| 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 | ( |  | ) |
| inline constexpr

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
| ) |  |
| inline constexpr

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
| inline constexpr

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 | ) |
| inline static constexpr

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::saturated::b
SI b
Definition: saturated_math.h:87
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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| ) |  |
| inline static constexpr

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
| ) |  |
| inline static constexpr

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 | ) |
| inline static constexpr

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
| ) |  |
| inline static constexpr

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
| ) |  |
| inline static constexpr

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 | ) |
| inline static

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
| ) |  |
| inline static

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 | ) |
| inline static

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 | ) |
| inline static

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 | ) |
| inline static

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
| ) |  |
| inline static constexpr

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 | ) |
| inline static constexpr

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 | ) |
| inline static constexpr

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
| ) |  |
| inline static constexpr

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
| ) |  |
| inline static constexpr

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 | ) |
| inline static constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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
| inline constexpr

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:

- impeller/geometry/matrix.h
- impeller/geometry/matrix.cc