };
- /**
- * @return {!goog.math.AffineTransform} A copy of this transform.
- */
- goog.math.AffineTransform.prototype.clone = function() {
- return new goog.math.AffineTransform(
- this.m00_, this.m10_, this.m01_, this.m11_, this.m02_, this.m12_);
- };
- /**
- * Sets this transform to the matrix specified by the 6 values.
- *
- * @param {number} m00 The m00 coordinate of the transform.
- * @param {number} m10 The m10 coordinate of the transform.
- * @param {number} m01 The m01 coordinate of the transform.
- * @param {number} m11 The m11 coordinate of the transform.
- * @param {number} m02 The m02 coordinate of the transform.
- * @param {number} m12 The m12 coordinate of the transform.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.setTransform = function(
- m00, m10, m01, m11, m02, m12) {
- if (!goog.isNumber(m00) || !goog.isNumber(m10) || !goog.isNumber(m01) ||
- !goog.isNumber(m11) || !goog.isNumber(m02) || !goog.isNumber(m12)) {
- throw Error('Invalid transform parameters');
- }
- this.m00_ = m00;
- this.m10_ = m10;
- this.m01_ = m01;
- this.m11_ = m11;
- this.m02_ = m02;
- this.m12_ = m12;
- return this;
- };
- /**
- * Sets this transform to be identical to the given transform.
- *
- * @param {!goog.math.AffineTransform} tx The transform to copy.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.copyFrom = function(tx) {
- this.m00_ = tx.m00_;
- this.m10_ = tx.m10_;
- this.m01_ = tx.m01_;
- this.m11_ = tx.m11_;
- this.m02_ = tx.m02_;
- this.m12_ = tx.m12_;
- return this;
- };
- /**
- * Concatenates this transform with a scaling transformation.
- *
- * @param {number} sx The x-axis scaling factor.
- * @param {number} sy The y-axis scaling factor.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.scale = function(sx, sy) {
- this.m00_ *= sx;
- this.m10_ *= sx;
- this.m01_ *= sy;
- this.m11_ *= sy;
- return this;
- };
- /**
- * Pre-concatenates this transform with a scaling transformation,
- * i.e. calculates the following matrix product:
- *
- * <pre>
- * [sx 0 0] [m00 m01 m02]
- * [ 0 sy 0] [m10 m11 m12]
- * [ 0 0 1] [ 0 0 1]
- * </pre>
- *
- * @param {number} sx The x-axis scaling factor.
- * @param {number} sy The y-axis scaling factor.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.preScale = function(sx, sy) {
- this.m00_ *= sx;
- this.m01_ *= sx;
- this.m02_ *= sx;
- this.m10_ *= sy;
- this.m11_ *= sy;
- this.m12_ *= sy;
- return this;
- };
- /**
- * Concatenates this transform with a translate transformation.
- *
- * @param {number} dx The distance to translate in the x direction.
- * @param {number} dy The distance to translate in the y direction.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.translate = function(dx, dy) {
- this.m02_ += dx * this.m00_ + dy * this.m01_;
- this.m12_ += dx * this.m10_ + dy * this.m11_;
- return this;
- };
- /**
- * Pre-concatenates this transform with a translate transformation,
- * i.e. calculates the following matrix product:
- *
- * <pre>
- * [1 0 dx] [m00 m01 m02]
- * [0 1 dy] [m10 m11 m12]
- * [0 0 1] [ 0 0 1]
- * </pre>
- *
- * @param {number} dx The distance to translate in the x direction.
- * @param {number} dy The distance to translate in the y direction.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.preTranslate = function(dx, dy) {
- this.m02_ += dx;
- this.m12_ += dy;
- return this;
- };
- /**
- * Concatenates this transform with a rotation transformation around an anchor
- * point.
- *
- * @param {number} theta The angle of rotation measured in radians.
- * @param {number} x The x coordinate of the anchor point.
- * @param {number} y The y coordinate of the anchor point.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.rotate = function(theta, x, y) {
- return this.concatenate(
- goog.math.AffineTransform.getRotateInstance(theta, x, y));
- };
- /**
- * Pre-concatenates this transform with a rotation transformation around an
- * anchor point.
- *
- * @param {number} theta The angle of rotation measured in radians.
- * @param {number} x The x coordinate of the anchor point.
- * @param {number} y The y coordinate of the anchor point.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.preRotate = function(theta, x, y) {
- return this.preConcatenate(
- goog.math.AffineTransform.getRotateInstance(theta, x, y));
- };
- /**
- * Concatenates this transform with a shear transformation.
- *
- * @param {number} shx The x shear factor.
- * @param {number} shy The y shear factor.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.shear = function(shx, shy) {
- var m00 = this.m00_;
- var m10 = this.m10_;
- this.m00_ += shy * this.m01_;
- this.m10_ += shy * this.m11_;
- this.m01_ += shx * m00;
- this.m11_ += shx * m10;
- return this;
- };
- /**
- * Pre-concatenates this transform with a shear transformation.
- * i.e. calculates the following matrix product:
- *
- * <pre>
- * [ 1 shx 0] [m00 m01 m02]
- * [shy 1 0] [m10 m11 m12]
- * [ 0 0 1] [ 0 0 1]
- * </pre>
- *
- * @param {number} shx The x shear factor.
- * @param {number} shy The y shear factor.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.preShear = function(shx, shy) {
- var m00 = this.m00_;
- var m01 = this.m01_;
- var m02 = this.m02_;
- this.m00_ += shx * this.m10_;
- this.m01_ += shx * this.m11_;
- this.m02_ += shx * this.m12_;
- this.m10_ += shy * m00;
- this.m11_ += shy * m01;
- this.m12_ += shy * m02;
- return this;
- };
- /**
- * @return {string} A string representation of this transform. The format of
- * of the string is compatible with SVG matrix notation, i.e.
- * "matrix(a,b,c,d,e,f)".
- * @override
- */
- goog.math.AffineTransform.prototype.toString = function() {
- return 'matrix(' +
- [this.m00_, this.m10_, this.m01_, this.m11_, this.m02_, this.m12_].join(
- ',') +
- ')';
- };
- /**
- * @return {number} The scaling factor in the x-direction (m00).
- */
- goog.math.AffineTransform.prototype.getScaleX = function() {
- return this.m00_;
- };
- /**
- * @return {number} The scaling factor in the y-direction (m11).
- */
- goog.math.AffineTransform.prototype.getScaleY = function() {
- return this.m11_;
- };
- /**
- * @return {number} The translation in the x-direction (m02).
- */
- goog.math.AffineTransform.prototype.getTranslateX = function() {
- return this.m02_;
- };
- /**
- * @return {number} The translation in the y-direction (m12).
- */
- goog.math.AffineTransform.prototype.getTranslateY = function() {
- return this.m12_;
- };
- /**
- * @return {number} The shear factor in the x-direction (m01).
- */
- goog.math.AffineTransform.prototype.getShearX = function() {
- return this.m01_;
- };
- /**
- * @return {number} The shear factor in the y-direction (m10).
- */
- goog.math.AffineTransform.prototype.getShearY = function() {
- return this.m10_;
- };
- /**
- * Concatenates an affine transform to this transform.
- *
- * @param {!goog.math.AffineTransform} tx The transform to concatenate.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.concatenate = function(tx) {
- var m0 = this.m00_;
- var m1 = this.m01_;
- this.m00_ = tx.m00_ * m0 + tx.m10_ * m1;
- this.m01_ = tx.m01_ * m0 + tx.m11_ * m1;
- this.m02_ += tx.m02_ * m0 + tx.m12_ * m1;
- m0 = this.m10_;
- m1 = this.m11_;
- this.m10_ = tx.m00_ * m0 + tx.m10_ * m1;
- this.m11_ = tx.m01_ * m0 + tx.m11_ * m1;
- this.m12_ += tx.m02_ * m0 + tx.m12_ * m1;
- return this;
- };
- /**
- * Pre-concatenates an affine transform to this transform.
- *
- * @param {!goog.math.AffineTransform} tx The transform to preconcatenate.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.preConcatenate = function(tx) {
- var m0 = this.m00_;
- var m1 = this.m10_;
- this.m00_ = tx.m00_ * m0 + tx.m01_ * m1;
- this.m10_ = tx.m10_ * m0 + tx.m11_ * m1;
- m0 = this.m01_;
- m1 = this.m11_;
- this.m01_ = tx.m00_ * m0 + tx.m01_ * m1;
- this.m11_ = tx.m10_ * m0 + tx.m11_ * m1;
- m0 = this.m02_;
- m1 = this.m12_;
- this.m02_ = tx.m00_ * m0 + tx.m01_ * m1 + tx.m02_;
- this.m12_ = tx.m10_ * m0 + tx.m11_ * m1 + tx.m12_;
- return this;
- };
- /**
- * Transforms an array of coordinates by this transform and stores the result
- * into a destination array.
- *
- * @param {!Array<number>} src The array containing the source points
- * as x, y value pairs.
- * @param {number} srcOff The offset to the first point to be transformed.
- * @param {!Array<number>} dst The array into which to store the transformed
- * point pairs.
- * @param {number} dstOff The offset of the location of the first transformed
- * point in the destination array.
- * @param {number} numPts The number of points to transform.
- */
- goog.math.AffineTransform.prototype.transform = function(
- src, srcOff, dst, dstOff, numPts) {
- var i = srcOff;
- var j = dstOff;
- var srcEnd = srcOff + 2 * numPts;
- while (i < srcEnd) {
- var x = src[i++];
- var y = src[i++];
- dst[j++] = x * this.m00_ + y * this.m01_ + this.m02_;
- dst[j++] = x * this.m10_ + y * this.m11_ + this.m12_;
- }
- };
- /**
- * @return {number} The determinant of this transform.
- */
- goog.math.AffineTransform.prototype.getDeterminant = function() {
- return this.m00_ * this.m11_ - this.m01_ * this.m10_;
- };
- /**
- * Returns whether the transform is invertible. A transform is not invertible
- * if the determinant is 0 or any value is non-finite or NaN.
- *
- * @return {boolean} Whether the transform is invertible.
- */
- goog.math.AffineTransform.prototype.isInvertible = function() {
- var det = this.getDeterminant();
- return isFinite(det) && isFinite(this.m02_) && isFinite(this.m12_) &&
- det != 0;
- };
- /**
- * @return {!goog.math.AffineTransform} An AffineTransform object
- * representing the inverse transformation.
- */
- goog.math.AffineTransform.prototype.createInverse = function() {
- var det = this.getDeterminant();
- return new goog.math.AffineTransform(
- this.m11_ / det, -this.m10_ / det, -this.m01_ / det, this.m00_ / det,
- (this.m01_ * this.m12_ - this.m11_ * this.m02_) / det,
- (this.m10_ * this.m02_ - this.m00_ * this.m12_) / det);
- };
- /**
- * Creates a transform representing a scaling transformation.
- *
- * @param {number} sx The x-axis scaling factor.
- * @param {number} sy The y-axis scaling factor.
- * @return {!goog.math.AffineTransform} A transform representing a scaling
- * transformation.
- */
- goog.math.AffineTransform.getScaleInstance = function(sx, sy) {
- return new goog.math.AffineTransform().setToScale(sx, sy);
- };
- /**
- * Creates a transform representing a translation transformation.
- *
- * @param {number} dx The distance to translate in the x direction.
- * @param {number} dy The distance to translate in the y direction.
- * @return {!goog.math.AffineTransform} A transform representing a
- * translation transformation.
- */
- goog.math.AffineTransform.getTranslateInstance = function(dx, dy) {
- return new goog.math.AffineTransform().setToTranslation(dx, dy);
- };
- /**
- * Creates a transform representing a shearing transformation.
- *
- * @param {number} shx The x-axis shear factor.
- * @param {number} shy The y-axis shear factor.
- * @return {!goog.math.AffineTransform} A transform representing a shearing
- * transformation.
- */
- goog.math.AffineTransform.getShearInstance = function(shx, shy) {
- return new goog.math.AffineTransform().setToShear(shx, shy);
- };
- /**
- * Creates a transform representing a rotation transformation.
- *
- * @param {number} theta The angle of rotation measured in radians.
- * @param {number} x The x coordinate of the anchor point.
- * @param {number} y The y coordinate of the anchor point.
- * @return {!goog.math.AffineTransform} A transform representing a rotation
- * transformation.
- */
- goog.math.AffineTransform.getRotateInstance = function(theta, x, y) {
- return new goog.math.AffineTransform().setToRotation(theta, x, y);
- };
- /**
- * Sets this transform to a scaling transformation.
- *
- * @param {number} sx The x-axis scaling factor.
- * @param {number} sy The y-axis scaling factor.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.setToScale = function(sx, sy) {
- return this.setTransform(sx, 0, 0, sy, 0, 0);
- };
- /**
- * Sets this transform to a translation transformation.
- *
- * @param {number} dx The distance to translate in the x direction.
- * @param {number} dy The distance to translate in the y direction.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.setToTranslation = function(dx, dy) {
- return this.setTransform(1, 0, 0, 1, dx, dy);
- };
- /**
- * Sets this transform to a shearing transformation.
- *
- * @param {number} shx The x-axis shear factor.
- * @param {number} shy The y-axis shear factor.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.setToShear = function(shx, shy) {
- return this.setTransform(1, shy, shx, 1, 0, 0);
- };
- /**
- * Sets this transform to a rotation transformation.
- *
- * @param {number} theta The angle of rotation measured in radians.
- * @param {number} x The x coordinate of the anchor point.
- * @param {number} y The y coordinate of the anchor point.
- * @return {!goog.math.AffineTransform} This affine transform.
- */
- goog.math.AffineTransform.prototype.setToRotation = function(theta, x, y) {
- var cos = Math.cos(theta);
- var sin = Math.sin(theta);
- return this.setTransform(
- cos, sin, -sin, cos, x - x * cos + y * sin, y - x * sin - y * cos);
- };
- /**
- * Compares two affine transforms for equality.
- *
- * @param {goog.math.AffineTransform} tx The other affine transform.
- * @return {boolean} whether the two transforms are equal.
- */
- goog.math.AffineTransform.prototype.equals = function(tx) {
- if (this == tx) {
- return true;
- }
- if (!tx) {
- return false;
- }
- return this.m00_ == tx.m00_ && this.m01_ == tx.m01_ && this.m02_ == tx.m02_ &&
- this.m10_ == tx.m10_ && this.m11_ == tx.m11_ && this.m12_ == tx.m12_;
- };
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