Flutter Impeller
Public Member Functions | Static Public Member Functions | Public Attributes | List of all members
impeller::Matrix Struct Reference

A 4x4 matrix using column-major storage. More...

#include <matrix.h>

Public Member Functions

constexpr Matrix ()
 
constexpr Matrix (Scalar m0, Scalar m1, Scalar m2, Scalar m3, Scalar m4, Scalar m5, Scalar m6, Scalar m7, Scalar m8, Scalar m9, Scalar m10, Scalar m11, Scalar m12, Scalar m13, Scalar m14, Scalar m15)
 
 Matrix (const MatrixDecomposition &decomposition)
 
constexpr Matrix Basis () const
 The Matrix without its w components (without translation). More...
 
constexpr Matrix Translate (const Vector3 &t) const
 
constexpr Matrix Scale (const Vector3 &s) const
 
constexpr Matrix Multiply (const Matrix &o) const
 
constexpr Matrix Transpose () const
 
Matrix Invert () const
 
Scalar GetDeterminant () const
 
Scalar GetMaxBasisLength () const
 
constexpr Scalar GetMaxBasisLengthXY () const
 
constexpr Vector3 GetBasisX () const
 
constexpr Vector3 GetBasisY () const
 
constexpr Vector3 GetBasisZ () const
 
constexpr Vector3 GetScale () const
 
constexpr Scalar GetDirectionScale (Vector3 direction) const
 
constexpr bool IsAffine () const
 
constexpr bool HasPerspective2D () const
 
constexpr bool HasPerspective () const
 
constexpr bool HasTranslation () const
 
constexpr bool IsAligned2D (Scalar tolerance=0) const
 
constexpr bool IsAligned (Scalar tolerance=0) const
 
constexpr bool IsIdentity () const
 
constexpr bool IsTranslationScaleOnly () const
 Returns true if the matrix has a scale-only basis and is non-projective. Note that an identity matrix meets this criteria. More...
 
std::optional< MatrixDecomposition > Decompose () const
 
constexpr bool operator== (const Matrix &m) const
 
constexpr bool operator!= (const Matrix &m) const
 
Matrix operator+ (const Vector3 &t) const
 
Matrix operator- (const Vector3 &t) const
 
Matrix operator* (const Matrix &m) const
 
Matrix operator+ (const Matrix &m) const
 
constexpr Vector4 operator* (const Vector4 &v) const
 
constexpr Vector3 operator* (const Vector3 &v) const
 
constexpr Point operator* (const Point &v) const
 
constexpr Vector3 TransformHomogenous (const Point &v) const
 
constexpr Vector4 TransformDirection (const Vector4 &v) const
 
constexpr Vector3 TransformDirection (const Vector3 &v) const
 
constexpr Vector2 TransformDirection (const Vector2 &v) const
 
constexpr Quad Transform (const Quad &quad) const
 

Static Public Member Functions

static constexpr Matrix MakeColumn (Scalar m0, Scalar m1, Scalar m2, Scalar m3, Scalar m4, Scalar m5, Scalar m6, Scalar m7, Scalar m8, Scalar m9, Scalar m10, Scalar m11, Scalar m12, Scalar m13, Scalar m14, Scalar m15)
 
static constexpr Matrix MakeRow (Scalar m0, Scalar m1, Scalar m2, Scalar m3, Scalar m4, Scalar m5, Scalar m6, Scalar m7, Scalar m8, Scalar m9, Scalar m10, Scalar m11, Scalar m12, Scalar m13, Scalar m14, Scalar m15)
 
static constexpr Matrix MakeTranslation (const Vector3 &t)
 
static constexpr Matrix MakeScale (const Vector3 &s)
 
static constexpr Matrix MakeScale (const Vector2 &s)
 
static constexpr Matrix MakeSkew (Scalar sx, Scalar sy)
 
static Matrix MakeRotation (Quaternion q)
 
static Matrix MakeRotation (Radians radians, const Vector4 &r)
 
static Matrix MakeRotationX (Radians r)
 
static Matrix MakeRotationY (Radians r)
 
static Matrix MakeRotationZ (Radians r)
 
template<class T >
static constexpr Matrix MakeOrthographic (TSize< T > size)
 
static constexpr Matrix MakePerspective (Radians fov_y, Scalar aspect_ratio, Scalar z_near, Scalar z_far)
 
template<class T >
static constexpr Matrix MakePerspective (Radians fov_y, TSize< T > size, Scalar z_near, Scalar z_far)
 
static constexpr Matrix MakeLookAt (Vector3 position, Vector3 target, Vector3 up)
 

Public Attributes

union {
   Scalar   m [16]
 
   Scalar   e [4][4]
 
   Vector4   vec [4]
 
}; 
 

Detailed Description

A 4x4 matrix using column-major storage. 

        Utility methods that need to make assumptions about normalized
        device coordinates must use the following convention:
          * Left-handed coordinate system. Positive rotation is
            clockwise about axis of rotation.
          * Lower left corner is -1.0f, -1.0.
          * Upper right corner is  1.0f,  1.0.
          * Visible z-space is from 0.0 to 1.0.
            * This is NOT the same as OpenGL! Be careful.
          * NDC origin is at (0.0f, 0.0f, 0.5f).

Definition at line 37 of file matrix.h.

Constructor & Destructor Documentation

◆ Matrix() [1/3]

constexpr impeller::Matrix::Matrix ( )
inlineconstexpr

Constructs a default identity matrix.

Definition at line 47 of file matrix.h.

49  : vec{ Vector4(1.0f, 0.0f, 0.0f, 0.0f),
50  Vector4(0.0f, 1.0f, 0.0f, 0.0f),
51  Vector4(0.0f, 0.0f, 1.0f, 0.0f),
52  Vector4(0.0f, 0.0f, 0.0f, 1.0f)} {}

Referenced by Basis(), MakeColumn(), MakeRotation(), MakeRotationX(), MakeRotationY(), MakeRotationZ(), MakeRow(), MakeScale(), MakeSkew(), MakeTranslation(), Multiply(), operator+(), Scale(), and Translate().

◆ Matrix() [2/3]

constexpr impeller::Matrix::Matrix ( Scalar  m0,
Scalar  m1,
Scalar  m2,
Scalar  m3,
Scalar  m4,
Scalar  m5,
Scalar  m6,
Scalar  m7,
Scalar  m8,
Scalar  m9,
Scalar  m10,
Scalar  m11,
Scalar  m12,
Scalar  m13,
Scalar  m14,
Scalar  m15 
)
inlineconstexpr

Definition at line 56 of file matrix.h.

60  : vec{Vector4(m0, m1, m2, m3),
61  Vector4(m4, m5, m6, m7),
62  Vector4(m8, m9, m10, m11),
63  Vector4(m12, m13, m14, m15)} {}

◆ Matrix() [3/3]

impeller::Matrix::Matrix ( const MatrixDecomposition &  decomposition)
explicit

Definition at line 12 of file matrix.cc.

12  : Matrix() {
13  /*
14  * Apply perspective.
15  */
16  for (int i = 0; i < 4; i++) {
17  e[i][3] = d.perspective.e[i];
18  }
19 
20  /*
21  * Apply translation.
22  */
23  for (int i = 0; i < 3; i++) {
24  for (int j = 0; j < 3; j++) {
25  e[3][i] += d.translation.e[j] * e[j][i];
26  }
27  }
28 
29  /*
30  * Apply rotation.
31  */
32 
33  Matrix rotation;
34 
35  const auto x = -d.rotation.x;
36  const auto y = -d.rotation.y;
37  const auto z = -d.rotation.z;
38  const auto w = d.rotation.w;
39 
40  /*
41  * Construct a composite rotation matrix from the quaternion values.
42  */
43 
44  rotation.e[0][0] = 1.0 - 2.0 * (y * y + z * z);
45  rotation.e[0][1] = 2.0 * (x * y - z * w);
46  rotation.e[0][2] = 2.0 * (x * z + y * w);
47  rotation.e[1][0] = 2.0 * (x * y + z * w);
48  rotation.e[1][1] = 1.0 - 2.0 * (x * x + z * z);
49  rotation.e[1][2] = 2.0 * (y * z - x * w);
50  rotation.e[2][0] = 2.0 * (x * z - y * w);
51  rotation.e[2][1] = 2.0 * (y * z + x * w);
52  rotation.e[2][2] = 1.0 - 2.0 * (x * x + y * y);
53 
54  *this = *this * rotation;
55 
56  /*
57  * Apply shear.
58  */
59  Matrix shear;
60 
61  if (d.shear.e[2] != 0) {
62  shear.e[2][1] = d.shear.e[2];
63  *this = *this * shear;
64  }
65 
66  if (d.shear.e[1] != 0) {
67  shear.e[2][1] = 0.0;
68  shear.e[2][0] = d.shear.e[1];
69  *this = *this * shear;
70  }
71 
72  if (d.shear.e[0] != 0) {
73  shear.e[2][0] = 0.0;
74  shear.e[1][0] = d.shear.e[0];
75  *this = *this * shear;
76  }
77 
78  /*
79  * Apply scale.
80  */
81  for (int i = 0; i < 3; i++) {
82  for (int j = 0; j < 3; j++) {
83  e[i][j] *= d.scale.e[i];
84  }
85  }
86 }

References impeller::Shear::e, impeller::Vector3::e, e, impeller::Vector4::e, impeller::MatrixDecomposition::perspective, impeller::MatrixDecomposition::rotation, impeller::MatrixDecomposition::scale, impeller::MatrixDecomposition::shear, impeller::MatrixDecomposition::translation, impeller::Quaternion::w, impeller::Quaternion::x, impeller::Quaternion::y, and impeller::Quaternion::z.

Member Function Documentation

◆ Basis()

constexpr Matrix impeller::Matrix::Basis ( ) const
inlineconstexpr

The Matrix without its w components (without translation).

Definition at line 229 of file matrix.h.

229  {
230  // clang-format off
231  return Matrix(
232  m[0], m[1], m[2], 0.0f,
233  m[4], m[5], m[6], 0.0f,
234  m[8], m[9], m[10], 0.0f,
235  0.0f, 0.0f, 0.0f, 1.0
236  );
237  // clang-format on
238  }

References m, and Matrix().

Referenced by GetDirectionScale(), impeller::DirectionalMorphologyFilterContents::GetFilterCoverage(), impeller::LocalMatrixFilterContents::GetFilterSourceCoverage(), impeller::GaussianBlurFilterContents::GetFilterSourceCoverage(), impeller::MatrixFilterContents::IsTranslationOnly(), impeller::TextContents::Render(), and impeller::testing::TEST().

◆ Decompose()

std::optional< MatrixDecomposition > impeller::Matrix::Decompose ( ) const

Definition at line 209 of file matrix.cc.

209  {
210  /*
211  * Normalize the matrix.
212  */
213  Matrix self = *this;
214 
215  if (self.e[3][3] == 0) {
216  return std::nullopt;
217  }
218 
219  for (int i = 0; i < 4; i++) {
220  for (int j = 0; j < 4; j++) {
221  self.e[i][j] /= self.e[3][3];
222  }
223  }
224 
225  /*
226  * `perspectiveMatrix` is used to solve for perspective, but it also provides
227  * an easy way to test for singularity of the upper 3x3 component.
228  */
229  Matrix perpectiveMatrix = self;
230  for (int i = 0; i < 3; i++) {
231  perpectiveMatrix.e[i][3] = 0;
232  }
233 
234  perpectiveMatrix.e[3][3] = 1;
235 
236  if (perpectiveMatrix.GetDeterminant() == 0.0) {
237  return std::nullopt;
238  }
239 
240  MatrixDecomposition result;
241 
242  /*
243  * ==========================================================================
244  * First, isolate perspective.
245  * ==========================================================================
246  */
247  if (self.e[0][3] != 0.0 || self.e[1][3] != 0.0 || self.e[2][3] != 0.0) {
248  /*
249  * prhs is the right hand side of the equation.
250  */
251  const Vector4 rightHandSide(self.e[0][3], //
252  self.e[1][3], //
253  self.e[2][3], //
254  self.e[3][3]);
255 
256  /*
257  * Solve the equation by inverting `perspectiveMatrix` and multiplying
258  * prhs by the inverse.
259  */
260 
261  result.perspective = perpectiveMatrix.Invert().Transpose() * rightHandSide;
262 
263  /*
264  * Clear the perspective partition.
265  */
266  self.e[0][3] = self.e[1][3] = self.e[2][3] = 0;
267  self.e[3][3] = 1;
268  }
269 
270  /*
271  * ==========================================================================
272  * Next, the translation.
273  * ==========================================================================
274  */
275  result.translation = {self.e[3][0], self.e[3][1], self.e[3][2]};
276  self.e[3][0] = self.e[3][1] = self.e[3][2] = 0.0;
277 
278  /*
279  * ==========================================================================
280  * Next, the scale and shear.
281  * ==========================================================================
282  */
283  Vector3 row[3];
284  for (int i = 0; i < 3; i++) {
285  row[i].x = self.e[i][0];
286  row[i].y = self.e[i][1];
287  row[i].z = self.e[i][2];
288  }
289 
290  /*
291  * Compute X scale factor and normalize first row.
292  */
293  result.scale.x = row[0].Length();
294  row[0] = row[0].Normalize();
295 
296  /*
297  * Compute XY shear factor and make 2nd row orthogonal to 1st.
298  */
299  result.shear.xy = row[0].Dot(row[1]);
300  row[1] = Vector3::Combine(row[1], 1.0, row[0], -result.shear.xy);
301 
302  /*
303  * Compute Y scale and normalize 2nd row.
304  */
305  result.scale.y = row[1].Length();
306  row[1] = row[1].Normalize();
307  result.shear.xy /= result.scale.y;
308 
309  /*
310  * Compute XZ and YZ shears, orthogonalize 3rd row.
311  */
312  result.shear.xz = row[0].Dot(row[2]);
313  row[2] = Vector3::Combine(row[2], 1.0, row[0], -result.shear.xz);
314  result.shear.yz = row[1].Dot(row[2]);
315  row[2] = Vector3::Combine(row[2], 1.0, row[1], -result.shear.yz);
316 
317  /*
318  * Next, get Z scale and normalize 3rd row.
319  */
320  result.scale.z = row[2].Length();
321  row[2] = row[2].Normalize();
322 
323  result.shear.xz /= result.scale.z;
324  result.shear.yz /= result.scale.z;
325 
326  /*
327  * At this point, the matrix (in rows[]) is orthonormal.
328  * Check for a coordinate system flip. If the determinant
329  * is -1, then negate the matrix and the scaling factors.
330  */
331  if (row[0].Dot(row[1].Cross(row[2])) < 0) {
332  result.scale.x *= -1;
333  result.scale.y *= -1;
334  result.scale.z *= -1;
335 
336  for (int i = 0; i < 3; i++) {
337  row[i].x *= -1;
338  row[i].y *= -1;
339  row[i].z *= -1;
340  }
341  }
342 
343  /*
344  * ==========================================================================
345  * Finally, get the rotations out.
346  * ==========================================================================
347  */
348  result.rotation.x =
349  0.5 * sqrt(fmax(1.0 + row[0].x - row[1].y - row[2].z, 0.0));
350  result.rotation.y =
351  0.5 * sqrt(fmax(1.0 - row[0].x + row[1].y - row[2].z, 0.0));
352  result.rotation.z =
353  0.5 * sqrt(fmax(1.0 - row[0].x - row[1].y + row[2].z, 0.0));
354  result.rotation.w =
355  0.5 * sqrt(fmax(1.0 + row[0].x + row[1].y + row[2].z, 0.0));
356 
357  if (row[2].y > row[1].z) {
358  result.rotation.x = -result.rotation.x;
359  }
360  if (row[0].z > row[2].x) {
361  result.rotation.y = -result.rotation.y;
362  }
363  if (row[1].x > row[0].y) {
364  result.rotation.z = -result.rotation.z;
365  }
366 
367  return result;
368 }

References impeller::Vector3::Combine(), impeller::Vector3::Dot(), impeller::Vector3::e, e, impeller::Vector4::e, GetDeterminant(), Invert(), impeller::Vector3::Length(), impeller::Vector3::Normalize(), impeller::MatrixDecomposition::perspective, impeller::MatrixDecomposition::rotation, impeller::MatrixDecomposition::scale, impeller::MatrixDecomposition::shear, impeller::MatrixDecomposition::translation, Transpose(), impeller::Quaternion::w, impeller::Quaternion::x, impeller::Vector3::x, impeller::Shear::xy, impeller::Shear::xz, impeller::Quaternion::y, impeller::Vector3::y, impeller::Shear::yz, impeller::Quaternion::z, and impeller::Vector3::z.

Referenced by impeller::testing::TEST().

◆ GetBasisX()

constexpr Vector3 impeller::Matrix::GetBasisX ( ) const
inlineconstexpr

Definition at line 305 of file matrix.h.

305 { return Vector3(m[0], m[1], m[2]); }

References m.

Referenced by impeller::Paint::MaskBlurDescriptor::CreateMaskBlur(), and GetScale().

◆ GetBasisY()

constexpr Vector3 impeller::Matrix::GetBasisY ( ) const
inlineconstexpr

Definition at line 307 of file matrix.h.

307 { return Vector3(m[4], m[5], m[6]); }

References m.

Referenced by impeller::Paint::MaskBlurDescriptor::CreateMaskBlur(), and GetScale().

◆ GetBasisZ()

constexpr Vector3 impeller::Matrix::GetBasisZ ( ) const
inlineconstexpr

Definition at line 309 of file matrix.h.

309 { return Vector3(m[8], m[9], m[10]); }

References m.

Referenced by GetScale().

◆ GetDeterminant()

Scalar impeller::Matrix::GetDeterminant ( ) const

Definition at line 162 of file matrix.cc.

162  {
163  auto a00 = e[0][0];
164  auto a01 = e[0][1];
165  auto a02 = e[0][2];
166  auto a03 = e[0][3];
167  auto a10 = e[1][0];
168  auto a11 = e[1][1];
169  auto a12 = e[1][2];
170  auto a13 = e[1][3];
171  auto a20 = e[2][0];
172  auto a21 = e[2][1];
173  auto a22 = e[2][2];
174  auto a23 = e[2][3];
175  auto a30 = e[3][0];
176  auto a31 = e[3][1];
177  auto a32 = e[3][2];
178  auto a33 = e[3][3];
179 
180  auto b00 = a00 * a11 - a01 * a10;
181  auto b01 = a00 * a12 - a02 * a10;
182  auto b02 = a00 * a13 - a03 * a10;
183  auto b03 = a01 * a12 - a02 * a11;
184  auto b04 = a01 * a13 - a03 * a11;
185  auto b05 = a02 * a13 - a03 * a12;
186  auto b06 = a20 * a31 - a21 * a30;
187  auto b07 = a20 * a32 - a22 * a30;
188  auto b08 = a20 * a33 - a23 * a30;
189  auto b09 = a21 * a32 - a22 * a31;
190  auto b10 = a21 * a33 - a23 * a31;
191  auto b11 = a22 * a33 - a23 * a32;
192 
193  return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
194 }

References e.

Referenced by Decompose().

◆ GetDirectionScale()

constexpr Scalar impeller::Matrix::GetDirectionScale ( Vector3  direction) const
inlineconstexpr

Definition at line 316 of file matrix.h.

316  {
317  return 1.0f / (this->Basis().Invert() * direction.Normalize()).Length() *
318  direction.Length();
319  }

References Basis(), Invert(), impeller::Vector3::Length(), and impeller::Vector3::Normalize().

Referenced by impeller::testing::TEST().

◆ GetMaxBasisLength()

Scalar impeller::Matrix::GetMaxBasisLength ( ) const

Definition at line 196 of file matrix.cc.

196  {
197  Scalar max = 0;
198  for (int i = 0; i < 3; i++) {
199  max = std::max(max,
200  e[i][0] * e[i][0] + e[i][1] * e[i][1] + e[i][2] * e[i][2]);
201  }
202  return std::sqrt(max);
203 }

References e.

Referenced by impeller::Tessellator::FilledCircle(), impeller::Tessellator::FilledEllipse(), impeller::Tessellator::FilledRoundRect(), impeller::Tessellator::RoundCapLine(), and impeller::Tessellator::StrokedCircle().

◆ GetMaxBasisLengthXY()

constexpr Scalar impeller::Matrix::GetMaxBasisLengthXY ( ) const
inlineconstexpr

Definition at line 300 of file matrix.h.

300  {
301  return std::sqrt(std::max(e[0][0] * e[0][0] + e[0][1] * e[0][1],
302  e[1][0] * e[1][0] + e[1][1] * e[1][1]));
303  }

References e.

Referenced by impeller::StrokePathGeometry::ComputeAlphaCoverage(), and impeller::Entity::DeriveTextScale().

◆ GetScale()

constexpr Vector3 impeller::Matrix::GetScale ( ) const
inlineconstexpr

Definition at line 311 of file matrix.h.

311  {
312  return Vector3(GetBasisX().Length(), GetBasisY().Length(),
313  GetBasisZ().Length());
314  }

References GetBasisX(), GetBasisY(), and GetBasisZ().

Referenced by impeller::DlDispatcherBase::drawShadow(), impeller::SceneContents::Render(), and impeller::testing::TEST_P().

◆ HasPerspective()

constexpr bool impeller::Matrix::HasPerspective ( ) const
inlineconstexpr

Definition at line 330 of file matrix.h.

330  {
331  return m[3] != 0 || m[7] != 0 || m[11] != 0 || m[15] != 1;
332  }

References m.

Referenced by impeller::DlDispatcherBase::drawDisplayList(), IsAligned(), and impeller::testing::TEST().

◆ HasPerspective2D()

constexpr bool impeller::Matrix::HasPerspective2D ( ) const
inlineconstexpr

Definition at line 326 of file matrix.h.

326  {
327  return m[3] != 0 || m[7] != 0 || m[15] != 1;
328  }

References m.

Referenced by IsAligned2D(), and impeller::testing::TEST().

◆ HasTranslation()

constexpr bool impeller::Matrix::HasTranslation ( ) const
inlineconstexpr

Definition at line 334 of file matrix.h.

334 { return m[12] != 0 || m[13] != 0; }

References m.

◆ Invert()

Matrix impeller::Matrix::Invert ( ) const

Definition at line 97 of file matrix.cc.

97  {
98  Matrix tmp{
99  m[5] * m[10] * m[15] - m[5] * m[11] * m[14] - m[9] * m[6] * m[15] +
100  m[9] * m[7] * m[14] + m[13] * m[6] * m[11] - m[13] * m[7] * m[10],
101 
102  -m[1] * m[10] * m[15] + m[1] * m[11] * m[14] + m[9] * m[2] * m[15] -
103  m[9] * m[3] * m[14] - m[13] * m[2] * m[11] + m[13] * m[3] * m[10],
104 
105  m[1] * m[6] * m[15] - m[1] * m[7] * m[14] - m[5] * m[2] * m[15] +
106  m[5] * m[3] * m[14] + m[13] * m[2] * m[7] - m[13] * m[3] * m[6],
107 
108  -m[1] * m[6] * m[11] + m[1] * m[7] * m[10] + m[5] * m[2] * m[11] -
109  m[5] * m[3] * m[10] - m[9] * m[2] * m[7] + m[9] * m[3] * m[6],
110 
111  -m[4] * m[10] * m[15] + m[4] * m[11] * m[14] + m[8] * m[6] * m[15] -
112  m[8] * m[7] * m[14] - m[12] * m[6] * m[11] + m[12] * m[7] * m[10],
113 
114  m[0] * m[10] * m[15] - m[0] * m[11] * m[14] - m[8] * m[2] * m[15] +
115  m[8] * m[3] * m[14] + m[12] * m[2] * m[11] - m[12] * m[3] * m[10],
116 
117  -m[0] * m[6] * m[15] + m[0] * m[7] * m[14] + m[4] * m[2] * m[15] -
118  m[4] * m[3] * m[14] - m[12] * m[2] * m[7] + m[12] * m[3] * m[6],
119 
120  m[0] * m[6] * m[11] - m[0] * m[7] * m[10] - m[4] * m[2] * m[11] +
121  m[4] * m[3] * m[10] + m[8] * m[2] * m[7] - m[8] * m[3] * m[6],
122 
123  m[4] * m[9] * m[15] - m[4] * m[11] * m[13] - m[8] * m[5] * m[15] +
124  m[8] * m[7] * m[13] + m[12] * m[5] * m[11] - m[12] * m[7] * m[9],
125 
126  -m[0] * m[9] * m[15] + m[0] * m[11] * m[13] + m[8] * m[1] * m[15] -
127  m[8] * m[3] * m[13] - m[12] * m[1] * m[11] + m[12] * m[3] * m[9],
128 
129  m[0] * m[5] * m[15] - m[0] * m[7] * m[13] - m[4] * m[1] * m[15] +
130  m[4] * m[3] * m[13] + m[12] * m[1] * m[7] - m[12] * m[3] * m[5],
131 
132  -m[0] * m[5] * m[11] + m[0] * m[7] * m[9] + m[4] * m[1] * m[11] -
133  m[4] * m[3] * m[9] - m[8] * m[1] * m[7] + m[8] * m[3] * m[5],
134 
135  -m[4] * m[9] * m[14] + m[4] * m[10] * m[13] + m[8] * m[5] * m[14] -
136  m[8] * m[6] * m[13] - m[12] * m[5] * m[10] + m[12] * m[6] * m[9],
137 
138  m[0] * m[9] * m[14] - m[0] * m[10] * m[13] - m[8] * m[1] * m[14] +
139  m[8] * m[2] * m[13] + m[12] * m[1] * m[10] - m[12] * m[2] * m[9],
140 
141  -m[0] * m[5] * m[14] + m[0] * m[6] * m[13] + m[4] * m[1] * m[14] -
142  m[4] * m[2] * m[13] - m[12] * m[1] * m[6] + m[12] * m[2] * m[5],
143 
144  m[0] * m[5] * m[10] - m[0] * m[6] * m[9] - m[4] * m[1] * m[10] +
145  m[4] * m[2] * m[9] + m[8] * m[1] * m[6] - m[8] * m[2] * m[5]};
146 
147  Scalar det =
148  m[0] * tmp.m[0] + m[1] * tmp.m[4] + m[2] * tmp.m[8] + m[3] * tmp.m[12];
149 
150  if (det == 0) {
151  return {};
152  }
153 
154  det = 1.0 / det;
155 
156  return {tmp.m[0] * det, tmp.m[1] * det, tmp.m[2] * det, tmp.m[3] * det,
157  tmp.m[4] * det, tmp.m[5] * det, tmp.m[6] * det, tmp.m[7] * det,
158  tmp.m[8] * det, tmp.m[9] * det, tmp.m[10] * det, tmp.m[11] * det,
159  tmp.m[12] * det, tmp.m[13] * det, tmp.m[14] * det, tmp.m[15] * det};
160 }

References m.

Referenced by Decompose(), GetDirectionScale(), impeller::MatrixFilterContents::GetFilterCoverage(), impeller::LocalMatrixFilterContents::GetFilterSourceCoverage(), impeller::Snapshot::GetUVTransform(), impeller::scene::Skin::MakeFromFlatbuffer(), impeller::ColorSourceContents::SetEffectTransform(), impeller::scene::Node::SetGlobalTransform(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ IsAffine()

constexpr bool impeller::Matrix::IsAffine ( ) const
inlineconstexpr

Definition at line 321 of file matrix.h.

321  {
322  return (m[2] == 0 && m[3] == 0 && m[6] == 0 && m[7] == 0 && m[8] == 0 &&
323  m[9] == 0 && m[10] == 1 && m[11] == 0 && m[14] == 0 && m[15] == 1);
324  }

References m.

◆ IsAligned()

constexpr bool impeller::Matrix::IsAligned ( Scalar  tolerance = 0) const
inlineconstexpr

Definition at line 351 of file matrix.h.

351  {
352  if (HasPerspective()) {
353  return false;
354  }
355  int v[] = {!ScalarNearlyZero(m[0], tolerance), //
356  !ScalarNearlyZero(m[1], tolerance), //
357  !ScalarNearlyZero(m[2], tolerance), //
358  !ScalarNearlyZero(m[4], tolerance), //
359  !ScalarNearlyZero(m[5], tolerance), //
360  !ScalarNearlyZero(m[6], tolerance), //
361  !ScalarNearlyZero(m[8], tolerance), //
362  !ScalarNearlyZero(m[9], tolerance), //
363  !ScalarNearlyZero(m[10], tolerance)};
364  // Check if all three basis vectors are aligned to an axis.
365  if (v[0] + v[1] + v[2] != 1 || //
366  v[3] + v[4] + v[5] != 1 || //
367  v[6] + v[7] + v[8] != 1) {
368  return false;
369  }
370  // Ensure that none of the basis vectors overlap.
371  if (v[0] + v[3] + v[6] != 1 || //
372  v[1] + v[4] + v[7] != 1 || //
373  v[2] + v[5] + v[8] != 1) {
374  return false;
375  }
376  return true;
377  }

References HasPerspective(), m, and impeller::ScalarNearlyZero().

Referenced by impeller::testing::TEST().

◆ IsAligned2D()

constexpr bool impeller::Matrix::IsAligned2D ( Scalar  tolerance = 0) const
inlineconstexpr

Definition at line 336 of file matrix.h.

336  {
337  if (HasPerspective2D()) {
338  return false;
339  }
340  if (ScalarNearlyZero(m[1], tolerance) &&
341  ScalarNearlyZero(m[4], tolerance)) {
342  return true;
343  }
344  if (ScalarNearlyZero(m[0], tolerance) &&
345  ScalarNearlyZero(m[5], tolerance)) {
346  return true;
347  }
348  return false;
349  }

References HasPerspective2D(), m, and impeller::ScalarNearlyZero().

Referenced by impeller::testing::TEST().

◆ IsIdentity()

constexpr bool impeller::Matrix::IsIdentity ( ) const
inlineconstexpr

Definition at line 379 of file matrix.h.

379  {
380  return (
381  // clang-format off
382  m[0] == 1.0f && m[1] == 0.0f && m[2] == 0.0f && m[3] == 0.0f &&
383  m[4] == 0.0f && m[5] == 1.0f && m[6] == 0.0f && m[7] == 0.0f &&
384  m[8] == 0.0f && m[9] == 0.0f && m[10] == 1.0f && m[11] == 0.0f &&
385  m[12] == 0.0f && m[13] == 0.0f && m[14] == 0.0f && m[15] == 1.0f
386  // clang-format on
387  );
388  }

References m.

Referenced by impeller::MatrixFilterContents::IsTranslationOnly(), and impeller::testing::TEST_P().

◆ IsTranslationScaleOnly()

constexpr bool impeller::Matrix::IsTranslationScaleOnly ( ) const
inlineconstexpr

Returns true if the matrix has a scale-only basis and is non-projective. Note that an identity matrix meets this criteria.

Definition at line 392 of file matrix.h.

392  {
393  return (
394  // clang-format off
395  m[0] != 0.0 && m[1] == 0.0 && m[2] == 0.0 && m[3] == 0.0 &&
396  m[4] == 0.0 && m[5] != 0.0 && m[6] == 0.0 && m[7] == 0.0 &&
397  m[8] == 0.0 && m[9] == 0.0 && m[10] != 0.0 && m[11] == 0.0 &&
398  m[15] == 1.0
399  // clang-format on
400  );
401  }

References m.

Referenced by impeller::ClipContents::Render(), and impeller::TextContents::Render().

◆ MakeColumn()

static constexpr Matrix impeller::Matrix::MakeColumn ( Scalar  m0,
Scalar  m1,
Scalar  m2,
Scalar  m3,
Scalar  m4,
Scalar  m5,
Scalar  m6,
Scalar  m7,
Scalar  m8,
Scalar  m9,
Scalar  m10,
Scalar  m11,
Scalar  m12,
Scalar  m13,
Scalar  m14,
Scalar  m15 
)
inlinestaticconstexpr

Definition at line 69 of file matrix.h.

73  {
74  return Matrix(m0, m1, m2, m3,
75  m4, m5, m6, m7,
76  m8, m9, m10, m11,
77  m12, m13, m14, m15);
78 
79  }

References Matrix().

Referenced by impeller::testing::TEST(), impeller::TextFrameDispatcher::transform2DAffine(), and impeller::TextFrameDispatcher::transformFullPerspective().

◆ MakeLookAt()

static constexpr Matrix impeller::Matrix::MakeLookAt ( Vector3  position,
Vector3  target,
Vector3  up 
)
inlinestaticconstexpr

Definition at line 532 of file matrix.h.

534  {
535  Vector3 forward = (target - position).Normalize();
536  Vector3 right = up.Cross(forward);
537  up = forward.Cross(right);
538 
539  // clang-format off
540  return {
541  right.x, up.x, forward.x, 0.0f,
542  right.y, up.y, forward.y, 0.0f,
543  right.z, up.z, forward.z, 0.0f,
544  -right.Dot(position), -up.Dot(position), -forward.Dot(position), 1.0f
545  };
546  // clang-format on
547  }

References impeller::Vector3::Cross(), impeller::Vector3::Dot(), impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

Referenced by impeller::scene::Camera::GetTransform(), and impeller::testing::TEST().

◆ MakeOrthographic()

template<class T >
static constexpr Matrix impeller::Matrix::MakeOrthographic ( TSize< T >  size)
inlinestaticconstexpr

Definition at line 497 of file matrix.h.

497  {
498  // Per assumptions about NDC documented above.
499  const auto scale =
500  MakeScale({2.0f / static_cast<Scalar>(size.width),
501  -2.0f / static_cast<Scalar>(size.height), 0.0f});
502  const auto translate = MakeTranslation({-1.0f, 1.0f, 0.5f});
503  return translate * scale;
504  }

References impeller::TSize< T >::height, MakeScale(), MakeTranslation(), scale, and impeller::TSize< T >::width.

Referenced by ImGui_ImplImpeller_RenderDrawData(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakePerspective() [1/2]

static constexpr Matrix impeller::Matrix::MakePerspective ( Radians  fov_y,
Scalar  aspect_ratio,
Scalar  z_near,
Scalar  z_far 
)
inlinestaticconstexpr

Definition at line 506 of file matrix.h.

509  {
510  Scalar height = std::tan(fov_y.radians * 0.5f);
511  Scalar width = height * aspect_ratio;
512 
513  // clang-format off
514  return {
515  1.0f / width, 0.0f, 0.0f, 0.0f,
516  0.0f, 1.0f / height, 0.0f, 0.0f,
517  0.0f, 0.0f, z_far / (z_far - z_near), 1.0f,
518  0.0f, 0.0f, -(z_far * z_near) / (z_far - z_near), 0.0f,
519  };
520  // clang-format on
521  }

References impeller::Radians::radians.

Referenced by impeller::scene::Camera::GetTransform(), MakePerspective(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakePerspective() [2/2]

template<class T >
static constexpr Matrix impeller::Matrix::MakePerspective ( Radians  fov_y,
TSize< T >  size,
Scalar  z_near,
Scalar  z_far 
)
inlinestaticconstexpr

Definition at line 524 of file matrix.h.

527  {
528  return MakePerspective(fov_y, static_cast<Scalar>(size.width) / size.height,
529  z_near, z_far);
530  }

References impeller::TSize< T >::height, MakePerspective(), and impeller::TSize< T >::width.

◆ MakeRotation() [1/2]

static Matrix impeller::Matrix::MakeRotation ( Quaternion  q)
inlinestatic

Definition at line 126 of file matrix.h.

126  {
127  // clang-format off
128  return Matrix(
129  1.0f - 2.0f * q.y * q.y - 2.0f * q.z * q.z,
130  2.0f * q.x * q.y + 2.0f * q.z * q.w,
131  2.0f * q.x * q.z - 2.0f * q.y * q.w,
132  0.0f,
133 
134  2.0f * q.x * q.y - 2.0f * q.z * q.w,
135  1.0f - 2.0f * q.x * q.x - 2.0f * q.z * q.z,
136  2.0f * q.y * q.z + 2.0f * q.x * q.w,
137  0.0f,
138 
139  2.0f * q.x * q.z + 2.0f * q.y * q.w,
140  2.0f * q.y * q.z - 2.0f * q.x * q.w,
141  1.0f - 2.0f * q.x * q.x - 2.0f * q.y * q.y,
142  0.0f,
143 
144  0.0f,
145  0.0f,
146  0.0f,
147  1.0f);
148  // clang-format on
149  }

References Matrix(), impeller::Quaternion::w, impeller::Quaternion::x, impeller::Quaternion::y, and impeller::Quaternion::z.

Referenced by impeller::scene::importer::ProcessNode(), impeller::testing::TEST(), and impeller::scene::testing::TEST_P().

◆ MakeRotation() [2/2]

static Matrix impeller::Matrix::MakeRotation ( Radians  radians,
const Vector4 &  r 
)
inlinestatic

Definition at line 151 of file matrix.h.

151  {
152  const Vector4 v = r.Normalize();
153 
154  const Vector2 cos_sin = CosSin(radians);
155  const Scalar cosine = cos_sin.x;
156  const Scalar cosp = 1.0f - cosine;
157  const Scalar sine = cos_sin.y;
158 
159  // clang-format off
160  return Matrix(
161  cosine + cosp * v.x * v.x,
162  cosp * v.x * v.y + v.z * sine,
163  cosp * v.x * v.z - v.y * sine,
164  0.0f,
165 
166  cosp * v.x * v.y - v.z * sine,
167  cosine + cosp * v.y * v.y,
168  cosp * v.y * v.z + v.x * sine,
169  0.0f,
170 
171  cosp * v.x * v.z + v.y * sine,
172  cosp * v.y * v.z - v.x * sine,
173  cosine + cosp * v.z * v.z,
174  0.0f,
175 
176  0.0f,
177  0.0f,
178  0.0f,
179  1.0f);
180  // clang-format on
181  }

References Matrix(), impeller::Vector4::Normalize(), impeller::TPoint< T >::x, impeller::Vector4::x, impeller::TPoint< T >::y, impeller::Vector4::y, and impeller::Vector4::z.

◆ MakeRotationX()

static Matrix impeller::Matrix::MakeRotationX ( Radians  r)
inlinestatic

Definition at line 183 of file matrix.h.

183  {
184  const Vector2 cos_sin = CosSin(r);
185  const Scalar cosine = cos_sin.x;
186  const Scalar sine = cos_sin.y;
187 
188  // clang-format off
189  return Matrix(
190  1.0f, 0.0f, 0.0f, 0.0f,
191  0.0f, cosine, sine, 0.0f,
192  0.0f, -sine, cosine, 0.0f,
193  0.0f, 0.0f, 0.0f, 1.0f
194  );
195  // clang-format on
196  }

References Matrix(), impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

Referenced by impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakeRotationY()

static Matrix impeller::Matrix::MakeRotationY ( Radians  r)
inlinestatic

Definition at line 198 of file matrix.h.

198  {
199  const Vector2 cos_sin = CosSin(r);
200  const Scalar cosine = cos_sin.x;
201  const Scalar sine = cos_sin.y;
202 
203  // clang-format off
204  return Matrix(
205  cosine, 0.0f, -sine, 0.0f,
206  0.0f, 1.0f, 0.0f, 0.0f,
207  sine, 0.0f, cosine, 0.0f,
208  0.0f, 0.0f, 0.0f, 1.0f
209  );
210  // clang-format on
211  }

References Matrix(), impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

Referenced by impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakeRotationZ()

static Matrix impeller::Matrix::MakeRotationZ ( Radians  r)
inlinestatic

Definition at line 213 of file matrix.h.

213  {
214  const Vector2 cos_sin = CosSin(r);
215  const Scalar cosine = cos_sin.x;
216  const Scalar sine = cos_sin.y;
217 
218  // clang-format off
219  return Matrix (
220  cosine, sine, 0.0f, 0.0f,
221  -sine, cosine, 0.0f, 0.0f,
222  0.0f, 0.0f, 1.0f, 0.0f,
223  0.0f, 0.0f, 0.0f, 1.0
224  );
225  // clang-format on
226  }

References Matrix(), impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

Referenced by impeller::Canvas::Rotate(), impeller::TextFrameDispatcher::rotate(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakeRow()

static constexpr Matrix impeller::Matrix::MakeRow ( Scalar  m0,
Scalar  m1,
Scalar  m2,
Scalar  m3,
Scalar  m4,
Scalar  m5,
Scalar  m6,
Scalar  m7,
Scalar  m8,
Scalar  m9,
Scalar  m10,
Scalar  m11,
Scalar  m12,
Scalar  m13,
Scalar  m14,
Scalar  m15 
)
inlinestaticconstexpr

Definition at line 83 of file matrix.h.

87  {
88  return Matrix(m0, m4, m8, m12,
89  m1, m5, m9, m13,
90  m2, m6, m10, m14,
91  m3, m7, m11, m15);
92  }

References Matrix().

Referenced by impeller::testing::TEST().

◆ MakeScale() [1/2]

static constexpr Matrix impeller::Matrix::MakeScale ( const Vector2 &  s)
inlinestaticconstexpr

Definition at line 113 of file matrix.h.

113  {
114  return MakeScale(Vector3(s.x, s.y, 1.0f));
115  }

References MakeScale(), impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

◆ MakeScale() [2/2]

static constexpr Matrix impeller::Matrix::MakeScale ( const Vector3 &  s)
inlinestaticconstexpr

Definition at line 104 of file matrix.h.

104  {
105  // clang-format off
106  return Matrix(s.x, 0.0f, 0.0f, 0.0f,
107  0.0f, s.y, 0.0f, 0.0f,
108  0.0f, 0.0f, s.z, 0.0f,
109  0.0f, 0.0f, 0.0f, 1.0f);
110  // clang-format on
111  }

References Matrix(), impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

Referenced by impeller::GaussianBlurFilterContents::CalculateUVs(), impeller::TRect< Scalar >::GetNormalizingTransform(), impeller::Entity::GetShaderTransform(), impeller::Snapshot::GetUVTransform(), MakeOrthographic(), MakeScale(), impeller::scene::importer::ParseGLTF(), impeller::scene::importer::ProcessNode(), impeller::SceneContents::Render(), impeller::TiledTextureContents::RenderToSnapshot(), impeller::TextureContents::RenderToSnapshot(), impeller::Canvas::Scale(), impeller::testing::TEST(), impeller::scene::testing::TEST_P(), and impeller::testing::TEST_P().

◆ MakeSkew()

static constexpr Matrix impeller::Matrix::MakeSkew ( Scalar  sx,
Scalar  sy 
)
inlinestaticconstexpr

Definition at line 117 of file matrix.h.

117  {
118  // clang-format off
119  return Matrix(1.0f, sy , 0.0f, 0.0f,
120  sx , 1.0f, 0.0f, 0.0f,
121  0.0f, 0.0f, 1.0f, 0.0f,
122  0.0f, 0.0f, 0.0f, 1.0f);
123  // clang-format on
124  }

References Matrix().

Referenced by impeller::Canvas::Skew(), impeller::TextFrameDispatcher::skew(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakeTranslation()

static constexpr Matrix impeller::Matrix::MakeTranslation ( const Vector3 &  t)
inlinestaticconstexpr

Definition at line 95 of file matrix.h.

95  {
96  // clang-format off
97  return Matrix(1.0f, 0.0f, 0.0f, 0.0f,
98  0.0f, 1.0f, 0.0f, 0.0f,
99  0.0f, 0.0f, 1.0f, 0.0f,
100  t.x, t.y, t.z, 1.0f);
101  // clang-format on
102  }

References Matrix(), impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

Referenced by impeller::AdvancedBlend(), impeller::DlDispatcherBase::drawShadow(), impeller::ExperimentalCanvas::DrawTextFrame(), impeller::TextFrameDispatcher::drawTextFrame(), impeller::Entity::GetShaderTransform(), MakeOrthographic(), impeller::PipelineBlend(), impeller::scene::importer::ProcessNode(), impeller::SolidRRectBlurContents::Render(), impeller::TiledTextureContents::RenderToSnapshot(), impeller::TextureContents::RenderToSnapshot(), impeller::Contents::RenderToSnapshot(), impeller::ExperimentalCanvas::Restore(), impeller::ExperimentalCanvas::SaveLayer(), impeller::Picture::Snapshot(), impeller::testing::TEST(), impeller::scene::testing::TEST_P(), impeller::testing::TEST_P(), and impeller::Canvas::Translate().

◆ Multiply()

constexpr Matrix impeller::Matrix::Multiply ( const Matrix &  o) const
inlineconstexpr

Definition at line 261 of file matrix.h.

261  {
262  // clang-format off
263  return Matrix(
264  m[0] * o.m[0] + m[4] * o.m[1] + m[8] * o.m[2] + m[12] * o.m[3],
265  m[1] * o.m[0] + m[5] * o.m[1] + m[9] * o.m[2] + m[13] * o.m[3],
266  m[2] * o.m[0] + m[6] * o.m[1] + m[10] * o.m[2] + m[14] * o.m[3],
267  m[3] * o.m[0] + m[7] * o.m[1] + m[11] * o.m[2] + m[15] * o.m[3],
268  m[0] * o.m[4] + m[4] * o.m[5] + m[8] * o.m[6] + m[12] * o.m[7],
269  m[1] * o.m[4] + m[5] * o.m[5] + m[9] * o.m[6] + m[13] * o.m[7],
270  m[2] * o.m[4] + m[6] * o.m[5] + m[10] * o.m[6] + m[14] * o.m[7],
271  m[3] * o.m[4] + m[7] * o.m[5] + m[11] * o.m[6] + m[15] * o.m[7],
272  m[0] * o.m[8] + m[4] * o.m[9] + m[8] * o.m[10] + m[12] * o.m[11],
273  m[1] * o.m[8] + m[5] * o.m[9] + m[9] * o.m[10] + m[13] * o.m[11],
274  m[2] * o.m[8] + m[6] * o.m[9] + m[10] * o.m[10] + m[14] * o.m[11],
275  m[3] * o.m[8] + m[7] * o.m[9] + m[11] * o.m[10] + m[15] * o.m[11],
276  m[0] * o.m[12] + m[4] * o.m[13] + m[8] * o.m[14] + m[12] * o.m[15],
277  m[1] * o.m[12] + m[5] * o.m[13] + m[9] * o.m[14] + m[13] * o.m[15],
278  m[2] * o.m[12] + m[6] * o.m[13] + m[10] * o.m[14] + m[14] * o.m[15],
279  m[3] * o.m[12] + m[7] * o.m[13] + m[11] * o.m[14] + m[15] * o.m[15]);
280  // clang-format on
281  }

References m, and Matrix().

Referenced by operator*().

◆ operator!=()

constexpr bool impeller::Matrix::operator!= ( const Matrix &  m) const
inlineconstexpr

Definition at line 414 of file matrix.h.

414  {
415  // clang-format off
416  return vec[0] != m.vec[0]
417  || vec[1] != m.vec[1]
418  || vec[2] != m.vec[2]
419  || vec[3] != m.vec[3];
420  // clang-format on
421  }

References m, and vec.

◆ operator*() [1/4]

Matrix impeller::Matrix::operator* ( const Matrix &  m) const
inline

Definition at line 427 of file matrix.h.

427 { return Multiply(m); }

References m, and Multiply().

◆ operator*() [2/4]

constexpr Point impeller::Matrix::operator* ( const Point &  v) const
inlineconstexpr

Definition at line 452 of file matrix.h.

452  {
453  Scalar w = v.x * m[3] + v.y * m[7] + m[15];
454  Point result(v.x * m[0] + v.y * m[4] + m[12],
455  v.x * m[1] + v.y * m[5] + m[13]);
456 
457  // This is Skia's behavior, but it may be reasonable to allow UB for the w=0
458  // case.
459  if (w) {
460  w = 1 / w;
461  }
462  return result * w;
463  }

References m, impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

◆ operator*() [3/4]

constexpr Vector3 impeller::Matrix::operator* ( const Vector3 &  v) const
inlineconstexpr

Definition at line 438 of file matrix.h.

438  {
439  Scalar w = v.x * m[3] + v.y * m[7] + v.z * m[11] + m[15];
440  Vector3 result(v.x * m[0] + v.y * m[4] + v.z * m[8] + m[12],
441  v.x * m[1] + v.y * m[5] + v.z * m[9] + m[13],
442  v.x * m[2] + v.y * m[6] + v.z * m[10] + m[14]);
443 
444  // This is Skia's behavior, but it may be reasonable to allow UB for the w=0
445  // case.
446  if (w) {
447  w = 1 / w;
448  }
449  return result * w;
450  }

References m, impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

◆ operator*() [4/4]

constexpr Vector4 impeller::Matrix::operator* ( const Vector4 &  v) const
inlineconstexpr

Definition at line 431 of file matrix.h.

431  {
432  return Vector4(v.x * m[0] + v.y * m[4] + v.z * m[8] + v.w * m[12],
433  v.x * m[1] + v.y * m[5] + v.z * m[9] + v.w * m[13],
434  v.x * m[2] + v.y * m[6] + v.z * m[10] + v.w * m[14],
435  v.x * m[3] + v.y * m[7] + v.z * m[11] + v.w * m[15]);
436  }

References m, impeller::Vector4::w, impeller::Vector4::x, impeller::Vector4::y, and impeller::Vector4::z.

◆ operator+() [1/2]

Matrix impeller::Matrix::operator+ ( const Matrix &  m) const

Definition at line 88 of file matrix.cc.

88  {
89  return Matrix(
90  m[0] + o.m[0], m[1] + o.m[1], m[2] + o.m[2], m[3] + o.m[3], //
91  m[4] + o.m[4], m[5] + o.m[5], m[6] + o.m[6], m[7] + o.m[7], //
92  m[8] + o.m[8], m[9] + o.m[9], m[10] + o.m[10], m[11] + o.m[11], //
93  m[12] + o.m[12], m[13] + o.m[13], m[14] + o.m[14], m[15] + o.m[15] //
94  );
95 }

References m, and Matrix().

◆ operator+() [2/2]

Matrix impeller::Matrix::operator+ ( const Vector3 &  t) const
inline

Definition at line 423 of file matrix.h.

423 { return Translate(t); }

References Translate().

◆ operator-()

Matrix impeller::Matrix::operator- ( const Vector3 &  t) const
inline

Definition at line 425 of file matrix.h.

425 { return Translate(-t); }

References Translate().

◆ operator==()

constexpr bool impeller::Matrix::operator== ( const Matrix &  m) const
inlineconstexpr

Definition at line 405 of file matrix.h.

405  {
406  // clang-format off
407  return vec[0] == m.vec[0]
408  && vec[1] == m.vec[1]
409  && vec[2] == m.vec[2]
410  && vec[3] == m.vec[3];
411  // clang-format on
412  }

References m, and vec.

◆ Scale()

constexpr Matrix impeller::Matrix::Scale ( const Vector3 &  s) const
inlineconstexpr

Definition at line 252 of file matrix.h.

252  {
253  // clang-format off
254  return Matrix(m[0] * s.x, m[1] * s.x, m[2] * s.x, m[3] * s.x,
255  m[4] * s.y, m[5] * s.y, m[6] * s.y, m[7] * s.y,
256  m[8] * s.z, m[9] * s.z, m[10] * s.z, m[11] * s.z,
257  m[12] , m[13] , m[14] , m[15] );
258  // clang-format on
259  }

References m, Matrix(), impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

Referenced by impeller::TextFrameDispatcher::scale().

◆ Transform()

constexpr Quad impeller::Matrix::Transform ( const Quad &  quad) const
inlineconstexpr

Definition at line 487 of file matrix.h.

487  {
488  return {
489  *this * quad[0],
490  *this * quad[1],
491  *this * quad[2],
492  *this * quad[3],
493  };
494  }

Referenced by impeller::GaussianBlurFilterContents::CalculateUVs().

◆ TransformDirection() [1/3]

constexpr Vector2 impeller::Matrix::TransformDirection ( const Vector2 &  v) const
inlineconstexpr

Definition at line 483 of file matrix.h.

483  {
484  return Vector2(v.x * m[0] + v.y * m[4], v.x * m[1] + v.y * m[5]);
485  }

References m, impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

◆ TransformDirection() [2/3]

constexpr Vector3 impeller::Matrix::TransformDirection ( const Vector3 &  v) const
inlineconstexpr

Definition at line 477 of file matrix.h.

477  {
478  return Vector3(v.x * m[0] + v.y * m[4] + v.z * m[8],
479  v.x * m[1] + v.y * m[5] + v.z * m[9],
480  v.x * m[2] + v.y * m[6] + v.z * m[10]);
481  }

References m, impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

◆ TransformDirection() [3/3]

constexpr Vector4 impeller::Matrix::TransformDirection ( const Vector4 &  v) const
inlineconstexpr

Definition at line 471 of file matrix.h.

471  {
472  return Vector4(v.x * m[0] + v.y * m[4] + v.z * m[8],
473  v.x * m[1] + v.y * m[5] + v.z * m[9],
474  v.x * m[2] + v.y * m[6] + v.z * m[10], v.w);
475  }

References m, impeller::Vector4::w, impeller::Vector4::x, impeller::Vector4::y, and impeller::Vector4::z.

Referenced by impeller::BorderMaskBlurFilterContents::GetFilterSourceCoverage(), and impeller::DirectionalMorphologyFilterContents::GetFilterSourceCoverage().

◆ TransformHomogenous()

constexpr Vector3 impeller::Matrix::TransformHomogenous ( const Point &  v) const
inlineconstexpr

Definition at line 465 of file matrix.h.

465  {
466  return Vector3(v.x * m[0] + v.y * m[4] + m[12],
467  v.x * m[1] + v.y * m[5] + m[13],
468  v.x * m[3] + v.y * m[7] + m[15]);
469  }

References m, impeller::TPoint< T >::x, and impeller::TPoint< T >::y.

Referenced by impeller::testing::TEST().

◆ Translate()

constexpr Matrix impeller::Matrix::Translate ( const Vector3 &  t) const
inlineconstexpr

Definition at line 240 of file matrix.h.

240  {
241  // clang-format off
242  return Matrix(m[0], m[1], m[2], m[3],
243  m[4], m[5], m[6], m[7],
244  m[8], m[9], m[10], m[11],
245  m[0] * t.x + m[4] * t.y + m[8] * t.z + m[12],
246  m[1] * t.x + m[5] * t.y + m[9] * t.z + m[13],
247  m[2] * t.x + m[6] * t.y + m[10] * t.z + m[14],
248  m[15]);
249  // clang-format on
250  }

References m, Matrix(), impeller::Vector3::x, impeller::Vector3::y, and impeller::Vector3::z.

Referenced by ImGui_ImplImpeller_RenderDrawData(), operator+(), operator-(), and impeller::TextFrameDispatcher::translate().

◆ Transpose()

constexpr Matrix impeller::Matrix::Transpose ( ) const
inlineconstexpr

Definition at line 283 of file matrix.h.

283  {
284  // clang-format off
285  return {
286  m[0], m[4], m[8], m[12],
287  m[1], m[5], m[9], m[13],
288  m[2], m[6], m[10], m[14],
289  m[3], m[7], m[11], m[15],
290  };
291  // clang-format on
292  }

References m.

Referenced by Decompose().

Member Data Documentation

◆ @13

union { ... }

◆ e

Scalar impeller::Matrix::e[4][4]

Definition at line 40 of file matrix.h.

Referenced by Decompose(), GetDeterminant(), GetMaxBasisLength(), GetMaxBasisLengthXY(), Matrix(), and std::operator<<().

◆ m

Scalar impeller::Matrix::m[16]

Definition at line 39 of file matrix.h.

Referenced by Basis(), GetBasisX(), GetBasisY(), GetBasisZ(), HasPerspective(), HasPerspective2D(), HasTranslation(), Invert(), IsAffine(), IsAligned(), IsAligned2D(), IsIdentity(), IsTranslationScaleOnly(), MatrixNear(), Multiply(), operator!=(), operator*(), operator+(), operator==(), Scale(), impeller::testing::TEST(), impeller::scene::importer::ToFBMatrix(), impeller::scene::importer::ToFBMatrixUniquePtr(), impeller::scene::importer::ToMatrix(), TransformDirection(), TransformHomogenous(), Translate(), and Transpose().

◆ vec

Vector4 impeller::Matrix::vec[4]

Definition at line 41 of file matrix.h.

Referenced by operator!=(), operator==(), and impeller::testing::TEST_P().

The documentation for this struct was generated from the following files:
impeller::Matrix::HasPerspective
constexpr bool HasPerspective() const
Definition: matrix.h:330
impeller::Matrix::m
Scalar m[16]
Definition: matrix.h:39
impeller::Matrix::Matrix
constexpr Matrix()
Definition: matrix.h:47
impeller::Scalar
float Scalar
Definition: scalar.h:18
impeller::Vector3::Combine
static constexpr Vector3 Combine(const Vector3 &a, Scalar aScale, const Vector3 &b, Scalar bScale)
Definition: vector.h:192
impeller::Vector2
Point Vector2
Definition: point.h:326
impeller::Matrix::MakeTranslation
static constexpr Matrix MakeTranslation(const Vector3 &t)
Definition: matrix.h:95
impeller::Matrix::e
Scalar e[4][4]
Definition: matrix.h:40
impeller::Matrix::vec
Vector4 vec[4]
Definition: matrix.h:41
impeller::Matrix::MakePerspective
static constexpr Matrix MakePerspective(Radians fov_y, Scalar aspect_ratio, Scalar z_near, Scalar z_far)
Definition: matrix.h:506
impeller::Matrix::Basis
constexpr Matrix Basis() const
The Matrix without its w components (without translation).
Definition: matrix.h:229
impeller::Point
TPoint< Scalar > Point
Definition: point.h:322
impeller::Matrix::Multiply
constexpr Matrix Multiply(const Matrix &o) const
Definition: matrix.h:261
impeller::Matrix::Translate
constexpr Matrix Translate(const Vector3 &t) const
Definition: matrix.h:240
impeller::ScalarNearlyZero
constexpr bool ScalarNearlyZero(Scalar x, Scalar tolerance=kEhCloseEnough)
Definition: scalar.h:25
impeller::Matrix::GetBasisZ
constexpr Vector3 GetBasisZ() const
Definition: matrix.h:309
impeller::Matrix::Invert
Matrix Invert() const
Definition: matrix.cc:97
scale
const Scalar scale
Definition: stroke_path_geometry.cc:308
impeller::Matrix::GetBasisY
constexpr Vector3 GetBasisY() const
Definition: matrix.h:307
impeller::Matrix::MakeScale
static constexpr Matrix MakeScale(const Vector3 &s)
Definition: matrix.h:104
impeller::Matrix::GetBasisX
constexpr Vector3 GetBasisX() const
Definition: matrix.h:305
impeller::Matrix::HasPerspective2D
constexpr bool HasPerspective2D() const
Definition: matrix.h:326