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
 
bool IsInvertible () 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 IsFinite () 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 IsTranslationOnly () const
 Returns true if the matrix has no entries other than translation components. Note that an identity matrix meets this criteria. More...
 
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
 
bool Equals (const Matrix &matrix, Scalar epsilon=1e-5f) 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 MakeTranslateScale (const Vector3 &s, const Vector3 &t)
 
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)
 
static constexpr Vector2 CosSin (Radians radians)
 

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)} {}
impeller::Matrix::vec
Vector4 vec[4]
Definition: matrix.h:41

Referenced by Basis(), MakeColumn(), MakeRotation(), MakeRotationX(), MakeRotationY(), MakeRotationZ(), MakeRow(), MakeScale(), MakeSkew(), MakeTranslateScale(), 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 }
x
int32_t x
Definition: dl_golden_unittests.cc:443
impeller::Matrix::Matrix
constexpr Matrix()
Definition: matrix.h:47
impeller::Matrix::e
Scalar e[4][4]
Definition: matrix.h:40

References impeller::Shear::e, impeller::Vector3::e, impeller::Vector4::e, e, impeller::MatrixDecomposition::perspective, impeller::MatrixDecomposition::rotation, impeller::MatrixDecomposition::scale, impeller::MatrixDecomposition::shear, impeller::MatrixDecomposition::translation, impeller::Quaternion::w, x, 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 239 of file matrix.h.

239  {
240  // clang-format off
241  return Matrix(
242  m[0], m[1], m[2], 0.0f,
243  m[4], m[5], m[6], 0.0f,
244  m[8], m[9], m[10], 0.0f,
245  0.0f, 0.0f, 0.0f, 1.0
246  );
247  // clang-format on
248  }
impeller::Matrix::m
Scalar m[16]
Definition: matrix.h:39

References m, and Matrix().

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

◆ CosSin()

static constexpr Vector2 impeller::Matrix::CosSin ( Radians  radians)
inlinestaticconstexpr

Definition at line 605 of file matrix.h.

605  {
606  // The precision of a float around 1.0 is much lower than it is
607  // around 0.0, so we end up with cases on quadrant rotations where
608  // we get a +/-1.0 for one of the values and a non-zero value for
609  // the other. This happens around quadrant rotations which makes it
610  // especially common and results in unclean quadrant rotation
611  // matrices which do not return true from |IsAligned[2D]| even
612  // though that is exactly where you need them to exhibit that property.
613  // It also injects small floating point mantissa errors into the
614  // matrices whenever you concatenate them with a quadrant rotation.
615  //
616  // This issue is also exacerbated by the fact that, in radians, the
617  // angles for quadrant rotations are irrational numbers. The measuring
618  // error for representing 90 degree multiples is small enough that
619  // either sin or cos will return a value near +/-1.0, but not small
620  // enough that the other value will be a clean 0.0.
621  //
622  // Some geometry packages simply discard very small numbers from
623  // sin/cos, but the following approach specifically targets just the
624  // area around a quadrant rotation (where either the sin or cos are
625  // measuring as +/-1.0) for symmetry of precision.
626 
627  Scalar sin = std::sin(radians.radians);
628  if (std::abs(sin) == 1.0f) {
629  // 90 or 270 degrees (mod 360)
630  return {0.0f, sin};
631  } else {
632  Scalar cos = std::cos(radians.radians);
633  if (std::abs(cos) == 1.0f) {
634  // 0 or 180 degrees (mod 360)
635  return {cos, 0.0f};
636  }
637  return {cos, sin};
638  }
639  }
impeller::Scalar
float Scalar
Definition: scalar.h:18

References impeller::Radians::radians.

Referenced by impeller::RSTransform::Make(), MakeRotation(), MakeRotationX(), MakeRotationY(), and MakeRotationZ().

◆ Decompose()

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

Definition at line 200 of file matrix.cc.

200  {
201  /*
202  * Normalize the matrix.
203  */
204  Matrix self = *this;
205 
206  if (self.e[3][3] == 0) {
207  return std::nullopt;
208  }
209 
210  for (int i = 0; i < 4; i++) {
211  for (int j = 0; j < 4; j++) {
212  self.e[i][j] /= self.e[3][3];
213  }
214  }
215 
216  /*
217  * `perspectiveMatrix` is used to solve for perspective, but it also provides
218  * an easy way to test for singularity of the upper 3x3 component.
219  */
220  Matrix perpectiveMatrix = self;
221  for (int i = 0; i < 3; i++) {
222  perpectiveMatrix.e[i][3] = 0;
223  }
224 
225  perpectiveMatrix.e[3][3] = 1;
226 
227  if (!perpectiveMatrix.IsInvertible()) {
228  return std::nullopt;
229  }
230 
231  MatrixDecomposition result;
232 
233  /*
234  * ==========================================================================
235  * First, isolate perspective.
236  * ==========================================================================
237  */
238  if (self.e[0][3] != 0.0 || self.e[1][3] != 0.0 || self.e[2][3] != 0.0) {
239  /*
240  * prhs is the right hand side of the equation.
241  */
242  const Vector4 rightHandSide(self.e[0][3], //
243  self.e[1][3], //
244  self.e[2][3], //
245  self.e[3][3]);
246 
247  /*
248  * Solve the equation by inverting `perspectiveMatrix` and multiplying
249  * prhs by the inverse.
250  */
251 
252  result.perspective = perpectiveMatrix.Invert().Transpose() * rightHandSide;
253 
254  /*
255  * Clear the perspective partition.
256  */
257  self.e[0][3] = self.e[1][3] = self.e[2][3] = 0;
258  self.e[3][3] = 1;
259  }
260 
261  /*
262  * ==========================================================================
263  * Next, the translation.
264  * ==========================================================================
265  */
266  result.translation = {self.e[3][0], self.e[3][1], self.e[3][2]};
267  self.e[3][0] = self.e[3][1] = self.e[3][2] = 0.0;
268 
269  /*
270  * ==========================================================================
271  * Next, the scale and shear.
272  * ==========================================================================
273  */
274  Vector3 row[3];
275  for (int i = 0; i < 3; i++) {
276  row[i].x = self.e[i][0];
277  row[i].y = self.e[i][1];
278  row[i].z = self.e[i][2];
279  }
280 
281  /*
282  * Compute X scale factor and normalize first row.
283  */
284  result.scale.x = row[0].GetLength();
285  row[0] = row[0].Normalize();
286 
287  /*
288  * Compute XY shear factor and make 2nd row orthogonal to 1st.
289  */
290  result.shear.xy = row[0].Dot(row[1]);
291  row[1] = Vector3::Combine(row[1], 1.0, row[0], -result.shear.xy);
292 
293  /*
294  * Compute Y scale and normalize 2nd row.
295  */
296  result.scale.y = row[1].GetLength();
297  row[1] = row[1].Normalize();
298  result.shear.xy /= result.scale.y;
299 
300  /*
301  * Compute XZ and YZ shears, orthogonalize 3rd row.
302  */
303  result.shear.xz = row[0].Dot(row[2]);
304  row[2] = Vector3::Combine(row[2], 1.0, row[0], -result.shear.xz);
305  result.shear.yz = row[1].Dot(row[2]);
306  row[2] = Vector3::Combine(row[2], 1.0, row[1], -result.shear.yz);
307 
308  /*
309  * Next, get Z scale and normalize 3rd row.
310  */
311  result.scale.z = row[2].GetLength();
312  row[2] = row[2].Normalize();
313 
314  result.shear.xz /= result.scale.z;
315  result.shear.yz /= result.scale.z;
316 
317  /*
318  * At this point, the matrix (in rows[]) is orthonormal.
319  * Check for a coordinate system flip. If the determinant
320  * is -1, then negate the matrix and the scaling factors.
321  */
322  if (row[0].Dot(row[1].Cross(row[2])) < 0) {
323  result.scale.x *= -1;
324  result.scale.y *= -1;
325  result.scale.z *= -1;
326 
327  for (int i = 0; i < 3; i++) {
328  row[i].x *= -1;
329  row[i].y *= -1;
330  row[i].z *= -1;
331  }
332  }
333 
334  /*
335  * ==========================================================================
336  * Finally, get the rotations out.
337  * ==========================================================================
338  */
339  result.rotation.x =
340  0.5 * sqrt(fmax(1.0 + row[0].x - row[1].y - row[2].z, 0.0));
341  result.rotation.y =
342  0.5 * sqrt(fmax(1.0 - row[0].x + row[1].y - row[2].z, 0.0));
343  result.rotation.z =
344  0.5 * sqrt(fmax(1.0 - row[0].x - row[1].y + row[2].z, 0.0));
345  result.rotation.w =
346  0.5 * sqrt(fmax(1.0 + row[0].x + row[1].y + row[2].z, 0.0));
347 
348  if (row[2].y > row[1].z) {
349  result.rotation.x = -result.rotation.x;
350  }
351  if (row[0].z > row[2].x) {
352  result.rotation.y = -result.rotation.y;
353  }
354  if (row[1].x > row[0].y) {
355  result.rotation.z = -result.rotation.z;
356  }
357 
358  return result;
359 }
impeller::Vector3::Combine
static constexpr Vector3 Combine(const Vector3 &a, Scalar aScale, const Vector3 &b, Scalar bScale)
Definition: vector.h:192

References impeller::Vector3::Combine(), impeller::Vector3::Dot(), impeller::Vector3::e, impeller::Vector4::e, e, impeller::Vector3::GetLength(), Invert(), IsInvertible(), impeller::Vector3::Normalize(), impeller::MatrixDecomposition::perspective, impeller::MatrixDecomposition::rotation, impeller::MatrixDecomposition::scale, impeller::MatrixDecomposition::shear, impeller::MatrixDecomposition::translation, Transpose(), impeller::Quaternion::w, x, 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().

◆ Equals()

bool impeller::Matrix::Equals ( const Matrix &  matrix,
Scalar  epsilon = 1e-5f 
) const
inline

Definition at line 440 of file matrix.h.

440  {
441  const Scalar* a = m;
442  const Scalar* b = matrix.m;
443  return ScalarNearlyEqual(a[0], b[0], epsilon) &&
444  ScalarNearlyEqual(a[1], b[1], epsilon) &&
445  ScalarNearlyEqual(a[2], b[2], epsilon) &&
446  ScalarNearlyEqual(a[3], b[3], epsilon) &&
447  ScalarNearlyEqual(a[4], b[4], epsilon) &&
448  ScalarNearlyEqual(a[5], b[5], epsilon) &&
449  ScalarNearlyEqual(a[6], b[6], epsilon) &&
450  ScalarNearlyEqual(a[7], b[7], epsilon) &&
451  ScalarNearlyEqual(a[8], b[8], epsilon) &&
452  ScalarNearlyEqual(a[9], b[9], epsilon) &&
453  ScalarNearlyEqual(a[10], b[10], epsilon) &&
454  ScalarNearlyEqual(a[11], b[11], epsilon) &&
455  ScalarNearlyEqual(a[12], b[12], epsilon) &&
456  ScalarNearlyEqual(a[13], b[13], epsilon) &&
457  ScalarNearlyEqual(a[14], b[14], epsilon) &&
458  ScalarNearlyEqual(a[15], b[15], epsilon);
459  }
impeller::ScalarNearlyEqual
constexpr bool ScalarNearlyEqual(Scalar x, Scalar y, Scalar tolerance=kEhCloseEnough)
Definition: scalar.h:35

References impeller::saturated::b, m, and impeller::ScalarNearlyEqual().

◆ GetBasisX()

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

Definition at line 322 of file matrix.h.

322 { 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 324 of file matrix.h.

324 { 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 326 of file matrix.h.

326 { 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 IsInvertible().

◆ GetDirectionScale()

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

Definition at line 333 of file matrix.h.

333  {
334  return 1.0f / (this->Basis().Invert() * direction.Normalize()).GetLength() *
335  direction.GetLength();
336  }
impeller::Matrix::Basis
constexpr Matrix Basis() const
The Matrix without its w components (without translation).
Definition: matrix.h:239
impeller::Matrix::Invert
Matrix Invert() const
Definition: matrix.cc:97

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

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

◆ GetMaxBasisLengthXY()

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

Definition at line 310 of file matrix.h.

310  {
311  // The full basis computation requires computing the squared scaling factor
312  // for translate/scale only matrices. This substantially limits the range of
313  // precision for small and large scales. Instead, check for the common cases
314  // and directly return the max scaling factor.
315  if (e[0][1] == 0 && e[1][0] == 0) {
316  return std::max(std::abs(e[0][0]), std::abs(e[1][1]));
317  }
318  return std::sqrt(std::max(e[0][0] * e[0][0] + e[0][1] * e[0][1],
319  e[1][0] * e[1][0] + e[1][1] * e[1][1]));
320  }

References e.

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

◆ GetScale()

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

Definition at line 328 of file matrix.h.

328  {
329  return Vector3(GetBasisX().GetLength(), GetBasisY().GetLength(),
330  GetBasisZ().GetLength());
331  }
impeller::Matrix::GetBasisY
constexpr Vector3 GetBasisY() const
Definition: matrix.h:324
impeller::Matrix::GetBasisZ
constexpr Vector3 GetBasisZ() const
Definition: matrix.h:326
impeller::Matrix::GetBasisX
constexpr Vector3 GetBasisX() const
Definition: matrix.h:322

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

Referenced by impeller::DlDispatcherBase::drawShadow().

◆ HasPerspective()

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

Definition at line 352 of file matrix.h.

352  {
353  return m[3] != 0 || m[7] != 0 || m[11] != 0 || m[15] != 1;
354  }

References m.

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

◆ HasPerspective2D()

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

Definition at line 348 of file matrix.h.

348  {
349  return m[3] != 0 || m[7] != 0 || m[15] != 1;
350  }

References m.

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

◆ HasTranslation()

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

Definition at line 356 of file matrix.h.

356 { 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::Canvas::Restore(), impeller::Canvas::SaveLayer(), impeller::ColorSourceContents::SetEffectTransform(), and impeller::testing::TEST().

◆ IsAffine()

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

Definition at line 343 of file matrix.h.

343  {
344  return (m[2] == 0 && m[3] == 0 && m[6] == 0 && m[7] == 0 && m[8] == 0 &&
345  m[9] == 0 && m[10] == 1 && m[11] == 0 && m[14] == 0 && m[15] == 1);
346  }

References m.

◆ IsAligned()

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

Definition at line 373 of file matrix.h.

373  {
374  if (HasPerspective()) {
375  return false;
376  }
377  int v[] = {!ScalarNearlyZero(m[0], tolerance), //
378  !ScalarNearlyZero(m[1], tolerance), //
379  !ScalarNearlyZero(m[2], tolerance), //
380  !ScalarNearlyZero(m[4], tolerance), //
381  !ScalarNearlyZero(m[5], tolerance), //
382  !ScalarNearlyZero(m[6], tolerance), //
383  !ScalarNearlyZero(m[8], tolerance), //
384  !ScalarNearlyZero(m[9], tolerance), //
385  !ScalarNearlyZero(m[10], tolerance)};
386  // Check if all three basis vectors are aligned to an axis.
387  if (v[0] + v[1] + v[2] != 1 || //
388  v[3] + v[4] + v[5] != 1 || //
389  v[6] + v[7] + v[8] != 1) {
390  return false;
391  }
392  // Ensure that none of the basis vectors overlap.
393  if (v[0] + v[3] + v[6] != 1 || //
394  v[1] + v[4] + v[7] != 1 || //
395  v[2] + v[5] + v[8] != 1) {
396  return false;
397  }
398  return true;
399  }
impeller::ScalarNearlyZero
constexpr bool ScalarNearlyZero(Scalar x, Scalar tolerance=kEhCloseEnough)
Definition: scalar.h:30
impeller::Matrix::HasPerspective
constexpr bool HasPerspective() const
Definition: matrix.h:352

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 358 of file matrix.h.

358  {
359  if (HasPerspective2D()) {
360  return false;
361  }
362  if (ScalarNearlyZero(m[1], tolerance) &&
363  ScalarNearlyZero(m[4], tolerance)) {
364  return true;
365  }
366  if (ScalarNearlyZero(m[0], tolerance) &&
367  ScalarNearlyZero(m[5], tolerance)) {
368  return true;
369  }
370  return false;
371  }
impeller::Matrix::HasPerspective2D
constexpr bool HasPerspective2D() const
Definition: matrix.h:348

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

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

◆ IsFinite()

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

Definition at line 338 of file matrix.h.

338  {
339  return vec[0].IsFinite() && vec[1].IsFinite() && vec[2].IsFinite() &&
340  vec[3].IsFinite();
341  }
impeller::Vector4::IsFinite
constexpr bool IsFinite() const
Definition: vector.h:258

References impeller::Vector4::IsFinite(), and vec.

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

◆ IsIdentity()

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

Definition at line 401 of file matrix.h.

401  {
402  return (
403  // clang-format off
404  m[0] == 1.0f && m[1] == 0.0f && m[2] == 0.0f && m[3] == 0.0f &&
405  m[4] == 0.0f && m[5] == 1.0f && m[6] == 0.0f && m[7] == 0.0f &&
406  m[8] == 0.0f && m[9] == 0.0f && m[10] == 1.0f && m[11] == 0.0f &&
407  m[12] == 0.0f && m[13] == 0.0f && m[14] == 0.0f && m[15] == 1.0f
408  // clang-format on
409  );
410  }

References m.

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

◆ IsInvertible()

bool impeller::Matrix::IsInvertible ( ) const
inline

Definition at line 308 of file matrix.h.

308 { return GetDeterminant() != 0; }
impeller::Matrix::GetDeterminant
Scalar GetDeterminant() const
Definition: matrix.cc:162

References GetDeterminant().

Referenced by Decompose().

◆ IsTranslationOnly()

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

Returns true if the matrix has no entries other than translation components. Note that an identity matrix meets this criteria.

Definition at line 414 of file matrix.h.

414  {
415  return (
416  // clang-format off
417  m[0] == 1.0 && m[1] == 0.0 && m[2] == 0.0 && m[3] == 0.0 &&
418  m[4] == 0.0 && m[5] == 1.0 && m[6] == 0.0 && m[7] == 0.0 &&
419  m[8] == 0.0 && m[9] == 0.0 && m[10] == 1.0 && m[11] == 0.0 &&
420  m[15] == 1.0
421  // clang-format on
422  );
423  }

References m.

◆ 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 427 of file matrix.h.

427  {
428  return (
429  // clang-format off
430  m[0] != 0.0 && m[1] == 0.0 && m[2] == 0.0 && m[3] == 0.0 &&
431  m[4] == 0.0 && m[5] != 0.0 && m[6] == 0.0 && m[7] == 0.0 &&
432  m[8] == 0.0 && m[9] == 0.0 && m[10] != 0.0 && m[11] == 0.0 &&
433  m[15] == 1.0
434  // clang-format on
435  );
436  }

References m.

Referenced by impeller::TextContents::ComputeVertexData(), impeller::TextContents::Render(), and impeller::testing::TEST().

◆ 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::FirstPassDispatcher::transform2DAffine(), and impeller::FirstPassDispatcher::transformFullPerspective().

◆ MakeLookAt()

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

Definition at line 588 of file matrix.h.

590  {
591  Vector3 forward = (target - position).Normalize();
592  Vector3 right = up.Cross(forward);
593  up = forward.Cross(right);
594 
595  // clang-format off
596  return {
597  right.x, up.x, forward.x, 0.0f,
598  right.y, up.y, forward.y, 0.0f,
599  right.z, up.z, forward.z, 0.0f,
600  -right.Dot(position), -up.Dot(position), -forward.Dot(position), 1.0f
601  };
602  // clang-format on
603  }

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

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

◆ MakeOrthographic()

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

Definition at line 553 of file matrix.h.

553  {
554  // Per assumptions about NDC documented above.
555  const auto scale =
556  MakeScale({2.0f / static_cast<Scalar>(size.width),
557  -2.0f / static_cast<Scalar>(size.height), 0.0f});
558  const auto translate = MakeTranslation({-1.0f, 1.0f, 0.5f});
559  return translate * scale;
560  }
scale
const Scalar scale
Definition: stroke_path_geometry.cc:316
impeller::Matrix::MakeTranslation
static constexpr Matrix MakeTranslation(const Vector3 &t)
Definition: matrix.h:95
impeller::Matrix::MakeScale
static constexpr Matrix MakeScale(const Vector3 &s)
Definition: matrix.h:104

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 562 of file matrix.h.

565  {
566  Scalar height = std::tan(fov_y.radians * 0.5f);
567  Scalar width = height * aspect_ratio;
568 
569  // clang-format off
570  return {
571  1.0f / width, 0.0f, 0.0f, 0.0f,
572  0.0f, 1.0f / height, 0.0f, 0.0f,
573  0.0f, 0.0f, z_far / (z_far - z_near), 1.0f,
574  0.0f, 0.0f, -(z_far * z_near) / (z_far - z_near), 0.0f,
575  };
576  // clang-format on
577  }

References impeller::Radians::radians.

Referenced by 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 580 of file matrix.h.

583  {
584  return MakePerspective(fov_y, static_cast<Scalar>(size.width) / size.height,
585  z_near, z_far);
586  }
impeller::Matrix::MakePerspective
static constexpr Matrix MakePerspective(Radians fov_y, Scalar aspect_ratio, Scalar z_near, Scalar z_far)
Definition: matrix.h:562

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 136 of file matrix.h.

136  {
137  // clang-format off
138  return Matrix(
139  1.0f - 2.0f * q.y * q.y - 2.0f * q.z * q.z,
140  2.0f * q.x * q.y + 2.0f * q.z * q.w,
141  2.0f * q.x * q.z - 2.0f * q.y * q.w,
142  0.0f,
143 
144  2.0f * q.x * q.y - 2.0f * q.z * q.w,
145  1.0f - 2.0f * q.x * q.x - 2.0f * q.z * q.z,
146  2.0f * q.y * q.z + 2.0f * q.x * q.w,
147  0.0f,
148 
149  2.0f * q.x * q.z + 2.0f * q.y * q.w,
150  2.0f * q.y * q.z - 2.0f * q.x * q.w,
151  1.0f - 2.0f * q.x * q.x - 2.0f * q.y * q.y,
152  0.0f,
153 
154  0.0f,
155  0.0f,
156  0.0f,
157  1.0f);
158  // clang-format on
159  }

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

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

◆ MakeRotation() [2/2]

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

Definition at line 161 of file matrix.h.

161  {
162  const Vector4 v = r.Normalize();
163 
164  const Vector2 cos_sin = CosSin(radians);
165  const Scalar cosine = cos_sin.x;
166  const Scalar cosp = 1.0f - cosine;
167  const Scalar sine = cos_sin.y;
168 
169  // clang-format off
170  return Matrix(
171  cosine + cosp * v.x * v.x,
172  cosp * v.x * v.y + v.z * sine,
173  cosp * v.x * v.z - v.y * sine,
174  0.0f,
175 
176  cosp * v.x * v.y - v.z * sine,
177  cosine + cosp * v.y * v.y,
178  cosp * v.y * v.z + v.x * sine,
179  0.0f,
180 
181  cosp * v.x * v.z + v.y * sine,
182  cosp * v.y * v.z - v.x * sine,
183  cosine + cosp * v.z * v.z,
184  0.0f,
185 
186  0.0f,
187  0.0f,
188  0.0f,
189  1.0f);
190  // clang-format on
191  }
impeller::Vector2
Point Vector2
Definition: point.h:331
impeller::Matrix::CosSin
static constexpr Vector2 CosSin(Radians radians)
Definition: matrix.h:605

References CosSin(), 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 193 of file matrix.h.

193  {
194  const Vector2 cos_sin = CosSin(r);
195  const Scalar cosine = cos_sin.x;
196  const Scalar sine = cos_sin.y;
197 
198  // clang-format off
199  return Matrix(
200  1.0f, 0.0f, 0.0f, 0.0f,
201  0.0f, cosine, sine, 0.0f,
202  0.0f, -sine, cosine, 0.0f,
203  0.0f, 0.0f, 0.0f, 1.0f
204  );
205  // clang-format on
206  }

References CosSin(), 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 208 of file matrix.h.

208  {
209  const Vector2 cos_sin = CosSin(r);
210  const Scalar cosine = cos_sin.x;
211  const Scalar sine = cos_sin.y;
212 
213  // clang-format off
214  return Matrix(
215  cosine, 0.0f, -sine, 0.0f,
216  0.0f, 1.0f, 0.0f, 0.0f,
217  sine, 0.0f, cosine, 0.0f,
218  0.0f, 0.0f, 0.0f, 1.0f
219  );
220  // clang-format on
221  }

References CosSin(), 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 223 of file matrix.h.

223  {
224  const Vector2 cos_sin = CosSin(r);
225  const Scalar cosine = cos_sin.x;
226  const Scalar sine = cos_sin.y;
227 
228  // clang-format off
229  return Matrix (
230  cosine, sine, 0.0f, 0.0f,
231  -sine, cosine, 0.0f, 0.0f,
232  0.0f, 0.0f, 1.0f, 0.0f,
233  0.0f, 0.0f, 0.0f, 1.0
234  );
235  // clang-format on
236  }

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

Referenced by impeller::FirstPassDispatcher::rotate(), impeller::Canvas::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::RSTransform::GetMatrix(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakeScale() [1/2]

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

Definition at line 123 of file matrix.h.

123  {
124  return MakeScale(Vector3(s.x, s.y, 1.0f));
125  }

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::TextContents::ComputeVertexData(), impeller::TRect< T >::GetNormalizingTransform(), impeller::Snapshot::GetUVTransform(), MakeOrthographic(), MakeScale(), impeller::TextureContents::RenderToSnapshot(), impeller::TiledTextureContents::RenderToSnapshot(), impeller::Canvas::Scale(), impeller::testing::TEST(), and impeller::testing::TEST_P().

◆ MakeSkew()

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

Definition at line 127 of file matrix.h.

127  {
128  // clang-format off
129  return Matrix(1.0f, sy , 0.0f, 0.0f,
130  sx , 1.0f, 0.0f, 0.0f,
131  0.0f, 0.0f, 1.0f, 0.0f,
132  0.0f, 0.0f, 0.0f, 1.0f);
133  // clang-format on
134  }

References Matrix().

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

◆ MakeTranslateScale()

static constexpr Matrix impeller::Matrix::MakeTranslateScale ( const Vector3 &  s,
const Vector3 &  t 
)
inlinestaticconstexpr

Definition at line 113 of file matrix.h.

114  {
115  // clang-format off
116  return Matrix(s.x, 0.0f, 0.0f, 0.0f,
117  0.0f, s.y, 0.0f, 0.0f,
118  0.0f, 0.0f, s.z, 0.0f,
119  t.x , t.y, t.z, 1.0f);
120  // clang-format on
121  }

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

Referenced by impeller::Canvas::DrawImageRect(), impeller::Entity::GetShaderTransform(), and impeller::testing::TEST().

◆ 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::Canvas::ClipGeometry(), impeller::DlDispatcherBase::drawShadow(), impeller::FirstPassDispatcher::drawTextFrame(), impeller::Canvas::DrawTextFrame(), impeller::TextFrame::GetOffsetTransform(), MakeOrthographic(), impeller::PipelineBlend(), impeller::SolidRRectBlurContents::Render(), impeller::Contents::RenderToSnapshot(), impeller::TextureContents::RenderToSnapshot(), impeller::TiledTextureContents::RenderToSnapshot(), impeller::Canvas::Restore(), impeller::Canvas::SaveLayer(), impeller::testing::TEST(), impeller::testing::TEST_P(), and impeller::Canvas::Translate().

◆ Multiply()

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

Definition at line 271 of file matrix.h.

271  {
272  // clang-format off
273  return Matrix(
274  m[0] * o.m[0] + m[4] * o.m[1] + m[8] * o.m[2] + m[12] * o.m[3],
275  m[1] * o.m[0] + m[5] * o.m[1] + m[9] * o.m[2] + m[13] * o.m[3],
276  m[2] * o.m[0] + m[6] * o.m[1] + m[10] * o.m[2] + m[14] * o.m[3],
277  m[3] * o.m[0] + m[7] * o.m[1] + m[11] * o.m[2] + m[15] * o.m[3],
278  m[0] * o.m[4] + m[4] * o.m[5] + m[8] * o.m[6] + m[12] * o.m[7],
279  m[1] * o.m[4] + m[5] * o.m[5] + m[9] * o.m[6] + m[13] * o.m[7],
280  m[2] * o.m[4] + m[6] * o.m[5] + m[10] * o.m[6] + m[14] * o.m[7],
281  m[3] * o.m[4] + m[7] * o.m[5] + m[11] * o.m[6] + m[15] * o.m[7],
282  m[0] * o.m[8] + m[4] * o.m[9] + m[8] * o.m[10] + m[12] * o.m[11],
283  m[1] * o.m[8] + m[5] * o.m[9] + m[9] * o.m[10] + m[13] * o.m[11],
284  m[2] * o.m[8] + m[6] * o.m[9] + m[10] * o.m[10] + m[14] * o.m[11],
285  m[3] * o.m[8] + m[7] * o.m[9] + m[11] * o.m[10] + m[15] * o.m[11],
286  m[0] * o.m[12] + m[4] * o.m[13] + m[8] * o.m[14] + m[12] * o.m[15],
287  m[1] * o.m[12] + m[5] * o.m[13] + m[9] * o.m[14] + m[13] * o.m[15],
288  m[2] * o.m[12] + m[6] * o.m[13] + m[10] * o.m[14] + m[14] * o.m[15],
289  m[3] * o.m[12] + m[7] * o.m[13] + m[11] * o.m[14] + m[15] * o.m[15]);
290  // clang-format on
291  }

References m, and Matrix().

Referenced by operator*().

◆ operator!=()

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

Definition at line 470 of file matrix.h.

470  {
471  // clang-format off
472  return vec[0] != m.vec[0]
473  || vec[1] != m.vec[1]
474  || vec[2] != m.vec[2]
475  || vec[3] != m.vec[3];
476  // clang-format on
477  }

References m, and vec.

◆ operator*() [1/4]

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

Definition at line 483 of file matrix.h.

483 { return Multiply(m); }
impeller::Matrix::Multiply
constexpr Matrix Multiply(const Matrix &o) const
Definition: matrix.h:271

References m, and Multiply().

◆ operator*() [2/4]

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

Definition at line 508 of file matrix.h.

508  {
509  Scalar w = v.x * m[3] + v.y * m[7] + m[15];
510  Point result(v.x * m[0] + v.y * m[4] + m[12],
511  v.x * m[1] + v.y * m[5] + m[13]);
512 
513  // This is Skia's behavior, but it may be reasonable to allow UB for the w=0
514  // case.
515  if (w) {
516  w = 1 / w;
517  }
518  return result * w;
519  }
impeller::Point
TPoint< Scalar > Point
Definition: point.h:327

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 494 of file matrix.h.

494  {
495  Scalar w = v.x * m[3] + v.y * m[7] + v.z * m[11] + m[15];
496  Vector3 result(v.x * m[0] + v.y * m[4] + v.z * m[8] + m[12],
497  v.x * m[1] + v.y * m[5] + v.z * m[9] + m[13],
498  v.x * m[2] + v.y * m[6] + v.z * m[10] + m[14]);
499 
500  // This is Skia's behavior, but it may be reasonable to allow UB for the w=0
501  // case.
502  if (w) {
503  w = 1 / w;
504  }
505  return result * w;
506  }

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 487 of file matrix.h.

487  {
488  return Vector4(v.x * m[0] + v.y * m[4] + v.z * m[8] + v.w * m[12],
489  v.x * m[1] + v.y * m[5] + v.z * m[9] + v.w * m[13],
490  v.x * m[2] + v.y * m[6] + v.z * m[10] + v.w * m[14],
491  v.x * m[3] + v.y * m[7] + v.z * m[11] + v.w * m[15]);
492  }

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 479 of file matrix.h.

479 { return Translate(t); }
impeller::Matrix::Translate
constexpr Matrix Translate(const Vector3 &t) const
Definition: matrix.h:250

References Translate().

◆ operator-()

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

Definition at line 481 of file matrix.h.

481 { return Translate(-t); }

References Translate().

◆ operator==()

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

Definition at line 461 of file matrix.h.

461  {
462  // clang-format off
463  return vec[0] == m.vec[0]
464  && vec[1] == m.vec[1]
465  && vec[2] == m.vec[2]
466  && vec[3] == m.vec[3];
467  // clang-format on
468  }

References m, and vec.

◆ Scale()

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

Definition at line 262 of file matrix.h.

262  {
263  // clang-format off
264  return Matrix(m[0] * s.x, m[1] * s.x, m[2] * s.x, m[3] * s.x,
265  m[4] * s.y, m[5] * s.y, m[6] * s.y, m[7] * s.y,
266  m[8] * s.z, m[9] * s.z, m[10] * s.z, m[11] * s.z,
267  m[12] , m[13] , m[14] , m[15] );
268  // clang-format on
269  }

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

Referenced by impeller::FirstPassDispatcher::scale(), and impeller::testing::TEST_P().

◆ Transform()

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

Definition at line 543 of file matrix.h.

543  {
544  return {
545  *this * quad[0],
546  *this * quad[1],
547  *this * quad[2],
548  *this * quad[3],
549  };
550  }

Referenced by impeller::GaussianBlurFilterContents::CalculateUVs(), and impeller::testing::TEST_P().

◆ TransformDirection() [1/3]

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

Definition at line 539 of file matrix.h.

539  {
540  return Vector2(v.x * m[0] + v.y * m[4], v.x * m[1] + v.y * m[5]);
541  }

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 533 of file matrix.h.

533  {
534  return Vector3(v.x * m[0] + v.y * m[4] + v.z * m[8],
535  v.x * m[1] + v.y * m[5] + v.z * m[9],
536  v.x * m[2] + v.y * m[6] + v.z * m[10]);
537  }

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 527 of file matrix.h.

527  {
528  return Vector4(v.x * m[0] + v.y * m[4] + v.z * m[8],
529  v.x * m[1] + v.y * m[5] + v.z * m[9],
530  v.x * m[2] + v.y * m[6] + v.z * m[10], v.w);
531  }

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 521 of file matrix.h.

521  {
522  return Vector3(v.x * m[0] + v.y * m[4] + m[12],
523  v.x * m[1] + v.y * m[5] + m[13],
524  v.x * m[3] + v.y * m[7] + m[15]);
525  }

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 250 of file matrix.h.

250  {
251  // clang-format off
252  return Matrix(m[0], m[1], m[2], m[3],
253  m[4], m[5], m[6], m[7],
254  m[8], m[9], m[10], m[11],
255  m[0] * t.x + m[4] * t.y + m[8] * t.z + m[12],
256  m[1] * t.x + m[5] * t.y + m[9] * t.z + m[13],
257  m[2] * t.x + m[6] * t.y + m[10] * t.z + m[14],
258  m[3] * t.x + m[7] * t.y + m[11] * t.z + m[15]);
259  // clang-format on
260  }

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

Referenced by ImGui_ImplImpeller_RenderDrawData(), operator+(), operator-(), impeller::testing::TEST(), impeller::testing::TEST_P(), and impeller::FirstPassDispatcher::translate().

◆ Transpose()

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

Definition at line 293 of file matrix.h.

293  {
294  // clang-format off
295  return {
296  m[0], m[4], m[8], m[12],
297  m[1], m[5], m[9], m[13],
298  m[2], m[6], m[10], m[14],
299  m[3], m[7], m[11], m[15],
300  };
301  // clang-format on
302  }

References m.

Referenced by Decompose().

Member Data Documentation

◆ 

union { ... }

◆ e

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

Definition at line 40 of file matrix.h.

Referenced by Decompose(), GetDeterminant(), GetMaxBasisLengthXY(), Matrix(), std::operator<<(), and impeller::testing::TEST().

◆ m

Scalar impeller::Matrix::m[16]

Definition at line 39 of file matrix.h.

Referenced by Basis(), impeller::TextContents::ComputeVertexData(), Equals(), impeller::interop::FromImpellerType(), GetBasisX(), GetBasisY(), GetBasisZ(), HasPerspective(), HasPerspective2D(), HasTranslation(), Invert(), IsAffine(), IsAligned(), IsAligned2D(), IsIdentity(), IsTranslationOnly(), IsTranslationScaleOnly(), MatrixNear(), Multiply(), operator!=(), operator*(), operator+(), operator==(), Scale(), impeller::testing::TEST(), impeller::testing::TEST_P(), impeller::interop::ToSkMatrix(), TransformDirection(), TransformHomogenous(), Translate(), and Transpose().

◆ vec

Vector4 impeller::Matrix::vec[4]

Definition at line 41 of file matrix.h.

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

The documentation for this struct was generated from the following files: