| // Copyright (c) 2015, Google Inc. Please see the AUTHORS file for details. |
| // All rights reserved. Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| part of vector_math; |
| |
| /// 4D Matrix. |
| /// Values are stored in column major order. |
| class Matrix4 { |
| final Float32List _m4storage; |
| |
| /// The components of the matrix. |
| Float32List get storage => _m4storage; |
| |
| /// Solve [A] * [x] = [b]. |
| static void solve2(Matrix4 A, Vector2 x, Vector2 b) { |
| final double a11 = A.entry(0, 0); |
| final double a12 = A.entry(0, 1); |
| final double a21 = A.entry(1, 0); |
| final double a22 = A.entry(1, 1); |
| final double bx = b.x - A._m4storage[8]; |
| final double by = b.y - A._m4storage[9]; |
| double det = a11 * a22 - a12 * a21; |
| |
| if (det != 0.0) { |
| det = 1.0 / det; |
| } |
| |
| x.x = det * (a22 * bx - a12 * by); |
| x.y = det * (a11 * by - a21 * bx); |
| } |
| |
| /// Solve [A] * [x] = [b]. |
| static void solve3(Matrix4 A, Vector3 x, Vector3 b) { |
| final double A0x = A.entry(0, 0); |
| final double A0y = A.entry(1, 0); |
| final double A0z = A.entry(2, 0); |
| final double A1x = A.entry(0, 1); |
| final double A1y = A.entry(1, 1); |
| final double A1z = A.entry(2, 1); |
| final double A2x = A.entry(0, 2); |
| final double A2y = A.entry(1, 2); |
| final double A2z = A.entry(2, 2); |
| final double bx = b.x - A._m4storage[12]; |
| final double by = b.y - A._m4storage[13]; |
| final double bz = b.z - A._m4storage[14]; |
| double rx, ry, rz; |
| double det; |
| |
| // Column1 cross Column 2 |
| rx = A1y * A2z - A1z * A2y; |
| ry = A1z * A2x - A1x * A2z; |
| rz = A1x * A2y - A1y * A2x; |
| |
| // A.getColumn(0).dot(x) |
| det = A0x * rx + A0y * ry + A0z * rz; |
| if (det != 0.0) { |
| det = 1.0 / det; |
| } |
| |
| // b dot [Column1 cross Column 2] |
| final double x_ = det * (bx * rx + by * ry + bz * rz); |
| |
| // Column2 cross b |
| rx = -(A2y * bz - A2z * by); |
| ry = -(A2z * bx - A2x * bz); |
| rz = -(A2x * by - A2y * bx); |
| // Column0 dot -[Column2 cross b (Column3)] |
| final double y_ = det * (A0x * rx + A0y * ry + A0z * rz); |
| |
| // b cross Column 1 |
| rx = -(by * A1z - bz * A1y); |
| ry = -(bz * A1x - bx * A1z); |
| rz = -(bx * A1y - by * A1x); |
| // Column0 dot -[b cross Column 1] |
| final double z_ = det * (A0x * rx + A0y * ry + A0z * rz); |
| |
| x.x = x_; |
| x.y = y_; |
| x.z = z_; |
| } |
| |
| /// Solve [A] * [x] = [b]. |
| static void solve(Matrix4 A, Vector4 x, Vector4 b) { |
| final double a00 = A._m4storage[0]; |
| final double a01 = A._m4storage[1]; |
| final double a02 = A._m4storage[2]; |
| final double a03 = A._m4storage[3]; |
| final double a10 = A._m4storage[4]; |
| final double a11 = A._m4storage[5]; |
| final double a12 = A._m4storage[6]; |
| final double a13 = A._m4storage[7]; |
| final double a20 = A._m4storage[8]; |
| final double a21 = A._m4storage[9]; |
| final double a22 = A._m4storage[10]; |
| final double a23 = A._m4storage[11]; |
| final double a30 = A._m4storage[12]; |
| final double a31 = A._m4storage[13]; |
| final double a32 = A._m4storage[14]; |
| final double a33 = A._m4storage[15]; |
| final double b00 = a00 * a11 - a01 * a10; |
| final double b01 = a00 * a12 - a02 * a10; |
| final double b02 = a00 * a13 - a03 * a10; |
| final double b03 = a01 * a12 - a02 * a11; |
| final double b04 = a01 * a13 - a03 * a11; |
| final double b05 = a02 * a13 - a03 * a12; |
| final double b06 = a20 * a31 - a21 * a30; |
| final double b07 = a20 * a32 - a22 * a30; |
| final double b08 = a20 * a33 - a23 * a30; |
| final double b09 = a21 * a32 - a22 * a31; |
| final double b10 = a21 * a33 - a23 * a31; |
| final double b11 = a22 * a33 - a23 * a32; |
| |
| final double bX = b.storage[0]; |
| final double bY = b.storage[1]; |
| final double bZ = b.storage[2]; |
| final double bW = b.storage[3]; |
| |
| double det = |
| b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
| |
| if (det != 0.0) { |
| det = 1.0 / det; |
| } |
| |
| x.x = det * |
| ((a11 * b11 - a12 * b10 + a13 * b09) * bX - |
| (a10 * b11 - a12 * b08 + a13 * b07) * bY + |
| (a10 * b10 - a11 * b08 + a13 * b06) * bZ - |
| (a10 * b09 - a11 * b07 + a12 * b06) * bW); |
| |
| x.y = det * |
| -((a01 * b11 - a02 * b10 + a03 * b09) * bX - |
| (a00 * b11 - a02 * b08 + a03 * b07) * bY + |
| (a00 * b10 - a01 * b08 + a03 * b06) * bZ - |
| (a00 * b09 - a01 * b07 + a02 * b06) * bW); |
| |
| x.z = det * |
| ((a31 * b05 - a32 * b04 + a33 * b03) * bX - |
| (a30 * b05 - a32 * b02 + a33 * b01) * bY + |
| (a30 * b04 - a31 * b02 + a33 * b00) * bZ - |
| (a30 * b03 - a31 * b01 + a32 * b00) * bW); |
| |
| x.w = det * |
| -((a21 * b05 - a22 * b04 + a23 * b03) * bX - |
| (a20 * b05 - a22 * b02 + a23 * b01) * bY + |
| (a20 * b04 - a21 * b02 + a23 * b00) * bZ - |
| (a20 * b03 - a21 * b01 + a22 * b00) * bW); |
| } |
| |
| /// Return index in storage for [row], [col] value. |
| int index(int row, int col) => (col * 4) + row; |
| |
| /// Value at [row], [col]. |
| double entry(int row, int col) { |
| assert((row >= 0) && (row < dimension)); |
| assert((col >= 0) && (col < dimension)); |
| |
| return _m4storage[index(row, col)]; |
| } |
| |
| /// Set value at [row], [col] to be [v]. |
| setEntry(int row, int col, double v) { |
| assert((row >= 0) && (row < dimension)); |
| assert((col >= 0) && (col < dimension)); |
| |
| _m4storage[index(row, col)] = v; |
| } |
| |
| /// Constructs a new mat4. |
| factory Matrix4( |
| double arg0, |
| double arg1, |
| double arg2, |
| double arg3, |
| double arg4, |
| double arg5, |
| double arg6, |
| double arg7, |
| double arg8, |
| double arg9, |
| double arg10, |
| double arg11, |
| double arg12, |
| double arg13, |
| double arg14, |
| double arg15) => |
| new Matrix4.zero() |
| ..setValues(arg0, arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9, |
| arg10, arg11, arg12, arg13, arg14, arg15); |
| |
| /// New matrix from [values]. |
| factory Matrix4.fromList(List<double> values) { |
| return new Matrix4.zero() |
| ..setValues( |
| values[0], |
| values[1], |
| values[2], |
| values[3], |
| values[4], |
| values[5], |
| values[6], |
| values[7], |
| values[8], |
| values[9], |
| values[10], |
| values[11], |
| values[12], |
| values[13], |
| values[14], |
| values[15]); |
| } |
| |
| /// Zero matrix. |
| Matrix4.zero() : _m4storage = new Float32List(16); |
| |
| /// Identity matrix. |
| factory Matrix4.identity() => new Matrix4.zero()..setIdentity(); |
| |
| /// Copies values from [other]. |
| factory Matrix4.copy(Matrix4 other) => new Matrix4.zero()..setFrom(other); |
| |
| /// Constructs a matrix that is the inverse of [other]. |
| factory Matrix4.inverted(Matrix4 other) { |
| Matrix4 r = new Matrix4.zero(); |
| double determinant = r.copyInverse(other); |
| if (determinant == 0.0) { |
| throw new ArgumentError.value( |
| other, 'other', 'Matrix cannot be inverted'); |
| } |
| return r; |
| } |
| |
| /// Constructs a new mat4 from columns. |
| factory Matrix4.columns( |
| Vector4 arg0, Vector4 arg1, Vector4 arg2, Vector4 arg3) => |
| new Matrix4.zero()..setColumns(arg0, arg1, arg2, arg3); |
| |
| /// Outer product of [u] and [v]. |
| factory Matrix4.outer(Vector4 u, Vector4 v) => |
| new Matrix4.zero()..setOuter(u, v); |
| |
| /// Rotation of [radians_] around X. |
| factory Matrix4.rotationX(double radians) => new Matrix4.zero() |
| .._m4storage[15] = 1.0 |
| ..setRotationX(radians); |
| |
| /// Rotation of [radians_] around Y. |
| factory Matrix4.rotationY(double radians) => new Matrix4.zero() |
| .._m4storage[15] = 1.0 |
| ..setRotationY(radians); |
| |
| /// Rotation of [radians_] around Z. |
| factory Matrix4.rotationZ(double radians) => new Matrix4.zero() |
| .._m4storage[15] = 1.0 |
| ..setRotationZ(radians); |
| |
| /// Translation matrix. |
| factory Matrix4.translation(Vector3 translation) => new Matrix4.zero() |
| ..setIdentity() |
| ..setTranslation(translation); |
| |
| /// Translation matrix. |
| factory Matrix4.translationValues(double x, double y, double z) => |
| new Matrix4.zero() |
| ..setIdentity() |
| ..setTranslationRaw(x, y, z); |
| |
| /// Scale matrix. |
| factory Matrix4.diagonal3(Vector3 scale) { |
| final m = new Matrix4.zero(); |
| final mStorage = m._m4storage; |
| final scaleStorage = scale._v3storage; |
| mStorage[15] = 1.0; |
| mStorage[10] = scaleStorage[2]; |
| mStorage[5] = scaleStorage[1]; |
| mStorage[0] = scaleStorage[0]; |
| return m; |
| } |
| |
| /// Scale matrix. |
| factory Matrix4.diagonal3Values(double x, double y, double z) => |
| new Matrix4.zero() |
| .._m4storage[15] = 1.0 |
| .._m4storage[10] = z |
| .._m4storage[5] = y |
| .._m4storage[0] = x; |
| |
| /// Skew matrix around X axis |
| factory Matrix4.skewX(double alpha) { |
| final m = new Matrix4.identity(); |
| m._m4storage[4] = Math.tan(alpha); |
| return m; |
| } |
| |
| /// Skew matrix around Y axis. |
| factory Matrix4.skewY(double beta) { |
| final m = new Matrix4.identity(); |
| m._m4storage[1] = Math.tan(beta); |
| return m; |
| } |
| |
| /// Skew matrix around X axis (alpha) and Y axis (beta). |
| factory Matrix4.skew(double alpha, double beta) { |
| final m = new Matrix4.identity(); |
| m._m4storage[1] = Math.tan(beta); |
| m._m4storage[4] = Math.tan(alpha); |
| return m; |
| } |
| |
| |
| /// Constructs Matrix4 with given [Float32List] as [storage]. |
| Matrix4.fromFloat32List(this._m4storage); |
| |
| /// Constructs Matrix4 with a [storage] that views given [buffer] starting at |
| /// [offset]. [offset] has to be multiple of [Float32List.BYTES_PER_ELEMENT]. |
| Matrix4.fromBuffer(ByteBuffer buffer, int offset) |
| : _m4storage = new Float32List.view(buffer, offset, 16); |
| |
| /// Constructs Matrix4 from [translation], [rotation] and [scale]. |
| factory Matrix4.compose( |
| Vector3 translation, Quaternion rotation, Vector3 scale) => |
| new Matrix4.zero() |
| ..setFromTranslationRotationScale(translation, rotation, scale); |
| |
| /// Sets the diagonal to [arg]. |
| void splatDiagonal(double arg) { |
| _m4storage[0] = arg; |
| _m4storage[5] = arg; |
| _m4storage[10] = arg; |
| _m4storage[15] = arg; |
| } |
| |
| /// Sets the matrix with specified values. |
| void setValues( |
| double arg0, |
| double arg1, |
| double arg2, |
| double arg3, |
| double arg4, |
| double arg5, |
| double arg6, |
| double arg7, |
| double arg8, |
| double arg9, |
| double arg10, |
| double arg11, |
| double arg12, |
| double arg13, |
| double arg14, |
| double arg15) { |
| _m4storage[15] = arg15; |
| _m4storage[14] = arg14; |
| _m4storage[13] = arg13; |
| _m4storage[12] = arg12; |
| _m4storage[11] = arg11; |
| _m4storage[10] = arg10; |
| _m4storage[9] = arg9; |
| _m4storage[8] = arg8; |
| _m4storage[7] = arg7; |
| _m4storage[6] = arg6; |
| _m4storage[5] = arg5; |
| _m4storage[4] = arg4; |
| _m4storage[3] = arg3; |
| _m4storage[2] = arg2; |
| _m4storage[1] = arg1; |
| _m4storage[0] = arg0; |
| } |
| |
| /// Sets the entire matrix to the column values. |
| void setColumns(Vector4 arg0, Vector4 arg1, Vector4 arg2, Vector4 arg3) { |
| final arg0Storage = arg0._v4storage; |
| final arg1Storage = arg1._v4storage; |
| final arg2Storage = arg2._v4storage; |
| final arg3Storage = arg3._v4storage; |
| _m4storage[0] = arg0Storage[0]; |
| _m4storage[1] = arg0Storage[1]; |
| _m4storage[2] = arg0Storage[2]; |
| _m4storage[3] = arg0Storage[3]; |
| _m4storage[4] = arg1Storage[0]; |
| _m4storage[5] = arg1Storage[1]; |
| _m4storage[6] = arg1Storage[2]; |
| _m4storage[7] = arg1Storage[3]; |
| _m4storage[8] = arg2Storage[0]; |
| _m4storage[9] = arg2Storage[1]; |
| _m4storage[10] = arg2Storage[2]; |
| _m4storage[11] = arg2Storage[3]; |
| _m4storage[12] = arg3Storage[0]; |
| _m4storage[13] = arg3Storage[1]; |
| _m4storage[14] = arg3Storage[2]; |
| _m4storage[15] = arg3Storage[3]; |
| } |
| |
| /// Sets the entire matrix to the matrix in [arg]. |
| void setFrom(Matrix4 arg) { |
| final argStorage = arg._m4storage; |
| _m4storage[15] = argStorage[15]; |
| _m4storage[14] = argStorage[14]; |
| _m4storage[13] = argStorage[13]; |
| _m4storage[12] = argStorage[12]; |
| _m4storage[11] = argStorage[11]; |
| _m4storage[10] = argStorage[10]; |
| _m4storage[9] = argStorage[9]; |
| _m4storage[8] = argStorage[8]; |
| _m4storage[7] = argStorage[7]; |
| _m4storage[6] = argStorage[6]; |
| _m4storage[5] = argStorage[5]; |
| _m4storage[4] = argStorage[4]; |
| _m4storage[3] = argStorage[3]; |
| _m4storage[2] = argStorage[2]; |
| _m4storage[1] = argStorage[1]; |
| _m4storage[0] = argStorage[0]; |
| } |
| |
| /// Sets the matrix from translation [arg0] and rotation [arg1]. |
| void setFromTranslationRotation(Vector3 arg0, Quaternion arg1) { |
| final arg1Storage = arg1._qStorage; |
| double x = arg1Storage[0]; |
| double y = arg1Storage[1]; |
| double z = arg1Storage[2]; |
| double w = arg1Storage[3]; |
| double x2 = x + x; |
| double y2 = y + y; |
| double z2 = z + z; |
| double xx = x * x2; |
| double xy = x * y2; |
| double xz = x * z2; |
| double yy = y * y2; |
| double yz = y * z2; |
| double zz = z * z2; |
| double wx = w * x2; |
| double wy = w * y2; |
| double wz = w * z2; |
| |
| final arg0Storage = arg0._v3storage; |
| _m4storage[0] = 1.0 - (yy + zz); |
| _m4storage[1] = xy + wz; |
| _m4storage[2] = xz - wy; |
| _m4storage[3] = 0.0; |
| _m4storage[4] = xy - wz; |
| _m4storage[5] = 1.0 - (xx + zz); |
| _m4storage[6] = yz + wx; |
| _m4storage[7] = 0.0; |
| _m4storage[8] = xz + wy; |
| _m4storage[9] = yz - wx; |
| _m4storage[10] = 1.0 - (xx + yy); |
| _m4storage[11] = 0.0; |
| _m4storage[12] = arg0Storage[0]; |
| _m4storage[13] = arg0Storage[1]; |
| _m4storage[14] = arg0Storage[2]; |
| _m4storage[15] = 1.0; |
| } |
| |
| /// Sets the matrix from [translation], [rotation] and [scale]. |
| void setFromTranslationRotationScale( |
| Vector3 translation, Quaternion rotation, Vector3 scale) { |
| setFromTranslationRotation(translation, rotation); |
| this.scale(scale); |
| } |
| |
| /// Sets the upper 2x2 of the matrix to be [arg]. |
| void setUpper2x2(Matrix2 arg) { |
| final argStorage = arg._m2storage; |
| _m4storage[0] = argStorage[0]; |
| _m4storage[1] = argStorage[1]; |
| _m4storage[4] = argStorage[2]; |
| _m4storage[5] = argStorage[3]; |
| } |
| |
| /// Sets the diagonal of the matrix to be [arg]. |
| void setDiagonal(Vector4 arg) { |
| final argStorage = arg._v4storage; |
| _m4storage[0] = argStorage[0]; |
| _m4storage[5] = argStorage[1]; |
| _m4storage[10] = argStorage[2]; |
| _m4storage[15] = argStorage[3]; |
| } |
| |
| void setOuter(Vector4 u, Vector4 v) { |
| final uStorage = u._v4storage; |
| final vStorage = v._v4storage; |
| _m4storage[0] = uStorage[0] * vStorage[0]; |
| _m4storage[1] = uStorage[0] * vStorage[1]; |
| _m4storage[2] = uStorage[0] * vStorage[2]; |
| _m4storage[3] = uStorage[0] * vStorage[3]; |
| _m4storage[4] = uStorage[1] * vStorage[0]; |
| _m4storage[5] = uStorage[1] * vStorage[1]; |
| _m4storage[6] = uStorage[1] * vStorage[2]; |
| _m4storage[7] = uStorage[1] * vStorage[3]; |
| _m4storage[8] = uStorage[2] * vStorage[0]; |
| _m4storage[9] = uStorage[2] * vStorage[1]; |
| _m4storage[10] = uStorage[2] * vStorage[2]; |
| _m4storage[11] = uStorage[2] * vStorage[3]; |
| _m4storage[12] = uStorage[3] * vStorage[0]; |
| _m4storage[13] = uStorage[3] * vStorage[1]; |
| _m4storage[14] = uStorage[3] * vStorage[2]; |
| _m4storage[15] = uStorage[3] * vStorage[3]; |
| } |
| |
| /// Returns a printable string |
| String toString() => '[0] ${getRow(0)}\n[1] ${getRow(1)}\n' |
| '[2] ${getRow(2)}\n[3] ${getRow(3)}\n'; |
| |
| /// Dimension of the matrix. |
| int get dimension => 4; |
| |
| /// Access the element of the matrix at the index [i]. |
| double operator [](int i) => _m4storage[i]; |
| |
| /// Set the element of the matrix at the index [i]. |
| void operator []=(int i, double v) { |
| _m4storage[i] = v; |
| } |
| |
| /// Check if two matrices are the same. |
| bool operator ==(other) { |
| return (other is Matrix4) && |
| (_m4storage[0] == other._m4storage[0]) && |
| (_m4storage[1] == other._m4storage[1]) && |
| (_m4storage[2] == other._m4storage[2]) && |
| (_m4storage[3] == other._m4storage[3]) && |
| (_m4storage[4] == other._m4storage[4]) && |
| (_m4storage[5] == other._m4storage[5]) && |
| (_m4storage[6] == other._m4storage[6]) && |
| (_m4storage[7] == other._m4storage[7]) && |
| (_m4storage[8] == other._m4storage[8]) && |
| (_m4storage[9] == other._m4storage[9]) && |
| (_m4storage[10] == other._m4storage[10]) && |
| (_m4storage[11] == other._m4storage[11]) && |
| (_m4storage[12] == other._m4storage[12]) && |
| (_m4storage[13] == other._m4storage[13]) && |
| (_m4storage[14] == other._m4storage[14]) && |
| (_m4storage[15] == other._m4storage[15]); |
| } |
| |
| int get hashCode => quiver.hashObjects(_m4storage); |
| |
| /// Returns row 0 |
| Vector4 get row0 => getRow(0); |
| |
| /// Returns row 1 |
| Vector4 get row1 => getRow(1); |
| |
| /// Returns row 2 |
| Vector4 get row2 => getRow(2); |
| |
| /// Returns row 3 |
| Vector4 get row3 => getRow(3); |
| |
| /// Sets row 0 to [arg] |
| set row0(Vector4 arg) => setRow(0, arg); |
| |
| /// Sets row 1 to [arg] |
| set row1(Vector4 arg) => setRow(1, arg); |
| |
| /// Sets row 2 to [arg] |
| set row2(Vector4 arg) => setRow(2, arg); |
| |
| /// Sets row 3 to [arg] |
| set row3(Vector4 arg) => setRow(3, arg); |
| |
| /// Assigns the [row] of the matrix [arg] |
| void setRow(int row, Vector4 arg) { |
| final argStorage = arg._v4storage; |
| _m4storage[index(row, 0)] = argStorage[0]; |
| _m4storage[index(row, 1)] = argStorage[1]; |
| _m4storage[index(row, 2)] = argStorage[2]; |
| _m4storage[index(row, 3)] = argStorage[3]; |
| } |
| |
| /// Gets the [row] of the matrix |
| Vector4 getRow(int row) { |
| Vector4 r = new Vector4.zero(); |
| final rStorage = r._v4storage; |
| rStorage[0] = _m4storage[index(row, 0)]; |
| rStorage[1] = _m4storage[index(row, 1)]; |
| rStorage[2] = _m4storage[index(row, 2)]; |
| rStorage[3] = _m4storage[index(row, 3)]; |
| return r; |
| } |
| |
| /// Assigns the [column] of the matrix [arg] |
| void setColumn(int column, Vector4 arg) { |
| int entry = column * 4; |
| final argStorage = arg._v4storage; |
| _m4storage[entry + 3] = argStorage[3]; |
| _m4storage[entry + 2] = argStorage[2]; |
| _m4storage[entry + 1] = argStorage[1]; |
| _m4storage[entry + 0] = argStorage[0]; |
| } |
| |
| /// Gets the [column] of the matrix |
| Vector4 getColumn(int column) { |
| Vector4 r = new Vector4.zero(); |
| final rStorage = r._v4storage; |
| int entry = column * 4; |
| rStorage[3] = _m4storage[entry + 3]; |
| rStorage[2] = _m4storage[entry + 2]; |
| rStorage[1] = _m4storage[entry + 1]; |
| rStorage[0] = _m4storage[entry + 0]; |
| return r; |
| } |
| |
| /// Clone matrix. |
| Matrix4 clone() => new Matrix4.copy(this); |
| |
| /// Copy into [arg]. |
| Matrix4 copyInto(Matrix4 arg) { |
| final argStorage = arg._m4storage; |
| argStorage[0] = _m4storage[0]; |
| argStorage[1] = _m4storage[1]; |
| argStorage[2] = _m4storage[2]; |
| argStorage[3] = _m4storage[3]; |
| argStorage[4] = _m4storage[4]; |
| argStorage[5] = _m4storage[5]; |
| argStorage[6] = _m4storage[6]; |
| argStorage[7] = _m4storage[7]; |
| argStorage[8] = _m4storage[8]; |
| argStorage[9] = _m4storage[9]; |
| argStorage[10] = _m4storage[10]; |
| argStorage[11] = _m4storage[11]; |
| argStorage[12] = _m4storage[12]; |
| argStorage[13] = _m4storage[13]; |
| argStorage[14] = _m4storage[14]; |
| argStorage[15] = _m4storage[15]; |
| return arg; |
| } |
| |
| /// Returns new matrix -this |
| Matrix4 operator -() => clone()..negate(); |
| |
| /// Returns a new vector or matrix by multiplying [this] with [arg]. |
| dynamic operator *(dynamic arg) { |
| if (arg is double) { |
| return scaled(arg); |
| } |
| if (arg is Vector4) { |
| return transformed(arg); |
| } |
| if (arg is Vector3) { |
| return transformed3(arg); |
| } |
| if (arg.dimension == 4) { |
| return multiplied(arg); |
| } |
| throw new ArgumentError(arg); |
| } |
| |
| /// Returns new matrix after component wise [this] + [arg] |
| Matrix4 operator +(Matrix4 arg) => clone()..add(arg); |
| |
| /// Returns new matrix after component wise [this] - [arg] |
| Matrix4 operator -(Matrix4 arg) => clone()..sub(arg); |
| |
| /// Translate this matrix by a [Vector3], [Vector4], or x,y,z |
| void translate(x, [double y = 0.0, double z = 0.0]) { |
| double tx; |
| double ty; |
| double tz; |
| double tw = x is Vector4 ? x.w : 1.0; |
| if (x is Vector3 || x is Vector4) { |
| tx = x.x; |
| ty = x.y; |
| tz = x.z; |
| } else { |
| tx = x; |
| ty = y; |
| tz = z; |
| } |
| var t1 = _m4storage[0] * tx + |
| _m4storage[4] * ty + |
| _m4storage[8] * tz + |
| _m4storage[12] * tw; |
| var t2 = _m4storage[1] * tx + |
| _m4storage[5] * ty + |
| _m4storage[9] * tz + |
| _m4storage[13] * tw; |
| var t3 = _m4storage[2] * tx + |
| _m4storage[6] * ty + |
| _m4storage[10] * tz + |
| _m4storage[14] * tw; |
| var t4 = _m4storage[3] * tx + |
| _m4storage[7] * ty + |
| _m4storage[11] * tz + |
| _m4storage[15] * tw; |
| _m4storage[12] = t1; |
| _m4storage[13] = t2; |
| _m4storage[14] = t3; |
| _m4storage[15] = t4; |
| } |
| |
| /// Multiply [this] by a translation from the left. |
| /// The translation can be specified with a [Vector3], [Vector4], or x, y, z. |
| void leftTranslate(x, [double y = 0.0, double z = 0.0]) { |
| double tx; |
| double ty; |
| double tz; |
| double tw = x is Vector4 ? x.w : 1.0; |
| if (x is Vector3 || x is Vector4) { |
| tx = x.x; |
| ty = x.y; |
| tz = x.z; |
| } else { |
| tx = x; |
| ty = y; |
| tz = z; |
| } |
| |
| // Column 1 |
| _m4storage[0] += tx * _m4storage[3]; |
| _m4storage[1] += ty * _m4storage[3]; |
| _m4storage[2] += tz * _m4storage[3]; |
| _m4storage[3] = tw * _m4storage[3]; |
| |
| // Column 2 |
| _m4storage[4] += tx * _m4storage[7]; |
| _m4storage[5] += ty * _m4storage[7]; |
| _m4storage[6] += tz * _m4storage[7]; |
| _m4storage[7] = tw * _m4storage[7]; |
| |
| // Column 3 |
| _m4storage[8] += tx * _m4storage[11]; |
| _m4storage[9] += ty * _m4storage[11]; |
| _m4storage[10] += tz * _m4storage[11]; |
| _m4storage[11] = tw * _m4storage[11]; |
| |
| // Column 4 |
| _m4storage[12] += tx * _m4storage[15]; |
| _m4storage[13] += ty * _m4storage[15]; |
| _m4storage[14] += tz * _m4storage[15]; |
| _m4storage[15] = tw * _m4storage[15]; |
| } |
| |
| /// Rotate this [angle] radians around [axis] |
| void rotate(Vector3 axis, double angle) { |
| var len = axis.length; |
| final axisStorage = axis._v3storage; |
| var x = axisStorage[0] / len; |
| var y = axisStorage[1] / len; |
| var z = axisStorage[2] / len; |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| var C = 1.0 - c; |
| var m11 = x * x * C + c; |
| var m12 = x * y * C - z * s; |
| var m13 = x * z * C + y * s; |
| var m21 = y * x * C + z * s; |
| var m22 = y * y * C + c; |
| var m23 = y * z * C - x * s; |
| var m31 = z * x * C - y * s; |
| var m32 = z * y * C + x * s; |
| var m33 = z * z * C + c; |
| var t1 = _m4storage[0] * m11 + _m4storage[4] * m21 + _m4storage[8] * m31; |
| var t2 = _m4storage[1] * m11 + _m4storage[5] * m21 + _m4storage[9] * m31; |
| var t3 = _m4storage[2] * m11 + _m4storage[6] * m21 + _m4storage[10] * m31; |
| var t4 = _m4storage[3] * m11 + _m4storage[7] * m21 + _m4storage[11] * m31; |
| var t5 = _m4storage[0] * m12 + _m4storage[4] * m22 + _m4storage[8] * m32; |
| var t6 = _m4storage[1] * m12 + _m4storage[5] * m22 + _m4storage[9] * m32; |
| var t7 = _m4storage[2] * m12 + _m4storage[6] * m22 + _m4storage[10] * m32; |
| var t8 = _m4storage[3] * m12 + _m4storage[7] * m22 + _m4storage[11] * m32; |
| var t9 = _m4storage[0] * m13 + _m4storage[4] * m23 + _m4storage[8] * m33; |
| var t10 = _m4storage[1] * m13 + _m4storage[5] * m23 + _m4storage[9] * m33; |
| var t11 = _m4storage[2] * m13 + _m4storage[6] * m23 + _m4storage[10] * m33; |
| var t12 = _m4storage[3] * m13 + _m4storage[7] * m23 + _m4storage[11] * m33; |
| _m4storage[0] = t1; |
| _m4storage[1] = t2; |
| _m4storage[2] = t3; |
| _m4storage[3] = t4; |
| _m4storage[4] = t5; |
| _m4storage[5] = t6; |
| _m4storage[6] = t7; |
| _m4storage[7] = t8; |
| _m4storage[8] = t9; |
| _m4storage[9] = t10; |
| _m4storage[10] = t11; |
| _m4storage[11] = t12; |
| } |
| |
| /// Rotate this [angle] radians around X |
| void rotateX(double angle) { |
| double cosAngle = Math.cos(angle); |
| double sinAngle = Math.sin(angle); |
| var t1 = _m4storage[4] * cosAngle + _m4storage[8] * sinAngle; |
| var t2 = _m4storage[5] * cosAngle + _m4storage[9] * sinAngle; |
| var t3 = _m4storage[6] * cosAngle + _m4storage[10] * sinAngle; |
| var t4 = _m4storage[7] * cosAngle + _m4storage[11] * sinAngle; |
| var t5 = _m4storage[4] * -sinAngle + _m4storage[8] * cosAngle; |
| var t6 = _m4storage[5] * -sinAngle + _m4storage[9] * cosAngle; |
| var t7 = _m4storage[6] * -sinAngle + _m4storage[10] * cosAngle; |
| var t8 = _m4storage[7] * -sinAngle + _m4storage[11] * cosAngle; |
| _m4storage[4] = t1; |
| _m4storage[5] = t2; |
| _m4storage[6] = t3; |
| _m4storage[7] = t4; |
| _m4storage[8] = t5; |
| _m4storage[9] = t6; |
| _m4storage[10] = t7; |
| _m4storage[11] = t8; |
| } |
| |
| /// Rotate this matrix [angle] radians around Y |
| void rotateY(double angle) { |
| double cosAngle = Math.cos(angle); |
| double sinAngle = Math.sin(angle); |
| var t1 = _m4storage[0] * cosAngle + _m4storage[8] * -sinAngle; |
| var t2 = _m4storage[1] * cosAngle + _m4storage[9] * -sinAngle; |
| var t3 = _m4storage[2] * cosAngle + _m4storage[10] * -sinAngle; |
| var t4 = _m4storage[3] * cosAngle + _m4storage[11] * -sinAngle; |
| var t5 = _m4storage[0] * sinAngle + _m4storage[8] * cosAngle; |
| var t6 = _m4storage[1] * sinAngle + _m4storage[9] * cosAngle; |
| var t7 = _m4storage[2] * sinAngle + _m4storage[10] * cosAngle; |
| var t8 = _m4storage[3] * sinAngle + _m4storage[11] * cosAngle; |
| _m4storage[0] = t1; |
| _m4storage[1] = t2; |
| _m4storage[2] = t3; |
| _m4storage[3] = t4; |
| _m4storage[8] = t5; |
| _m4storage[9] = t6; |
| _m4storage[10] = t7; |
| _m4storage[11] = t8; |
| } |
| |
| /// Rotate this matrix [angle] radians around Z |
| void rotateZ(double angle) { |
| double cosAngle = Math.cos(angle); |
| double sinAngle = Math.sin(angle); |
| var t1 = _m4storage[0] * cosAngle + _m4storage[4] * sinAngle; |
| var t2 = _m4storage[1] * cosAngle + _m4storage[5] * sinAngle; |
| var t3 = _m4storage[2] * cosAngle + _m4storage[6] * sinAngle; |
| var t4 = _m4storage[3] * cosAngle + _m4storage[7] * sinAngle; |
| var t5 = _m4storage[0] * -sinAngle + _m4storage[4] * cosAngle; |
| var t6 = _m4storage[1] * -sinAngle + _m4storage[5] * cosAngle; |
| var t7 = _m4storage[2] * -sinAngle + _m4storage[6] * cosAngle; |
| var t8 = _m4storage[3] * -sinAngle + _m4storage[7] * cosAngle; |
| _m4storage[0] = t1; |
| _m4storage[1] = t2; |
| _m4storage[2] = t3; |
| _m4storage[3] = t4; |
| _m4storage[4] = t5; |
| _m4storage[5] = t6; |
| _m4storage[6] = t7; |
| _m4storage[7] = t8; |
| } |
| |
| /// Scale this matrix by a [Vector3], [Vector4], or x,y,z |
| void scale(x, [double y, double z]) { |
| double sx; |
| double sy; |
| double sz; |
| double sw = x is Vector4 ? x.w : 1.0; |
| if (x is Vector3 || x is Vector4) { |
| sx = x.x; |
| sy = x.y; |
| sz = x.z; |
| } else { |
| sx = x; |
| sy = y == null ? x : y.toDouble(); |
| sz = z == null ? x : z.toDouble(); |
| } |
| _m4storage[0] *= sx; |
| _m4storage[1] *= sx; |
| _m4storage[2] *= sx; |
| _m4storage[3] *= sx; |
| _m4storage[4] *= sy; |
| _m4storage[5] *= sy; |
| _m4storage[6] *= sy; |
| _m4storage[7] *= sy; |
| _m4storage[8] *= sz; |
| _m4storage[9] *= sz; |
| _m4storage[10] *= sz; |
| _m4storage[11] *= sz; |
| _m4storage[12] *= sw; |
| _m4storage[13] *= sw; |
| _m4storage[14] *= sw; |
| _m4storage[15] *= sw; |
| } |
| |
| /// Create a copy of [this] scaled by a [Vector3], [Vector4] or [x],[y], and |
| /// [z]. |
| Matrix4 scaled(x, [double y = null, double z = null]) => |
| clone()..scale(x, y, z); |
| |
| /// Zeros [this]. |
| void setZero() { |
| _m4storage[0] = 0.0; |
| _m4storage[1] = 0.0; |
| _m4storage[2] = 0.0; |
| _m4storage[3] = 0.0; |
| _m4storage[4] = 0.0; |
| _m4storage[5] = 0.0; |
| _m4storage[6] = 0.0; |
| _m4storage[7] = 0.0; |
| _m4storage[8] = 0.0; |
| _m4storage[9] = 0.0; |
| _m4storage[10] = 0.0; |
| _m4storage[11] = 0.0; |
| _m4storage[12] = 0.0; |
| _m4storage[13] = 0.0; |
| _m4storage[14] = 0.0; |
| _m4storage[15] = 0.0; |
| } |
| |
| /// Makes [this] into the identity matrix. |
| void setIdentity() { |
| _m4storage[0] = 1.0; |
| _m4storage[1] = 0.0; |
| _m4storage[2] = 0.0; |
| _m4storage[3] = 0.0; |
| _m4storage[4] = 0.0; |
| _m4storage[5] = 1.0; |
| _m4storage[6] = 0.0; |
| _m4storage[7] = 0.0; |
| _m4storage[8] = 0.0; |
| _m4storage[9] = 0.0; |
| _m4storage[10] = 1.0; |
| _m4storage[11] = 0.0; |
| _m4storage[12] = 0.0; |
| _m4storage[13] = 0.0; |
| _m4storage[14] = 0.0; |
| _m4storage[15] = 1.0; |
| } |
| |
| /// Returns the tranpose of this. |
| Matrix4 transposed() => clone()..transpose(); |
| |
| void transpose() { |
| double temp; |
| temp = _m4storage[4]; |
| _m4storage[4] = _m4storage[1]; |
| _m4storage[1] = temp; |
| temp = _m4storage[8]; |
| _m4storage[8] = _m4storage[2]; |
| _m4storage[2] = temp; |
| temp = _m4storage[12]; |
| _m4storage[12] = _m4storage[3]; |
| _m4storage[3] = temp; |
| temp = _m4storage[9]; |
| _m4storage[9] = _m4storage[6]; |
| _m4storage[6] = temp; |
| temp = _m4storage[13]; |
| _m4storage[13] = _m4storage[7]; |
| _m4storage[7] = temp; |
| temp = _m4storage[14]; |
| _m4storage[14] = _m4storage[11]; |
| _m4storage[11] = temp; |
| } |
| |
| /// Returns the component wise absolute value of this. |
| Matrix4 absolute() { |
| Matrix4 r = new Matrix4.zero(); |
| final rStorage = r._m4storage; |
| rStorage[0] = _m4storage[0].abs(); |
| rStorage[1] = _m4storage[1].abs(); |
| rStorage[2] = _m4storage[2].abs(); |
| rStorage[3] = _m4storage[3].abs(); |
| rStorage[4] = _m4storage[4].abs(); |
| rStorage[5] = _m4storage[5].abs(); |
| rStorage[6] = _m4storage[6].abs(); |
| rStorage[7] = _m4storage[7].abs(); |
| rStorage[8] = _m4storage[8].abs(); |
| rStorage[9] = _m4storage[9].abs(); |
| rStorage[10] = _m4storage[10].abs(); |
| rStorage[11] = _m4storage[11].abs(); |
| rStorage[12] = _m4storage[12].abs(); |
| rStorage[13] = _m4storage[13].abs(); |
| rStorage[14] = _m4storage[14].abs(); |
| rStorage[15] = _m4storage[15].abs(); |
| return r; |
| } |
| |
| /// Returns the determinant of this matrix. |
| double determinant() { |
| double det2_01_01 = |
| _m4storage[0] * _m4storage[5] - _m4storage[1] * _m4storage[4]; |
| double det2_01_02 = |
| _m4storage[0] * _m4storage[6] - _m4storage[2] * _m4storage[4]; |
| double det2_01_03 = |
| _m4storage[0] * _m4storage[7] - _m4storage[3] * _m4storage[4]; |
| double det2_01_12 = |
| _m4storage[1] * _m4storage[6] - _m4storage[2] * _m4storage[5]; |
| double det2_01_13 = |
| _m4storage[1] * _m4storage[7] - _m4storage[3] * _m4storage[5]; |
| double det2_01_23 = |
| _m4storage[2] * _m4storage[7] - _m4storage[3] * _m4storage[6]; |
| double det3_201_012 = _m4storage[8] * det2_01_12 - |
| _m4storage[9] * det2_01_02 + |
| _m4storage[10] * det2_01_01; |
| double det3_201_013 = _m4storage[8] * det2_01_13 - |
| _m4storage[9] * det2_01_03 + |
| _m4storage[11] * det2_01_01; |
| double det3_201_023 = _m4storage[8] * det2_01_23 - |
| _m4storage[10] * det2_01_03 + |
| _m4storage[11] * det2_01_02; |
| double det3_201_123 = _m4storage[9] * det2_01_23 - |
| _m4storage[10] * det2_01_13 + |
| _m4storage[11] * det2_01_12; |
| return -det3_201_123 * _m4storage[12] + |
| det3_201_023 * _m4storage[13] - |
| det3_201_013 * _m4storage[14] + |
| det3_201_012 * _m4storage[15]; |
| } |
| |
| /// Returns the dot product of row [i] and [v]. |
| double dotRow(int i, Vector4 v) { |
| final vStorage = v._v4storage; |
| return _m4storage[i] * vStorage[0] + |
| _m4storage[4 + i] * vStorage[1] + |
| _m4storage[8 + i] * vStorage[2] + |
| _m4storage[12 + i] * vStorage[3]; |
| } |
| |
| /// Returns the dot product of column [j] and [v]. |
| double dotColumn(int j, Vector4 v) { |
| final vStorage = v._v4storage; |
| return _m4storage[j * 4] * vStorage[0] + |
| _m4storage[j * 4 + 1] * vStorage[1] + |
| _m4storage[j * 4 + 2] * vStorage[2] + |
| _m4storage[j * 4 + 3] * vStorage[3]; |
| } |
| |
| /// Returns the trace of the matrix. The trace of a matrix is the sum of the |
| /// diagonal entries. |
| double trace() { |
| double t = 0.0; |
| t += _m4storage[0]; |
| t += _m4storage[5]; |
| t += _m4storage[10]; |
| t += _m4storage[15]; |
| return t; |
| } |
| |
| /// Returns infinity norm of the matrix. Used for numerical analysis. |
| double infinityNorm() { |
| double norm = 0.0; |
| { |
| double row_norm = 0.0; |
| row_norm += _m4storage[0].abs(); |
| row_norm += _m4storage[1].abs(); |
| row_norm += _m4storage[2].abs(); |
| row_norm += _m4storage[3].abs(); |
| norm = row_norm > norm ? row_norm : norm; |
| } |
| { |
| double row_norm = 0.0; |
| row_norm += _m4storage[4].abs(); |
| row_norm += _m4storage[5].abs(); |
| row_norm += _m4storage[6].abs(); |
| row_norm += _m4storage[7].abs(); |
| norm = row_norm > norm ? row_norm : norm; |
| } |
| { |
| double row_norm = 0.0; |
| row_norm += _m4storage[8].abs(); |
| row_norm += _m4storage[9].abs(); |
| row_norm += _m4storage[10].abs(); |
| row_norm += _m4storage[11].abs(); |
| norm = row_norm > norm ? row_norm : norm; |
| } |
| { |
| double row_norm = 0.0; |
| row_norm += _m4storage[12].abs(); |
| row_norm += _m4storage[13].abs(); |
| row_norm += _m4storage[14].abs(); |
| row_norm += _m4storage[15].abs(); |
| norm = row_norm > norm ? row_norm : norm; |
| } |
| return norm; |
| } |
| |
| /// Returns relative error between [this] and [correct] |
| double relativeError(Matrix4 correct) { |
| Matrix4 diff = correct - this; |
| double correct_norm = correct.infinityNorm(); |
| double diff_norm = diff.infinityNorm(); |
| return diff_norm / correct_norm; |
| } |
| |
| /// Returns absolute error between [this] and [correct] |
| double absoluteError(Matrix4 correct) { |
| double this_norm = infinityNorm(); |
| double correct_norm = correct.infinityNorm(); |
| double diff_norm = (this_norm - correct_norm).abs(); |
| return diff_norm; |
| } |
| |
| /// Returns the translation vector from this homogeneous transformation matrix. |
| Vector3 getTranslation() { |
| double z = _m4storage[14]; |
| double y = _m4storage[13]; |
| double x = _m4storage[12]; |
| return new Vector3(x, y, z); |
| } |
| |
| /// Sets the translation vector in this homogeneous transformation matrix. |
| void setTranslation(Vector3 t) { |
| final tStorage = t._v3storage; |
| double z = tStorage[2]; |
| double y = tStorage[1]; |
| double x = tStorage[0]; |
| _m4storage[14] = z; |
| _m4storage[13] = y; |
| _m4storage[12] = x; |
| } |
| |
| /// Sets the translation vector in this homogeneous transformation matrix. |
| void setTranslationRaw(double x, double y, double z) { |
| _m4storage[14] = z; |
| _m4storage[13] = y; |
| _m4storage[12] = x; |
| } |
| |
| /// Returns the rotation matrix from this homogeneous transformation matrix. |
| Matrix3 getRotation() { |
| Matrix3 r = new Matrix3.zero(); |
| copyRotation(r); |
| return r; |
| } |
| |
| /// Copies the rotation matrix from this homogeneous transformation matrix |
| /// into [rotation]. |
| void copyRotation(Matrix3 rotation) { |
| final rStorage = rotation._m3storage; |
| rStorage[0] = _m4storage[0]; |
| rStorage[1] = _m4storage[1]; |
| rStorage[2] = _m4storage[2]; |
| rStorage[3] = _m4storage[4]; |
| rStorage[4] = _m4storage[5]; |
| rStorage[5] = _m4storage[6]; |
| rStorage[6] = _m4storage[8]; |
| rStorage[7] = _m4storage[9]; |
| rStorage[8] = _m4storage[10]; |
| } |
| |
| /// Sets the rotation matrix in this homogeneous transformation matrix. |
| void setRotation(Matrix3 r) { |
| final rStorage = r._m3storage; |
| _m4storage[0] = rStorage[0]; |
| _m4storage[1] = rStorage[1]; |
| _m4storage[2] = rStorage[2]; |
| _m4storage[4] = rStorage[3]; |
| _m4storage[5] = rStorage[4]; |
| _m4storage[6] = rStorage[5]; |
| _m4storage[8] = rStorage[6]; |
| _m4storage[9] = rStorage[7]; |
| _m4storage[10] = rStorage[8]; |
| } |
| |
| /// Returns the normal matrix from this homogeneous transformation matrix. The normal |
| /// matrix is the transpose of the inverse of the top-left 3x3 part of this 4x4 matrix. |
| Matrix3 getNormalMatrix() => new Matrix3.identity()..copyNormalMatrix(this); |
| |
| /// Returns the max scale value of the 3 axes. |
| double getMaxScaleOnAxis() { |
| final scaleXSq = _m4storage[0] * _m4storage[0] + |
| _m4storage[1] * _m4storage[1] + |
| _m4storage[2] * _m4storage[2]; |
| final scaleYSq = _m4storage[4] * _m4storage[4] + |
| _m4storage[5] * _m4storage[5] + |
| _m4storage[6] * _m4storage[6]; |
| final scaleZSq = _m4storage[8] * _m4storage[8] + |
| _m4storage[9] * _m4storage[9] + |
| _m4storage[10] * _m4storage[10]; |
| return Math.sqrt(Math.max(scaleXSq, Math.max(scaleYSq, scaleZSq))); |
| } |
| |
| /// Transposes just the upper 3x3 rotation matrix. |
| void transposeRotation() { |
| double temp; |
| temp = _m4storage[1]; |
| _m4storage[1] = _m4storage[4]; |
| _m4storage[4] = temp; |
| temp = _m4storage[2]; |
| _m4storage[2] = _m4storage[8]; |
| _m4storage[8] = temp; |
| temp = _m4storage[4]; |
| _m4storage[4] = _m4storage[1]; |
| _m4storage[1] = temp; |
| temp = _m4storage[6]; |
| _m4storage[6] = _m4storage[9]; |
| _m4storage[9] = temp; |
| temp = _m4storage[8]; |
| _m4storage[8] = _m4storage[2]; |
| _m4storage[2] = temp; |
| temp = _m4storage[9]; |
| _m4storage[9] = _m4storage[6]; |
| _m4storage[6] = temp; |
| } |
| |
| /// Invert [this]. |
| double invert() => copyInverse(this); |
| |
| /// Set this matrix to be the inverse of [arg] |
| double copyInverse(Matrix4 arg) { |
| final argStorage = arg._m4storage; |
| double a00 = argStorage[0]; |
| double a01 = argStorage[1]; |
| double a02 = argStorage[2]; |
| double a03 = argStorage[3]; |
| double a10 = argStorage[4]; |
| double a11 = argStorage[5]; |
| double a12 = argStorage[6]; |
| double a13 = argStorage[7]; |
| double a20 = argStorage[8]; |
| double a21 = argStorage[9]; |
| double a22 = argStorage[10]; |
| double a23 = argStorage[11]; |
| double a30 = argStorage[12]; |
| double a31 = argStorage[13]; |
| double a32 = argStorage[14]; |
| double a33 = argStorage[15]; |
| var b00 = a00 * a11 - a01 * a10; |
| var b01 = a00 * a12 - a02 * a10; |
| var b02 = a00 * a13 - a03 * a10; |
| var b03 = a01 * a12 - a02 * a11; |
| var b04 = a01 * a13 - a03 * a11; |
| var b05 = a02 * a13 - a03 * a12; |
| var b06 = a20 * a31 - a21 * a30; |
| var b07 = a20 * a32 - a22 * a30; |
| var b08 = a20 * a33 - a23 * a30; |
| var b09 = a21 * a32 - a22 * a31; |
| var b10 = a21 * a33 - a23 * a31; |
| var b11 = a22 * a33 - a23 * a32; |
| var det = |
| (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06); |
| if (det == 0.0) { |
| setFrom(arg); |
| return 0.0; |
| } |
| var invDet = 1.0 / det; |
| _m4storage[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet; |
| _m4storage[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet; |
| _m4storage[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet; |
| _m4storage[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet; |
| _m4storage[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet; |
| _m4storage[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet; |
| _m4storage[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet; |
| _m4storage[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet; |
| _m4storage[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet; |
| _m4storage[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet; |
| _m4storage[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet; |
| _m4storage[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet; |
| _m4storage[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet; |
| _m4storage[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet; |
| _m4storage[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet; |
| _m4storage[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet; |
| return det; |
| } |
| |
| double invertRotation() { |
| double det = determinant(); |
| if (det == 0.0) { |
| return 0.0; |
| } |
| double invDet = 1.0 / det; |
| double ix; |
| double iy; |
| double iz; |
| double jx; |
| double jy; |
| double jz; |
| double kx; |
| double ky; |
| double kz; |
| ix = invDet * |
| (_m4storage[5] * _m4storage[10] - _m4storage[6] * _m4storage[9]); |
| iy = invDet * |
| (_m4storage[2] * _m4storage[9] - _m4storage[1] * _m4storage[10]); |
| iz = invDet * |
| (_m4storage[1] * _m4storage[6] - _m4storage[2] * _m4storage[5]); |
| jx = invDet * |
| (_m4storage[6] * _m4storage[8] - _m4storage[4] * _m4storage[10]); |
| jy = invDet * |
| (_m4storage[0] * _m4storage[10] - _m4storage[2] * _m4storage[8]); |
| jz = invDet * |
| (_m4storage[2] * _m4storage[4] - _m4storage[0] * _m4storage[6]); |
| kx = invDet * |
| (_m4storage[4] * _m4storage[9] - _m4storage[5] * _m4storage[8]); |
| ky = invDet * |
| (_m4storage[1] * _m4storage[8] - _m4storage[0] * _m4storage[9]); |
| kz = invDet * |
| (_m4storage[0] * _m4storage[5] - _m4storage[1] * _m4storage[4]); |
| _m4storage[0] = ix; |
| _m4storage[1] = iy; |
| _m4storage[2] = iz; |
| _m4storage[4] = jx; |
| _m4storage[5] = jy; |
| _m4storage[6] = jz; |
| _m4storage[8] = kx; |
| _m4storage[9] = ky; |
| _m4storage[10] = kz; |
| return det; |
| } |
| |
| /// Sets the upper 3x3 to a rotation of [radians] around X |
| void setRotationX(double radians) { |
| double c = Math.cos(radians); |
| double s = Math.sin(radians); |
| _m4storage[0] = 1.0; |
| _m4storage[1] = 0.0; |
| _m4storage[2] = 0.0; |
| _m4storage[4] = 0.0; |
| _m4storage[5] = c; |
| _m4storage[6] = s; |
| _m4storage[8] = 0.0; |
| _m4storage[9] = -s; |
| _m4storage[10] = c; |
| _m4storage[3] = 0.0; |
| _m4storage[7] = 0.0; |
| _m4storage[11] = 0.0; |
| } |
| |
| /// Sets the upper 3x3 to a rotation of [radians] around Y |
| void setRotationY(double radians) { |
| double c = Math.cos(radians); |
| double s = Math.sin(radians); |
| _m4storage[0] = c; |
| _m4storage[1] = 0.0; |
| _m4storage[2] = -s; |
| _m4storage[4] = 0.0; |
| _m4storage[5] = 1.0; |
| _m4storage[6] = 0.0; |
| _m4storage[8] = s; |
| _m4storage[9] = 0.0; |
| _m4storage[10] = c; |
| _m4storage[3] = 0.0; |
| _m4storage[7] = 0.0; |
| _m4storage[11] = 0.0; |
| } |
| |
| /// Sets the upper 3x3 to a rotation of [radians] around Z |
| void setRotationZ(double radians) { |
| double c = Math.cos(radians); |
| double s = Math.sin(radians); |
| _m4storage[0] = c; |
| _m4storage[1] = s; |
| _m4storage[2] = 0.0; |
| _m4storage[4] = -s; |
| _m4storage[5] = c; |
| _m4storage[6] = 0.0; |
| _m4storage[8] = 0.0; |
| _m4storage[9] = 0.0; |
| _m4storage[10] = 1.0; |
| _m4storage[3] = 0.0; |
| _m4storage[7] = 0.0; |
| _m4storage[11] = 0.0; |
| } |
| |
| /// Converts into Adjugate matrix and scales by [scale] |
| void scaleAdjoint(double scale) { |
| // Adapted from code by Richard Carling. |
| double a1 = _m4storage[0]; |
| double b1 = _m4storage[4]; |
| double c1 = _m4storage[8]; |
| double d1 = _m4storage[12]; |
| double a2 = _m4storage[1]; |
| double b2 = _m4storage[5]; |
| double c2 = _m4storage[9]; |
| double d2 = _m4storage[13]; |
| double a3 = _m4storage[2]; |
| double b3 = _m4storage[6]; |
| double c3 = _m4storage[10]; |
| double d3 = _m4storage[14]; |
| double a4 = _m4storage[3]; |
| double b4 = _m4storage[7]; |
| double c4 = _m4storage[11]; |
| double d4 = _m4storage[15]; |
| _m4storage[0] = (b2 * (c3 * d4 - c4 * d3) - |
| c2 * (b3 * d4 - b4 * d3) + |
| d2 * (b3 * c4 - b4 * c3)) * |
| scale; |
| _m4storage[1] = -(a2 * (c3 * d4 - c4 * d3) - |
| c2 * (a3 * d4 - a4 * d3) + |
| d2 * (a3 * c4 - a4 * c3)) * |
| scale; |
| _m4storage[2] = (a2 * (b3 * d4 - b4 * d3) - |
| b2 * (a3 * d4 - a4 * d3) + |
| d2 * (a3 * b4 - a4 * b3)) * |
| scale; |
| _m4storage[3] = -(a2 * (b3 * c4 - b4 * c3) - |
| b2 * (a3 * c4 - a4 * c3) + |
| c2 * (a3 * b4 - a4 * b3)) * |
| scale; |
| _m4storage[4] = -(b1 * (c3 * d4 - c4 * d3) - |
| c1 * (b3 * d4 - b4 * d3) + |
| d1 * (b3 * c4 - b4 * c3)) * |
| scale; |
| _m4storage[5] = (a1 * (c3 * d4 - c4 * d3) - |
| c1 * (a3 * d4 - a4 * d3) + |
| d1 * (a3 * c4 - a4 * c3)) * |
| scale; |
| _m4storage[6] = -(a1 * (b3 * d4 - b4 * d3) - |
| b1 * (a3 * d4 - a4 * d3) + |
| d1 * (a3 * b4 - a4 * b3)) * |
| scale; |
| _m4storage[7] = (a1 * (b3 * c4 - b4 * c3) - |
| b1 * (a3 * c4 - a4 * c3) + |
| c1 * (a3 * b4 - a4 * b3)) * |
| scale; |
| _m4storage[8] = (b1 * (c2 * d4 - c4 * d2) - |
| c1 * (b2 * d4 - b4 * d2) + |
| d1 * (b2 * c4 - b4 * c2)) * |
| scale; |
| _m4storage[9] = -(a1 * (c2 * d4 - c4 * d2) - |
| c1 * (a2 * d4 - a4 * d2) + |
| d1 * (a2 * c4 - a4 * c2)) * |
| scale; |
| _m4storage[10] = (a1 * (b2 * d4 - b4 * d2) - |
| b1 * (a2 * d4 - a4 * d2) + |
| d1 * (a2 * b4 - a4 * b2)) * |
| scale; |
| _m4storage[11] = -(a1 * (b2 * c4 - b4 * c2) - |
| b1 * (a2 * c4 - a4 * c2) + |
| c1 * (a2 * b4 - a4 * b2)) * |
| scale; |
| _m4storage[12] = -(b1 * (c2 * d3 - c3 * d2) - |
| c1 * (b2 * d3 - b3 * d2) + |
| d1 * (b2 * c3 - b3 * c2)) * |
| scale; |
| _m4storage[13] = (a1 * (c2 * d3 - c3 * d2) - |
| c1 * (a2 * d3 - a3 * d2) + |
| d1 * (a2 * c3 - a3 * c2)) * |
| scale; |
| _m4storage[14] = -(a1 * (b2 * d3 - b3 * d2) - |
| b1 * (a2 * d3 - a3 * d2) + |
| d1 * (a2 * b3 - a3 * b2)) * |
| scale; |
| _m4storage[15] = (a1 * (b2 * c3 - b3 * c2) - |
| b1 * (a2 * c3 - a3 * c2) + |
| c1 * (a2 * b3 - a3 * b2)) * |
| scale; |
| } |
| |
| /// Rotates [arg] by the absolute rotation of [this] |
| /// Returns [arg]. |
| /// Primarily used by AABB transformation code. |
| Vector3 absoluteRotate(Vector3 arg) { |
| double m00 = _m4storage[0].abs(); |
| double m01 = _m4storage[4].abs(); |
| double m02 = _m4storage[8].abs(); |
| double m10 = _m4storage[1].abs(); |
| double m11 = _m4storage[5].abs(); |
| double m12 = _m4storage[9].abs(); |
| double m20 = _m4storage[2].abs(); |
| double m21 = _m4storage[6].abs(); |
| double m22 = _m4storage[10].abs(); |
| final argStorage = arg._v3storage; |
| double x = argStorage[0]; |
| double y = argStorage[1]; |
| double z = argStorage[2]; |
| argStorage[0] = x * m00 + y * m01 + z * m02 + 0.0 * 0.0; |
| argStorage[1] = x * m10 + y * m11 + z * m12 + 0.0 * 0.0; |
| argStorage[2] = x * m20 + y * m21 + z * m22 + 0.0 * 0.0; |
| return arg; |
| } |
| |
| /// Adds [o] to [this]. |
| void add(Matrix4 o) { |
| final oStorage = o._m4storage; |
| _m4storage[0] = _m4storage[0] + oStorage[0]; |
| _m4storage[1] = _m4storage[1] + oStorage[1]; |
| _m4storage[2] = _m4storage[2] + oStorage[2]; |
| _m4storage[3] = _m4storage[3] + oStorage[3]; |
| _m4storage[4] = _m4storage[4] + oStorage[4]; |
| _m4storage[5] = _m4storage[5] + oStorage[5]; |
| _m4storage[6] = _m4storage[6] + oStorage[6]; |
| _m4storage[7] = _m4storage[7] + oStorage[7]; |
| _m4storage[8] = _m4storage[8] + oStorage[8]; |
| _m4storage[9] = _m4storage[9] + oStorage[9]; |
| _m4storage[10] = _m4storage[10] + oStorage[10]; |
| _m4storage[11] = _m4storage[11] + oStorage[11]; |
| _m4storage[12] = _m4storage[12] + oStorage[12]; |
| _m4storage[13] = _m4storage[13] + oStorage[13]; |
| _m4storage[14] = _m4storage[14] + oStorage[14]; |
| _m4storage[15] = _m4storage[15] + oStorage[15]; |
| } |
| |
| /// Subtracts [o] from [this]. |
| void sub(Matrix4 o) { |
| final oStorage = o._m4storage; |
| _m4storage[0] = _m4storage[0] - oStorage[0]; |
| _m4storage[1] = _m4storage[1] - oStorage[1]; |
| _m4storage[2] = _m4storage[2] - oStorage[2]; |
| _m4storage[3] = _m4storage[3] - oStorage[3]; |
| _m4storage[4] = _m4storage[4] - oStorage[4]; |
| _m4storage[5] = _m4storage[5] - oStorage[5]; |
| _m4storage[6] = _m4storage[6] - oStorage[6]; |
| _m4storage[7] = _m4storage[7] - oStorage[7]; |
| _m4storage[8] = _m4storage[8] - oStorage[8]; |
| _m4storage[9] = _m4storage[9] - oStorage[9]; |
| _m4storage[10] = _m4storage[10] - oStorage[10]; |
| _m4storage[11] = _m4storage[11] - oStorage[11]; |
| _m4storage[12] = _m4storage[12] - oStorage[12]; |
| _m4storage[13] = _m4storage[13] - oStorage[13]; |
| _m4storage[14] = _m4storage[14] - oStorage[14]; |
| _m4storage[15] = _m4storage[15] - oStorage[15]; |
| } |
| |
| /// Negate [this]. |
| void negate() { |
| _m4storage[0] = -_m4storage[0]; |
| _m4storage[1] = -_m4storage[1]; |
| _m4storage[2] = -_m4storage[2]; |
| _m4storage[3] = -_m4storage[3]; |
| _m4storage[4] = -_m4storage[4]; |
| _m4storage[5] = -_m4storage[5]; |
| _m4storage[6] = -_m4storage[6]; |
| _m4storage[7] = -_m4storage[7]; |
| _m4storage[8] = -_m4storage[8]; |
| _m4storage[9] = -_m4storage[9]; |
| _m4storage[10] = -_m4storage[10]; |
| _m4storage[11] = -_m4storage[11]; |
| _m4storage[12] = -_m4storage[12]; |
| _m4storage[13] = -_m4storage[13]; |
| _m4storage[14] = -_m4storage[14]; |
| _m4storage[15] = -_m4storage[15]; |
| } |
| |
| /// Multiply [this] by [arg]. |
| void multiply(Matrix4 arg) { |
| final m00 = _m4storage[0]; |
| final m01 = _m4storage[4]; |
| final m02 = _m4storage[8]; |
| final m03 = _m4storage[12]; |
| final m10 = _m4storage[1]; |
| final m11 = _m4storage[5]; |
| final m12 = _m4storage[9]; |
| final m13 = _m4storage[13]; |
| final m20 = _m4storage[2]; |
| final m21 = _m4storage[6]; |
| final m22 = _m4storage[10]; |
| final m23 = _m4storage[14]; |
| final m30 = _m4storage[3]; |
| final m31 = _m4storage[7]; |
| final m32 = _m4storage[11]; |
| final m33 = _m4storage[15]; |
| final argStorage = arg._m4storage; |
| final n00 = argStorage[0]; |
| final n01 = argStorage[4]; |
| final n02 = argStorage[8]; |
| final n03 = argStorage[12]; |
| final n10 = argStorage[1]; |
| final n11 = argStorage[5]; |
| final n12 = argStorage[9]; |
| final n13 = argStorage[13]; |
| final n20 = argStorage[2]; |
| final n21 = argStorage[6]; |
| final n22 = argStorage[10]; |
| final n23 = argStorage[14]; |
| final n30 = argStorage[3]; |
| final n31 = argStorage[7]; |
| final n32 = argStorage[11]; |
| final n33 = argStorage[15]; |
| _m4storage[0] = (m00 * n00) + (m01 * n10) + (m02 * n20) + (m03 * n30); |
| _m4storage[4] = (m00 * n01) + (m01 * n11) + (m02 * n21) + (m03 * n31); |
| _m4storage[8] = (m00 * n02) + (m01 * n12) + (m02 * n22) + (m03 * n32); |
| _m4storage[12] = (m00 * n03) + (m01 * n13) + (m02 * n23) + (m03 * n33); |
| _m4storage[1] = (m10 * n00) + (m11 * n10) + (m12 * n20) + (m13 * n30); |
| _m4storage[5] = (m10 * n01) + (m11 * n11) + (m12 * n21) + (m13 * n31); |
| _m4storage[9] = (m10 * n02) + (m11 * n12) + (m12 * n22) + (m13 * n32); |
| _m4storage[13] = (m10 * n03) + (m11 * n13) + (m12 * n23) + (m13 * n33); |
| _m4storage[2] = (m20 * n00) + (m21 * n10) + (m22 * n20) + (m23 * n30); |
| _m4storage[6] = (m20 * n01) + (m21 * n11) + (m22 * n21) + (m23 * n31); |
| _m4storage[10] = (m20 * n02) + (m21 * n12) + (m22 * n22) + (m23 * n32); |
| _m4storage[14] = (m20 * n03) + (m21 * n13) + (m22 * n23) + (m23 * n33); |
| _m4storage[3] = (m30 * n00) + (m31 * n10) + (m32 * n20) + (m33 * n30); |
| _m4storage[7] = (m30 * n01) + (m31 * n11) + (m32 * n21) + (m33 * n31); |
| _m4storage[11] = (m30 * n02) + (m31 * n12) + (m32 * n22) + (m33 * n32); |
| _m4storage[15] = (m30 * n03) + (m31 * n13) + (m32 * n23) + (m33 * n33); |
| } |
| |
| /// Multiply a copy of [this] with [arg]. |
| Matrix4 multiplied(Matrix4 arg) => clone()..multiply(arg); |
| |
| /// Multiply a transposed [this] with [arg]. |
| void transposeMultiply(Matrix4 arg) { |
| double m00 = _m4storage[0]; |
| double m01 = _m4storage[1]; |
| double m02 = _m4storage[2]; |
| double m03 = _m4storage[3]; |
| double m10 = _m4storage[4]; |
| double m11 = _m4storage[5]; |
| double m12 = _m4storage[6]; |
| double m13 = _m4storage[7]; |
| double m20 = _m4storage[8]; |
| double m21 = _m4storage[9]; |
| double m22 = _m4storage[10]; |
| double m23 = _m4storage[11]; |
| double m30 = _m4storage[12]; |
| double m31 = _m4storage[13]; |
| double m32 = _m4storage[14]; |
| double m33 = _m4storage[15]; |
| final argStorage = arg._m4storage; |
| _m4storage[0] = (m00 * argStorage[0]) + |
| (m01 * argStorage[1]) + |
| (m02 * argStorage[2]) + |
| (m03 * argStorage[3]); |
| _m4storage[4] = (m00 * argStorage[4]) + |
| (m01 * argStorage[5]) + |
| (m02 * argStorage[6]) + |
| (m03 * argStorage[7]); |
| _m4storage[8] = (m00 * argStorage[8]) + |
| (m01 * argStorage[9]) + |
| (m02 * argStorage[10]) + |
| (m03 * argStorage[11]); |
| _m4storage[12] = (m00 * argStorage[12]) + |
| (m01 * argStorage[13]) + |
| (m02 * argStorage[14]) + |
| (m03 * argStorage[15]); |
| _m4storage[1] = (m10 * argStorage[0]) + |
| (m11 * argStorage[1]) + |
| (m12 * argStorage[2]) + |
| (m13 * argStorage[3]); |
| _m4storage[5] = (m10 * argStorage[4]) + |
| (m11 * argStorage[5]) + |
| (m12 * argStorage[6]) + |
| (m13 * argStorage[7]); |
| _m4storage[9] = (m10 * argStorage[8]) + |
| (m11 * argStorage[9]) + |
| (m12 * argStorage[10]) + |
| (m13 * argStorage[11]); |
| _m4storage[13] = (m10 * argStorage[12]) + |
| (m11 * argStorage[13]) + |
| (m12 * argStorage[14]) + |
| (m13 * argStorage[15]); |
| _m4storage[2] = (m20 * argStorage[0]) + |
| (m21 * argStorage[1]) + |
| (m22 * argStorage[2]) + |
| (m23 * argStorage[3]); |
| _m4storage[6] = (m20 * argStorage[4]) + |
| (m21 * argStorage[5]) + |
| (m22 * argStorage[6]) + |
| (m23 * argStorage[7]); |
| _m4storage[10] = (m20 * argStorage[8]) + |
| (m21 * argStorage[9]) + |
| (m22 * argStorage[10]) + |
| (m23 * argStorage[11]); |
| _m4storage[14] = (m20 * argStorage[12]) + |
| (m21 * argStorage[13]) + |
| (m22 * argStorage[14]) + |
| (m23 * argStorage[15]); |
| _m4storage[3] = (m30 * argStorage[0]) + |
| (m31 * argStorage[1]) + |
| (m32 * argStorage[2]) + |
| (m33 * argStorage[3]); |
| _m4storage[7] = (m30 * argStorage[4]) + |
| (m31 * argStorage[5]) + |
| (m32 * argStorage[6]) + |
| (m33 * argStorage[7]); |
| _m4storage[11] = (m30 * argStorage[8]) + |
| (m31 * argStorage[9]) + |
| (m32 * argStorage[10]) + |
| (m33 * argStorage[11]); |
| _m4storage[15] = (m30 * argStorage[12]) + |
| (m31 * argStorage[13]) + |
| (m32 * argStorage[14]) + |
| (m33 * argStorage[15]); |
| } |
| |
| /// Multiply [this] with a transposed [arg]. |
| void multiplyTranspose(Matrix4 arg) { |
| double m00 = _m4storage[0]; |
| double m01 = _m4storage[4]; |
| double m02 = _m4storage[8]; |
| double m03 = _m4storage[12]; |
| double m10 = _m4storage[1]; |
| double m11 = _m4storage[5]; |
| double m12 = _m4storage[9]; |
| double m13 = _m4storage[13]; |
| double m20 = _m4storage[2]; |
| double m21 = _m4storage[6]; |
| double m22 = _m4storage[10]; |
| double m23 = _m4storage[14]; |
| double m30 = _m4storage[3]; |
| double m31 = _m4storage[7]; |
| double m32 = _m4storage[11]; |
| double m33 = _m4storage[15]; |
| final argStorage = arg._m4storage; |
| _m4storage[0] = (m00 * argStorage[0]) + |
| (m01 * argStorage[4]) + |
| (m02 * argStorage[8]) + |
| (m03 * argStorage[12]); |
| _m4storage[4] = (m00 * argStorage[1]) + |
| (m01 * argStorage[5]) + |
| (m02 * argStorage[9]) + |
| (m03 * argStorage[13]); |
| _m4storage[8] = (m00 * argStorage[2]) + |
| (m01 * argStorage[6]) + |
| (m02 * argStorage[10]) + |
| (m03 * argStorage[14]); |
| _m4storage[12] = (m00 * argStorage[3]) + |
| (m01 * argStorage[7]) + |
| (m02 * argStorage[11]) + |
| (m03 * argStorage[15]); |
| _m4storage[1] = (m10 * argStorage[0]) + |
| (m11 * argStorage[4]) + |
| (m12 * argStorage[8]) + |
| (m13 * argStorage[12]); |
| _m4storage[5] = (m10 * argStorage[1]) + |
| (m11 * argStorage[5]) + |
| (m12 * argStorage[9]) + |
| (m13 * argStorage[13]); |
| _m4storage[9] = (m10 * argStorage[2]) + |
| (m11 * argStorage[6]) + |
| (m12 * argStorage[10]) + |
| (m13 * argStorage[14]); |
| _m4storage[13] = (m10 * argStorage[3]) + |
| (m11 * argStorage[7]) + |
| (m12 * argStorage[11]) + |
| (m13 * argStorage[15]); |
| _m4storage[2] = (m20 * argStorage[0]) + |
| (m21 * argStorage[4]) + |
| (m22 * argStorage[8]) + |
| (m23 * argStorage[12]); |
| _m4storage[6] = (m20 * argStorage[1]) + |
| (m21 * argStorage[5]) + |
| (m22 * argStorage[9]) + |
| (m23 * argStorage[13]); |
| _m4storage[10] = (m20 * argStorage[2]) + |
| (m21 * argStorage[6]) + |
| (m22 * argStorage[10]) + |
| (m23 * argStorage[14]); |
| _m4storage[14] = (m20 * argStorage[3]) + |
| (m21 * argStorage[7]) + |
| (m22 * argStorage[11]) + |
| (m23 * argStorage[15]); |
| _m4storage[3] = (m30 * argStorage[0]) + |
| (m31 * argStorage[4]) + |
| (m32 * argStorage[8]) + |
| (m33 * argStorage[12]); |
| _m4storage[7] = (m30 * argStorage[1]) + |
| (m31 * argStorage[5]) + |
| (m32 * argStorage[9]) + |
| (m33 * argStorage[13]); |
| _m4storage[11] = (m30 * argStorage[2]) + |
| (m31 * argStorage[6]) + |
| (m32 * argStorage[10]) + |
| (m33 * argStorage[14]); |
| _m4storage[15] = (m30 * argStorage[3]) + |
| (m31 * argStorage[7]) + |
| (m32 * argStorage[11]) + |
| (m33 * argStorage[15]); |
| } |
| |
| /// Decomposes [this] into [translation], [rotation] and [scale] components. |
| void decompose(Vector3 translation, Quaternion rotation, Vector3 scale) { |
| final v = new Vector3.zero(); |
| var sx = (v..setValues(_m4storage[0], _m4storage[1], _m4storage[2])).length; |
| var sy = (v..setValues(_m4storage[4], _m4storage[5], _m4storage[6])).length; |
| var sz = |
| (v..setValues(_m4storage[8], _m4storage[9], _m4storage[10])).length; |
| |
| if (determinant() < 0) sx = -sx; |
| |
| translation._v3storage[0] = _m4storage[12]; |
| translation._v3storage[1] = _m4storage[13]; |
| translation._v3storage[2] = _m4storage[14]; |
| |
| final invSX = 1.0 / sx; |
| final invSY = 1.0 / sy; |
| final invSZ = 1.0 / sz; |
| |
| final m = new Matrix4.copy(this); |
| m._m4storage[0] *= invSX; |
| m._m4storage[1] *= invSX; |
| m._m4storage[2] *= invSX; |
| m._m4storage[4] *= invSY; |
| m._m4storage[5] *= invSY; |
| m._m4storage[6] *= invSY; |
| m._m4storage[8] *= invSZ; |
| m._m4storage[9] *= invSZ; |
| m._m4storage[10] *= invSZ; |
| |
| rotation.setFromRotation(m.getRotation()); |
| |
| scale._v3storage[0] = sx; |
| scale._v3storage[1] = sy; |
| scale._v3storage[2] = sz; |
| } |
| |
| /// Rotate [arg] of type [Vector3] using the rotation defined by [this]. |
| Vector3 rotate3(Vector3 arg) { |
| final argStorage = arg._v3storage; |
| final x_ = (_m4storage[0] * argStorage[0]) + |
| (_m4storage[4] * argStorage[1]) + |
| (_m4storage[8] * argStorage[2]); |
| final y_ = (_m4storage[1] * argStorage[0]) + |
| (_m4storage[5] * argStorage[1]) + |
| (_m4storage[9] * argStorage[2]); |
| final z_ = (_m4storage[2] * argStorage[0]) + |
| (_m4storage[6] * argStorage[1]) + |
| (_m4storage[10] * argStorage[2]); |
| argStorage[0] = x_; |
| argStorage[1] = y_; |
| argStorage[2] = z_; |
| return arg; |
| } |
| |
| /// Rotate a copy of [arg] of type [Vector3] using the rotation defined by |
| /// [this]. If a [out] parameter is supplied, the copy is stored in [out]. |
| Vector3 rotated3(Vector3 arg, [Vector3 out]) { |
| if (out == null) { |
| out = new Vector3.copy(arg); |
| } else { |
| out.setFrom(arg); |
| } |
| return rotate3(out); |
| } |
| |
| /// Transform [arg] of type [Vector3] using the transformation defined by |
| /// [this]. |
| Vector3 transform3(Vector3 arg) { |
| final argStorage = arg._v3storage; |
| final x_ = (_m4storage[0] * argStorage[0]) + |
| (_m4storage[4] * argStorage[1]) + |
| (_m4storage[8] * argStorage[2]) + |
| _m4storage[12]; |
| final y_ = (_m4storage[1] * argStorage[0]) + |
| (_m4storage[5] * argStorage[1]) + |
| (_m4storage[9] * argStorage[2]) + |
| _m4storage[13]; |
| final z_ = (_m4storage[2] * argStorage[0]) + |
| (_m4storage[6] * argStorage[1]) + |
| (_m4storage[10] * argStorage[2]) + |
| _m4storage[14]; |
| argStorage[0] = x_; |
| argStorage[1] = y_; |
| argStorage[2] = z_; |
| return arg; |
| } |
| |
| /// Transform a copy of [arg] of type [Vector3] using the transformation |
| /// defined by [this]. If a [out] parameter is supplied, the copy is stored in |
| /// [out]. |
| Vector3 transformed3(Vector3 arg, [Vector3 out]) { |
| if (out == null) { |
| out = new Vector3.copy(arg); |
| } else { |
| out.setFrom(arg); |
| } |
| return transform3(out); |
| } |
| |
| /// Transform [arg] of type [Vector4] using the transformation defined by |
| /// [this]. |
| Vector4 transform(Vector4 arg) { |
| final argStorage = arg._v4storage; |
| final x_ = (_m4storage[0] * argStorage[0]) + |
| (_m4storage[4] * argStorage[1]) + |
| (_m4storage[8] * argStorage[2]) + |
| (_m4storage[12] * argStorage[3]); |
| final y_ = (_m4storage[1] * argStorage[0]) + |
| (_m4storage[5] * argStorage[1]) + |
| (_m4storage[9] * argStorage[2]) + |
| (_m4storage[13] * argStorage[3]); |
| final z_ = (_m4storage[2] * argStorage[0]) + |
| (_m4storage[6] * argStorage[1]) + |
| (_m4storage[10] * argStorage[2]) + |
| (_m4storage[14] * argStorage[3]); |
| final w_ = (_m4storage[3] * argStorage[0]) + |
| (_m4storage[7] * argStorage[1]) + |
| (_m4storage[11] * argStorage[2]) + |
| (_m4storage[15] * argStorage[3]); |
| argStorage[0] = x_; |
| argStorage[1] = y_; |
| argStorage[2] = z_; |
| argStorage[3] = w_; |
| return arg; |
| } |
| |
| /// Transform [arg] of type [Vector3] using the perspective transformation |
| /// defined by [this]. |
| Vector3 perspectiveTransform(Vector3 arg) { |
| final argStorage = arg._v3storage; |
| final x_ = (_m4storage[0] * argStorage[0]) + |
| (_m4storage[4] * argStorage[1]) + |
| (_m4storage[8] * argStorage[2]) + |
| _m4storage[12]; |
| final y_ = (_m4storage[1] * argStorage[0]) + |
| (_m4storage[5] * argStorage[1]) + |
| (_m4storage[9] * argStorage[2]) + |
| _m4storage[13]; |
| final z_ = (_m4storage[2] * argStorage[0]) + |
| (_m4storage[6] * argStorage[1]) + |
| (_m4storage[10] * argStorage[2]) + |
| _m4storage[14]; |
| final w_ = 1.0 / |
| ((_m4storage[3] * argStorage[0]) + |
| (_m4storage[7] * argStorage[1]) + |
| (_m4storage[11] * argStorage[2]) + |
| _m4storage[15]); |
| argStorage[0] = x_ * w_; |
| argStorage[1] = y_ * w_; |
| argStorage[2] = z_ * w_; |
| return arg; |
| } |
| |
| /// Transform a copy of [arg] of type [Vector4] using the transformation |
| /// defined by [this]. If a [out] parameter is supplied, the copy is stored in |
| /// [out]. |
| Vector4 transformed(Vector4 arg, [Vector4 out]) { |
| if (out == null) { |
| out = new Vector4.copy(arg); |
| } else { |
| out.setFrom(arg); |
| } |
| return transform(out); |
| } |
| |
| /// Copies [this] into [array] starting at [offset]. |
| void copyIntoArray(List<num> array, [int offset = 0]) { |
| int i = offset; |
| array[i + 15] = _m4storage[15]; |
| array[i + 14] = _m4storage[14]; |
| array[i + 13] = _m4storage[13]; |
| array[i + 12] = _m4storage[12]; |
| array[i + 11] = _m4storage[11]; |
| array[i + 10] = _m4storage[10]; |
| array[i + 9] = _m4storage[9]; |
| array[i + 8] = _m4storage[8]; |
| array[i + 7] = _m4storage[7]; |
| array[i + 6] = _m4storage[6]; |
| array[i + 5] = _m4storage[5]; |
| array[i + 4] = _m4storage[4]; |
| array[i + 3] = _m4storage[3]; |
| array[i + 2] = _m4storage[2]; |
| array[i + 1] = _m4storage[1]; |
| array[i + 0] = _m4storage[0]; |
| } |
| |
| /// Copies elements from [array] into [this] starting at [offset]. |
| void copyFromArray(List<double> array, [int offset = 0]) { |
| int i = offset; |
| _m4storage[15] = array[i + 15]; |
| _m4storage[14] = array[i + 14]; |
| _m4storage[13] = array[i + 13]; |
| _m4storage[12] = array[i + 12]; |
| _m4storage[11] = array[i + 11]; |
| _m4storage[10] = array[i + 10]; |
| _m4storage[9] = array[i + 9]; |
| _m4storage[8] = array[i + 8]; |
| _m4storage[7] = array[i + 7]; |
| _m4storage[6] = array[i + 6]; |
| _m4storage[5] = array[i + 5]; |
| _m4storage[4] = array[i + 4]; |
| _m4storage[3] = array[i + 3]; |
| _m4storage[2] = array[i + 2]; |
| _m4storage[1] = array[i + 1]; |
| _m4storage[0] = array[i + 0]; |
| } |
| |
| /// Multiply [this] to each set of xyz values in [array] starting at [offset]. |
| List<double> applyToVector3Array(List<double> array, [int offset = 0]) { |
| for (var i = 0, j = offset; i < array.length; i += 3, j += 3) { |
| final v = new Vector3.array(array, j)..applyMatrix4(this); |
| array[j] = v.storage[0]; |
| array[j + 1] = v.storage[1]; |
| array[j + 2] = v.storage[2]; |
| } |
| |
| return array; |
| } |
| |
| Vector3 get right { |
| double x = _m4storage[0]; |
| double y = _m4storage[1]; |
| double z = _m4storage[2]; |
| return new Vector3(x, y, z); |
| } |
| |
| Vector3 get up { |
| double x = _m4storage[4]; |
| double y = _m4storage[5]; |
| double z = _m4storage[6]; |
| return new Vector3(x, y, z); |
| } |
| |
| Vector3 get forward { |
| double x = _m4storage[8]; |
| double y = _m4storage[9]; |
| double z = _m4storage[10]; |
| return new Vector3(x, y, z); |
| } |
| |
| /// Is [this] the identity matrix? |
| bool isIdentity() { |
| return _m4storage[0] == 1.0 // col 1 |
| && _m4storage[1] == 0.0 |
| && _m4storage[2] == 0.0 |
| && _m4storage[3] == 0.0 |
| && _m4storage[4] == 0.0 // col 2 |
| && _m4storage[5] == 1.0 |
| && _m4storage[6] == 0.0 |
| && _m4storage[7] == 0.0 |
| && _m4storage[8] == 0.0 // col 3 |
| && _m4storage[9] == 0.0 |
| && _m4storage[10] == 1.0 |
| && _m4storage[11] == 0.0 |
| && _m4storage[12] == 0.0 // col 4 |
| && _m4storage[13] == 0.0 |
| && _m4storage[14] == 0.0 |
| && _m4storage[15] == 1.0; |
| } |
| |
| /// Is [this] the zero matrix? |
| bool isZero() { |
| return _m4storage[0] == 0.0 // col 1 |
| && _m4storage[1] == 0.0 |
| && _m4storage[2] == 0.0 |
| && _m4storage[3] == 0.0 |
| && _m4storage[4] == 0.0 // col 2 |
| && _m4storage[5] == 0.0 |
| && _m4storage[6] == 0.0 |
| && _m4storage[7] == 0.0 |
| && _m4storage[8] == 0.0 // col 3 |
| && _m4storage[9] == 0.0 |
| && _m4storage[10] == 0.0 |
| && _m4storage[11] == 0.0 |
| && _m4storage[12] == 0.0 // col 4 |
| && _m4storage[13] == 0.0 |
| && _m4storage[14] == 0.0 |
| && _m4storage[15] == 0.0; |
| } |
| } |
