flutter / mirrors / flutter / 8893e89d11555096ee44f5f0aa97ec40c3d61b5b / . / packages / flutter / lib / src / painting / matrix_utils.dart

// Copyright 2014 The Flutter Authors. All rights reserved. | |

// Use of this source code is governed by a BSD-style license that can be | |

// found in the LICENSE file. | |

import 'dart:typed_data'; | |

import 'package:flutter/foundation.dart'; | |

import 'package:vector_math/vector_math_64.dart'; | |

import 'basic_types.dart'; | |

/// Utility functions for working with matrices. | |

class MatrixUtils { | |

// This class is not meant to be instantiated or extended; this constructor | |

// prevents instantiation and extension. | |

MatrixUtils._(); | |

/// Returns the given [transform] matrix as an [Offset], if the matrix is | |

/// nothing but a 2D translation. | |

/// | |

/// Otherwise, returns null. | |

static Offset? getAsTranslation(Matrix4 transform) { | |

assert(transform != null); | |

final Float64List values = transform.storage; | |

// Values are stored in column-major order. | |

if (values[0] == 1.0 && // col 1 | |

values[1] == 0.0 && | |

values[2] == 0.0 && | |

values[3] == 0.0 && | |

values[4] == 0.0 && // col 2 | |

values[5] == 1.0 && | |

values[6] == 0.0 && | |

values[7] == 0.0 && | |

values[8] == 0.0 && // col 3 | |

values[9] == 0.0 && | |

values[10] == 1.0 && | |

values[11] == 0.0 && | |

values[14] == 0.0 && // bottom of col 4 (values 12 and 13 are the x and y offsets) | |

values[15] == 1.0) { | |

return Offset(values[12], values[13]); | |

} | |

return null; | |

} | |

/// Returns the given [transform] matrix as a [double] describing a uniform | |

/// scale, if the matrix is nothing but a symmetric 2D scale transform. | |

/// | |

/// Otherwise, returns null. | |

static double? getAsScale(Matrix4 transform) { | |

assert(transform != null); | |

final Float64List values = transform.storage; | |

// Values are stored in column-major order. | |

if (values[1] == 0.0 && // col 1 (value 0 is the scale) | |

values[2] == 0.0 && | |

values[3] == 0.0 && | |

values[4] == 0.0 && // col 2 (value 5 is the scale) | |

values[6] == 0.0 && | |

values[7] == 0.0 && | |

values[8] == 0.0 && // col 3 | |

values[9] == 0.0 && | |

values[10] == 1.0 && | |

values[11] == 0.0 && | |

values[12] == 0.0 && // col 4 | |

values[13] == 0.0 && | |

values[14] == 0.0 && | |

values[15] == 1.0 && | |

values[0] == values[5]) { // uniform scale | |

return values[0]; | |

} | |

return null; | |

} | |

/// Returns true if the given matrices are exactly equal, and false | |

/// otherwise. Null values are assumed to be the identity matrix. | |

static bool matrixEquals(Matrix4? a, Matrix4? b) { | |

if (identical(a, b)) | |

return true; | |

assert(a != null || b != null); | |

if (a == null) | |

return isIdentity(b!); | |

if (b == null) | |

return isIdentity(a); | |

assert(a != null && b != null); | |

return a.storage[0] == b.storage[0] | |

&& a.storage[1] == b.storage[1] | |

&& a.storage[2] == b.storage[2] | |

&& a.storage[3] == b.storage[3] | |

&& a.storage[4] == b.storage[4] | |

&& a.storage[5] == b.storage[5] | |

&& a.storage[6] == b.storage[6] | |

&& a.storage[7] == b.storage[7] | |

&& a.storage[8] == b.storage[8] | |

&& a.storage[9] == b.storage[9] | |

&& a.storage[10] == b.storage[10] | |

&& a.storage[11] == b.storage[11] | |

&& a.storage[12] == b.storage[12] | |

&& a.storage[13] == b.storage[13] | |

&& a.storage[14] == b.storage[14] | |

&& a.storage[15] == b.storage[15]; | |

} | |

/// Whether the given matrix is the identity matrix. | |

static bool isIdentity(Matrix4 a) { | |

assert(a != null); | |

return a.storage[0] == 1.0 // col 1 | |

&& a.storage[1] == 0.0 | |

&& a.storage[2] == 0.0 | |

&& a.storage[3] == 0.0 | |

&& a.storage[4] == 0.0 // col 2 | |

&& a.storage[5] == 1.0 | |

&& a.storage[6] == 0.0 | |

&& a.storage[7] == 0.0 | |

&& a.storage[8] == 0.0 // col 3 | |

&& a.storage[9] == 0.0 | |

&& a.storage[10] == 1.0 | |

&& a.storage[11] == 0.0 | |

&& a.storage[12] == 0.0 // col 4 | |

&& a.storage[13] == 0.0 | |

&& a.storage[14] == 0.0 | |

&& a.storage[15] == 1.0; | |

} | |

/// Applies the given matrix as a perspective transform to the given point. | |

/// | |

/// This function assumes the given point has a z-coordinate of 0.0. The | |

/// z-coordinate of the result is ignored. | |

/// | |

/// While not common, this method may return (NaN, NaN), iff the given `point` | |

/// results in a "point at infinity" in homogeneous coordinates after applying | |

/// the `transform`. For example, a [RenderObject] may set its transform to | |

/// the zero matrix to indicate its content is currently not visible. Trying | |

/// to convert an `Offset` to its coordinate space always results in | |

/// (NaN, NaN). | |

static Offset transformPoint(Matrix4 transform, Offset point) { | |

final Float64List storage = transform.storage; | |

final double x = point.dx; | |

final double y = point.dy; | |

// Directly simulate the transform of the vector (x, y, 0, 1), | |

// dropping the resulting Z coordinate, and normalizing only | |

// if needed. | |

final double rx = storage[0] * x + storage[4] * y + storage[12]; | |

final double ry = storage[1] * x + storage[5] * y + storage[13]; | |

final double rw = storage[3] * x + storage[7] * y + storage[15]; | |

if (rw == 1.0) { | |

return Offset(rx, ry); | |

} else { | |

return Offset(rx / rw, ry / rw); | |

} | |

} | |

/// Returns a rect that bounds the result of applying the given matrix as a | |

/// perspective transform to the given rect. | |

/// | |

/// This version of the operation is slower than the regular transformRect | |

/// method, but it avoids creating infinite values from large finite values | |

/// if it can. | |

static Rect _safeTransformRect(Matrix4 transform, Rect rect) { | |

final Float64List storage = transform.storage; | |

final bool isAffine = storage[3] == 0.0 && | |

storage[7] == 0.0 && | |

storage[15] == 1.0; | |

_accumulate(storage, rect.left, rect.top, true, isAffine); | |

_accumulate(storage, rect.right, rect.top, false, isAffine); | |

_accumulate(storage, rect.left, rect.bottom, false, isAffine); | |

_accumulate(storage, rect.right, rect.bottom, false, isAffine); | |

return Rect.fromLTRB(_minMax[0], _minMax[1], _minMax[2], _minMax[3]); | |

} | |

static late final Float64List _minMax = Float64List(4); | |

static void _accumulate(Float64List m, double x, double y, bool first, bool isAffine) { | |

final double w = isAffine ? 1.0 : 1.0 / (m[3] * x + m[7] * y + m[15]); | |

final double tx = (m[0] * x + m[4] * y + m[12]) * w; | |

final double ty = (m[1] * x + m[5] * y + m[13]) * w; | |

if (first) { | |

_minMax[0] = _minMax[2] = tx; | |

_minMax[1] = _minMax[3] = ty; | |

} else { | |

if (tx < _minMax[0]) { | |

_minMax[0] = tx; | |

} | |

if (ty < _minMax[1]) { | |

_minMax[1] = ty; | |

} | |

if (tx > _minMax[2]) { | |

_minMax[2] = tx; | |

} | |

if (ty > _minMax[3]) { | |

_minMax[3] = ty; | |

} | |

} | |

} | |

/// Returns a rect that bounds the result of applying the given matrix as a | |

/// perspective transform to the given rect. | |

/// | |

/// This function assumes the given rect is in the plane with z equals 0.0. | |

/// The transformed rect is then projected back into the plane with z equals | |

/// 0.0 before computing its bounding rect. | |

static Rect transformRect(Matrix4 transform, Rect rect) { | |

final Float64List storage = transform.storage; | |

final double x = rect.left; | |

final double y = rect.top; | |

final double w = rect.right - x; | |

final double h = rect.bottom - y; | |

// We want to avoid turning a finite rect into an infinite one if we can. | |

if (!w.isFinite || !h.isFinite) { | |

return _safeTransformRect(transform, rect); | |

} | |

// Transforming the 4 corners of a rectangle the straightforward way | |

// incurs the cost of transforming 4 points using vector math which | |

// involves 48 multiplications and 48 adds and then normalizing | |

// the points using 4 inversions of the homogeneous weight factor | |

// and then 12 multiplies. Once we have transformed all of the points | |

// we then need to turn them into a bounding box using 4 min/max | |

// operations each on 4 values yielding 12 total comparisons. | |

// | |

// On top of all of those operations, using the vector_math package to | |

// do the work for us involves allocating several objects in order to | |

// communicate the values back and forth - 4 allocating getters to extract | |

// the [Offset] objects for the corners of the [Rect], 4 conversions to | |

// a [Vector3] to use [Matrix4.perspectiveTransform()], and then 4 new | |

// [Offset] objects allocated to hold those results, yielding 8 [Offset] | |

// and 4 [Vector3] object allocations per rectangle transformed. | |

// | |

// But the math we really need to get our answer is actually much less | |

// than that. | |

// | |

// First, consider that a full point transform using the vector math | |

// package involves expanding it out into a vector3 with a Z coordinate | |

// of 0.0 and then performing 3 multiplies and 3 adds per coordinate: | |

// ``` | |

// xt = x*m00 + y*m10 + z*m20 + m30; | |

// yt = x*m01 + y*m11 + z*m21 + m31; | |

// zt = x*m02 + y*m12 + z*m22 + m32; | |

// wt = x*m03 + y*m13 + z*m23 + m33; | |

// ``` | |

// Immediately we see that we can get rid of the 3rd column of multiplies | |

// since we know that Z=0.0. We can also get rid of the 3rd row because | |

// we ignore the resulting Z coordinate. Finally we can get rid of the | |

// last row if we don't have a perspective transform since we can verify | |

// that the results are 1.0 for all points. This gets us down to 16 | |

// multiplies and 16 adds in the non-perspective case and 24 of each for | |

// the perspective case. (Plus the 12 comparisons to turn them back into | |

// a bounding box.) | |

// | |

// But we can do even better than that. | |

// | |

// Under optimal conditions of no perspective transformation, | |

// which is actually a very common condition, we can transform | |

// a rectangle in as little as 3 operations: | |

// | |

// (rx,ry) = transform of upper left corner of rectangle | |

// (wx,wy) = delta transform of the (w, 0) width relative vector | |

// (hx,hy) = delta transform of the (0, h) height relative vector | |

// | |

// A delta transform is a transform of all elements of the matrix except | |

// for the translation components. The translation components are added | |

// in at the end of each transform computation so they represent a | |

// constant offset for each point transformed. A delta transform of | |

// a horizontal or vertical vector involves a single multiplication due | |

// to the fact that it only has one non-zero coordinate and no addition | |

// of the translation component. | |

// | |

// In the absence of a perspective transform, the transformed | |

// rectangle will be mapped into a parallelogram with corners at: | |

// corner1 = (rx, ry) | |

// corner2 = corner1 + dTransformed width vector = (rx+wx, ry+wy) | |

// corner3 = corner1 + dTransformed height vector = (rx+hx, ry+hy) | |

// corner4 = corner1 + both dTransformed vectors = (rx+wx+hx, ry+wy+hy) | |

// In all, this method of transforming the rectangle requires only | |

// 8 multiplies and 12 additions (which we can reduce to 8 additions if | |

// we only need a bounding box, see below). | |

// | |

// In the presence of a perspective transform, the above conditions | |

// continue to hold with respect to the non-normalized coordinates so | |

// we can still save a lot of multiplications by computing the 4 | |

// non-normalized coordinates using relative additions before we normalize | |

// them and they lose their "pseudo-parallelogram" relationships. We still | |

// have to do the normalization divisions and min/max all 4 points to | |

// get the resulting transformed bounding box, but we save a lot of | |

// calculations over blindly transforming all 4 coordinates independently. | |

// In all, we need 12 multiplies and 22 additions to construct the | |

// non-normalized vectors and then 8 divisions (or 4 inversions and 8 | |

// multiplies) for normalization (plus the standard set of 12 comparisons | |

// for the min/max bounds operations). | |

// | |

// Back to the non-perspective case, the optimization that lets us get | |

// away with fewer additions if we only need a bounding box comes from | |

// analyzing the impact of the relative vectors on expanding the | |

// bounding box of the parallelogram. First, the bounding box always | |

// contains the transformed upper-left corner of the rectangle. Next, | |

// each relative vector either pushes on the left or right side of the | |

// bounding box and also either the top or bottom side, depending on | |

// whether it is positive or negative. Finally, you can consider the | |

// impact of each vector on the bounding box independently. If, say, | |

// wx and hx have the same sign, then the limiting point in the bounding | |

// box will be the one that involves adding both of them to the origin | |

// point. If they have opposite signs, then one will push one wall one | |

// way and the other will push the opposite wall the other way and when | |

// you combine both of them, the resulting "opposite corner" will | |

// actually be between the limits they established by pushing the walls | |

// away from each other, as below: | |

// ``` | |

// +---------(originx,originy)--------------+ | |

// | -----^---- | | |

// | ----- ---- | | |

// | ----- ---- | | |

// (+hx,+hy)< ---- | | |

// | ---- ---- | | |

// | ---- >(+wx,+wy) | |

// | ---- ----- | | |

// | ---- ----- | | |

// | ---- ----- | | |

// | v | | |

// +---------------(+wx+hx,+wy+hy)----------+ | |

// ``` | |

// In this diagram, consider that: | |

// ``` | |

// wx would be a positive number | |

// hx would be a negative number | |

// wy and hy would both be positive numbers | |

// ``` | |

// As a result, wx pushes out the right wall, hx pushes out the left wall, | |

// and both wy and hy push down the bottom wall of the bounding box. The | |

// wx,hx pair (of opposite signs) worked on opposite walls and the final | |

// opposite corner had an X coordinate between the limits they established. | |

// The wy,hy pair (of the same sign) both worked together to push the | |

// bottom wall down by their sum. | |

// | |

// This relationship allows us to simply start with the point computed by | |

// transforming the upper left corner of the rectangle, and then | |

// conditionally adding wx, wy, hx, and hy to either the left or top | |

// or right or bottom of the bounding box independently depending on sign. | |

// In that case we only need 4 comparisons and 4 additions total to | |

// compute the bounding box, combined with the 8 multiplications and | |

// 4 additions to compute the transformed point and relative vectors | |

// for a total of 8 multiplies, 8 adds, and 4 comparisons. | |

// | |

// An astute observer will note that we do need to do 2 subtractions at | |

// the top of the method to compute the width and height. Add those to | |

// all of the relative solutions listed above. The test for perspective | |

// also adds 3 compares to the affine case and up to 3 compares to the | |

// perspective case (depending on which test fails, the rest are omitted). | |

// | |

// The final tally: | |

// basic method = 60 mul + 48 add + 12 compare | |

// optimized perspective = 12 mul + 22 add + 15 compare + 2 sub | |

// optimized affine = 8 mul + 8 add + 7 compare + 2 sub | |

// | |

// Since compares are essentially subtractions and subtractions are | |

// the same cost as adds, we end up with: | |

// basic method = 60 mul + 60 add/sub/compare | |

// optimized perspective = 12 mul + 39 add/sub/compare | |

// optimized affine = 8 mul + 17 add/sub/compare | |

final double wx = storage[0] * w; | |

final double hx = storage[4] * h; | |

final double rx = storage[0] * x + storage[4] * y + storage[12]; | |

final double wy = storage[1] * w; | |

final double hy = storage[5] * h; | |

final double ry = storage[1] * x + storage[5] * y + storage[13]; | |

if (storage[3] == 0.0 && storage[7] == 0.0 && storage[15] == 1.0) { | |

double left = rx; | |

double right = rx; | |

if (wx < 0) { | |

left += wx; | |

} else { | |

right += wx; | |

} | |

if (hx < 0) { | |

left += hx; | |

} else { | |

right += hx; | |

} | |

double top = ry; | |

double bottom = ry; | |

if (wy < 0) { | |

top += wy; | |

} else { | |

bottom += wy; | |

} | |

if (hy < 0) { | |

top += hy; | |

} else { | |

bottom += hy; | |

} | |

return Rect.fromLTRB(left, top, right, bottom); | |

} else { | |

final double ww = storage[3] * w; | |

final double hw = storage[7] * h; | |

final double rw = storage[3] * x + storage[7] * y + storage[15]; | |

final double ulx = rx / rw; | |

final double uly = ry / rw; | |

final double urx = (rx + wx) / (rw + ww); | |

final double ury = (ry + wy) / (rw + ww); | |

final double llx = (rx + hx) / (rw + hw); | |

final double lly = (ry + hy) / (rw + hw); | |

final double lrx = (rx + wx + hx) / (rw + ww + hw); | |

final double lry = (ry + wy + hy) / (rw + ww + hw); | |

return Rect.fromLTRB( | |

_min4(ulx, urx, llx, lrx), | |

_min4(uly, ury, lly, lry), | |

_max4(ulx, urx, llx, lrx), | |

_max4(uly, ury, lly, lry), | |

); | |

} | |

} | |

static double _min4(double a, double b, double c, double d) { | |

final double e = (a < b) ? a : b; | |

final double f = (c < d) ? c : d; | |

return (e < f) ? e : f; | |

} | |

static double _max4(double a, double b, double c, double d) { | |

final double e = (a > b) ? a : b; | |

final double f = (c > d) ? c : d; | |

return (e > f) ? e : f; | |

} | |

/// Returns a rect that bounds the result of applying the inverse of the given | |

/// matrix as a perspective transform to the given rect. | |

/// | |

/// This function assumes the given rect is in the plane with z equals 0.0. | |

/// The transformed rect is then projected back into the plane with z equals | |

/// 0.0 before computing its bounding rect. | |

static Rect inverseTransformRect(Matrix4 transform, Rect rect) { | |

assert(rect != null); | |

// As exposed by `unrelated_type_equality_checks`, this assert was a no-op. | |

// Fixing it introduces a bunch of runtime failures; for more context see: | |

// https://github.com/flutter/flutter/pull/31568 | |

// assert(transform.determinant != 0.0); | |

if (isIdentity(transform)) | |

return rect; | |

transform = Matrix4.copy(transform)..invert(); | |

return transformRect(transform, rect); | |

} | |

/// Create a transformation matrix which mimics the effects of tangentially | |

/// wrapping the plane on which this transform is applied around a cylinder | |

/// and then looking at the cylinder from a point outside the cylinder. | |

/// | |

/// The `radius` simulates the radius of the cylinder the plane is being | |

/// wrapped onto. If the transformation is applied to a 0-dimensional dot | |

/// instead of a plane, the dot would simply translate by +/- `radius` pixels | |

/// along the `orientation` [Axis] when rotating from 0 to +/- 90 degrees. | |

/// | |

/// A positive radius means the object is closest at 0 `angle` and a negative | |

/// radius means the object is closest at π `angle` or 180 degrees. | |

/// | |

/// The `angle` argument is the difference in angle in radians between the | |

/// object and the viewing point. A positive `angle` on a positive `radius` | |

/// moves the object up when `orientation` is vertical and right when | |

/// horizontal. | |

/// | |

/// The transformation is always done such that a 0 `angle` keeps the | |

/// transformed object at exactly the same size as before regardless of | |

/// `radius` and `perspective` when `radius` is positive. | |

/// | |

/// The `perspective` argument is a number between 0 and 1 where 0 means | |

/// looking at the object from infinitely far with an infinitely narrow field | |

/// of view and 1 means looking at the object from infinitely close with an | |

/// infinitely wide field of view. Defaults to a sane but arbitrary 0.001. | |

/// | |

/// The `orientation` is the direction of the rotation axis. | |

/// | |

/// Because the viewing position is a point, it's never possible to see the | |

/// outer side of the cylinder at or past +/- π / 2 or 90 degrees and it's | |

/// almost always possible to end up seeing the inner side of the cylinder | |

/// or the back side of the transformed plane before π / 2 when perspective > 0. | |

static Matrix4 createCylindricalProjectionTransform({ | |

required double radius, | |

required double angle, | |

double perspective = 0.001, | |

Axis orientation = Axis.vertical, | |

}) { | |

assert(radius != null); | |

assert(angle != null); | |

assert(perspective >= 0 && perspective <= 1.0); | |

assert(orientation != null); | |

// Pre-multiplied matrix of a projection matrix and a view matrix. | |

// | |

// Projection matrix is a simplified perspective matrix | |

// http://web.iitd.ac.in/~hegde/cad/lecture/L9_persproj.pdf | |

// in the form of | |

// [[1.0, 0.0, 0.0, 0.0], | |

// [0.0, 1.0, 0.0, 0.0], | |

// [0.0, 0.0, 1.0, 0.0], | |

// [0.0, 0.0, -perspective, 1.0]] | |

// | |

// View matrix is a simplified camera view matrix. | |

// Basically re-scales to keep object at original size at angle = 0 at | |

// any radius in the form of | |

// [[1.0, 0.0, 0.0, 0.0], | |

// [0.0, 1.0, 0.0, 0.0], | |

// [0.0, 0.0, 1.0, -radius], | |

// [0.0, 0.0, 0.0, 1.0]] | |

Matrix4 result = Matrix4.identity() | |

..setEntry(3, 2, -perspective) | |

..setEntry(2, 3, -radius) | |

..setEntry(3, 3, perspective * radius + 1.0); | |

// Model matrix by first translating the object from the origin of the world | |

// by radius in the z axis and then rotating against the world. | |

result = result * (( | |

orientation == Axis.horizontal | |

? Matrix4.rotationY(angle) | |

: Matrix4.rotationX(angle) | |

) * Matrix4.translationValues(0.0, 0.0, radius)) as Matrix4; | |

// Essentially perspective * view * model. | |

return result; | |

} | |

/// Returns a matrix that transforms every point to [offset]. | |

static Matrix4 forceToPoint(Offset offset) { | |

return Matrix4.identity() | |

..setRow(0, Vector4(0, 0, 0, offset.dx)) | |

..setRow(1, Vector4(0, 0, 0, offset.dy)); | |

} | |

} | |

/// Returns a list of strings representing the given transform in a format | |

/// useful for [TransformProperty]. | |

/// | |

/// If the argument is null, returns a list with the single string "null". | |

List<String> debugDescribeTransform(Matrix4? transform) { | |

if (transform == null) | |

return const <String>['null']; | |

return <String>[ | |

'[0] ${debugFormatDouble(transform.entry(0, 0))},${debugFormatDouble(transform.entry(0, 1))},${debugFormatDouble(transform.entry(0, 2))},${debugFormatDouble(transform.entry(0, 3))}', | |

'[1] ${debugFormatDouble(transform.entry(1, 0))},${debugFormatDouble(transform.entry(1, 1))},${debugFormatDouble(transform.entry(1, 2))},${debugFormatDouble(transform.entry(1, 3))}', | |

'[2] ${debugFormatDouble(transform.entry(2, 0))},${debugFormatDouble(transform.entry(2, 1))},${debugFormatDouble(transform.entry(2, 2))},${debugFormatDouble(transform.entry(2, 3))}', | |

'[3] ${debugFormatDouble(transform.entry(3, 0))},${debugFormatDouble(transform.entry(3, 1))},${debugFormatDouble(transform.entry(3, 2))},${debugFormatDouble(transform.entry(3, 3))}', | |

]; | |

} | |

/// Property which handles [Matrix4] that represent transforms. | |

class TransformProperty extends DiagnosticsProperty<Matrix4> { | |

/// Create a diagnostics property for [Matrix4] objects. | |

/// | |

/// The [showName] and [level] arguments must not be null. | |

TransformProperty( | |

String name, | |

Matrix4? value, { | |

bool showName = true, | |

Object? defaultValue = kNoDefaultValue, | |

DiagnosticLevel level = DiagnosticLevel.info, | |

}) : assert(showName != null), | |

assert(level != null), | |

super( | |

name, | |

value, | |

showName: showName, | |

defaultValue: defaultValue, | |

level: level, | |

); | |

@override | |

String valueToString({ TextTreeConfiguration? parentConfiguration }) { | |

if (parentConfiguration != null && !parentConfiguration.lineBreakProperties) { | |

// Format the value on a single line to be compatible with the parent's | |

// style. | |

final List<String> values = <String>[ | |

'${debugFormatDouble(value!.entry(0, 0))},${debugFormatDouble(value!.entry(0, 1))},${debugFormatDouble(value!.entry(0, 2))},${debugFormatDouble(value!.entry(0, 3))}', | |

'${debugFormatDouble(value!.entry(1, 0))},${debugFormatDouble(value!.entry(1, 1))},${debugFormatDouble(value!.entry(1, 2))},${debugFormatDouble(value!.entry(1, 3))}', | |

'${debugFormatDouble(value!.entry(2, 0))},${debugFormatDouble(value!.entry(2, 1))},${debugFormatDouble(value!.entry(2, 2))},${debugFormatDouble(value!.entry(2, 3))}', | |

'${debugFormatDouble(value!.entry(3, 0))},${debugFormatDouble(value!.entry(3, 1))},${debugFormatDouble(value!.entry(3, 2))},${debugFormatDouble(value!.entry(3, 3))}', | |

]; | |

return '[${values.join('; ')}]'; | |

} | |

return debugDescribeTransform(value).join('\n'); | |

} | |

} |