| // 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'); |
| } |
| } |
