| Flutter Impeller |

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

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

`#include <matrix.h>`

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

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

## Public Attributes
union {
Scalar m [16]
Scalar e [4][4]
Vector4 vec [4]
}; |

## Detailed Description

A 4x4 matrix using column-major storage.

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

Definition at line 37 of file matrix.h.

## Constructor & Destructor Documentation

## ◆ Matrix() [1/3]

constexpr impeller::Matrix::Matrix | ( |  | ) |
| 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)} {}

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

## ◆ Matrix() [2/3]

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

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

## Member Function Documentation

## ◆ Basis()

constexpr Matrix impeller::Matrix::Basis | ( |  | ) | const
| inline constexpr

The Matrix without its `w` components (without translation).

Definition at line 224 of file matrix.h.

224 {
225 // clang-format off
226 return Matrix(
227 m[0], m[1], m[2], 0.0f,
228 m[4], m[5], m[6], 0.0f,
229 m[8], m[9], m[10], 0.0f,
230 0.0f, 0.0f, 0.0f, 1.0
231 );
232 // clang-format on
233 }

References m, and Matrix().

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

## ◆ Decompose()

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

Definition at line 217 of file matrix.cc.

217 {
218 /*
219 * Normalize the matrix.
220 */
221 Matrix self = *this;
222
223 if (self.e[3][3] == 0) {
224 return std::nullopt;
225 }
226
227 for (int i = 0; i < 4; i++) {
228 for (int j = 0; j < 4; j++) {
229 self.e[i][j] /= self.e[3][3];
230 }
231 }
232
233 /*
234 * `perspectiveMatrix` is used to solve for perspective, but it also provides
235 * an easy way to test for singularity of the upper 3x3 component.
236 */
237 Matrix perpectiveMatrix = self;
238 for (int i = 0; i < 3; i++) {
239 perpectiveMatrix.e[i][3] = 0;
240 }
241
242 perpectiveMatrix.e[3][3] = 1;
243
244 if (perpectiveMatrix.GetDeterminant() == 0.0) {
245 return std::nullopt;
246 }
247
248 MatrixDecomposition result;
249
250 /*
251 * ==========================================================================
252 * First, isolate perspective.
253 * ==========================================================================
254 */
255 if (self.e[0][3] != 0.0 || self.e[1][3] != 0.0 || self.e[2][3] != 0.0) {
256 /*
257 * prhs is the right hand side of the equation.
258 */
259 const Vector4 rightHandSide(self.e[0][3], //
260 self.e[1][3], //
261 self.e[2][3], //
262 self.e[3][3]);
263
264 /*
265 * Solve the equation by inverting `perspectiveMatrix` and multiplying
266 * prhs by the inverse.
267 */
268
269 result.perspective = perpectiveMatrix.Invert().Transpose() * rightHandSide;
270
271 /*
272 * Clear the perspective partition.
273 */
274 self.e[0][3] = self.e[1][3] = self.e[2][3] = 0;
275 self.e[3][3] = 1;
276 }
277
278 /*
279 * ==========================================================================
280 * Next, the translation.
281 * ==========================================================================
282 */
283 result.translation = {self.e[3][0], self.e[3][1], self.e[3][2]};
284 self.e[3][0] = self.e[3][1] = self.e[3][2] = 0.0;
285
286 /*
287 * ==========================================================================
288 * Next, the scale and shear.
289 * ==========================================================================
290 */
291 Vector3 row[3];
292 for (int i = 0; i < 3; i++) {
293 row[i].x = self.e[i][0];
294 row[i].y = self.e[i][1];
295 row[i].z = self.e[i][2];
296 }
297
298 /*
299 * Compute X scale factor and normalize first row.
300 */
301 result.scale.x = row[0].Length();
302 row[0] = row[0].Normalize();
303
304 /*
305 * Compute XY shear factor and make 2nd row orthogonal to 1st.
306 */
307 result.shear.xy = row[0].Dot(row[1]);
308 row[1] = Vector3::Combine(row[1], 1.0, row[0], -result.shear.xy);
309
310 /*
311 * Compute Y scale and normalize 2nd row.
312 */
313 result.scale.y = row[1].Length();
314 row[1] = row[1].Normalize();
315 result.shear.xy /= result.scale.y;
316
317 /*
318 * Compute XZ and YZ shears, orthogonalize 3rd row.
319 */
320 result.shear.xz = row[0].Dot(row[2]);
321 row[2] = Vector3::Combine(row[2], 1.0, row[0], -result.shear.xz);
322 result.shear.yz = row[1].Dot(row[2]);
323 row[2] = Vector3::Combine(row[2], 1.0, row[1], -result.shear.yz);
324
325 /*
326 * Next, get Z scale and normalize 3rd row.
327 */
328 result.scale.z = row[2].Length();
329 row[2] = row[2].Normalize();
330
331 result.shear.xz /= result.scale.z;
332 result.shear.yz /= result.scale.z;
333
334 /*
335 * At this point, the matrix (in rows[]) is orthonormal.
336 * Check for a coordinate system flip. If the determinant
337 * is -1, then negate the matrix and the scaling factors.
338 */
339 if (row[0].Dot(row[1].Cross(row[2])) < 0) {
340 result.scale.x *= -1;
341 result.scale.y *= -1;
342 result.scale.z *= -1;
343
344 for (int i = 0; i < 3; i++) {
345 row[i].x *= -1;
346 row[i].y *= -1;
347 row[i].z *= -1;
348 }
349 }
350
351 /*
352 * ==========================================================================
353 * Finally, get the rotations out.
354 * ==========================================================================
355 */
356 result.rotation.x =
357 0.5 * sqrt(fmax(1.0 + row[0].x - row[1].y - row[2].z, 0.0));
358 result.rotation.y =
359 0.5 * sqrt(fmax(1.0 - row[0].x + row[1].y - row[2].z, 0.0));
360 result.rotation.z =
361 0.5 * sqrt(fmax(1.0 - row[0].x - row[1].y + row[2].z, 0.0));
362 result.rotation.w =
363 0.5 * sqrt(fmax(1.0 + row[0].x + row[1].y + row[2].z, 0.0));
364
365 if (row[2].y > row[1].z) {
366 result.rotation.x = -result.rotation.x;
367 }
368 if (row[0].z > row[2].x) {
369 result.rotation.y = -result.rotation.y;
370 }
371 if (row[1].x > row[0].y) {
372 result.rotation.z = -result.rotation.z;
373 }
374
375 return result;
376 }

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

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

## ◆ GetBasisX()

constexpr Vector3 impeller::Matrix::GetBasisX | ( |  | ) | const
| inline constexpr

Definition at line 297 of file matrix.h.

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

References m.

Referenced by GetScale().

## ◆ GetBasisY()

constexpr Vector3 impeller::Matrix::GetBasisY | ( |  | ) | const
| inline constexpr

Definition at line 299 of file matrix.h.

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

References m.

Referenced by GetScale().

## ◆ GetBasisZ()

constexpr Vector3 impeller::Matrix::GetBasisZ | ( |  | ) | const
| inline constexpr

Definition at line 301 of file matrix.h.

301 { 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 impeller::LineGeometry::ComputePixelHalfWidth(), and Decompose().

## ◆ GetDirectionScale()

constexpr Scalar impeller::Matrix::GetDirectionScale | ( | Vector3 | direction | ) | const
| inline constexpr

Definition at line 308 of file matrix.h.

308 {
309 return 1.0f / (this->Basis().Invert() * direction.Normalize()).Length() *
310 direction.Length();
311 }

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

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

## ◆ GetMaxBasisLength()

Scalar impeller::Matrix::GetMaxBasisLength | ( |  | ) | const

Definition at line 196 of file matrix.cc.

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

References e.

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

## ◆ GetMaxBasisLengthXY()

Scalar impeller::Matrix::GetMaxBasisLengthXY | ( |  | ) | const

Definition at line 205 of file matrix.cc.

205 {
206 Scalar max = 0;
207 for (int i = 0; i < 3; i++) {
208 max = std::max(max, e[i][0] * e[i][0] + e[i][1] * e[i][1]);
209 }
210 return std::sqrt(max);
211 }

References e.

Referenced by impeller::Entity::DeriveTextScale().

## ◆ GetScale()

constexpr Vector3 impeller::Matrix::GetScale | ( |  | ) | const
| inline constexpr

Definition at line 303 of file matrix.h.

303 {
304 return Vector3(GetBasisX().Length(), GetBasisY().Length(),
305 GetBasisZ().Length());
306 }

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

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

## ◆ HasPerspective()

constexpr bool impeller::Matrix::HasPerspective | ( |  | ) | const
| inline constexpr

Definition at line 318 of file matrix.h.

318 {
319 return m[3] != 0 || m[7] != 0 || m[11] != 0 || m[15] != 1;
320 }

References m.

Referenced by impeller::DlDispatcher::drawDisplayList().

## ◆ Invert()

Matrix impeller::Matrix::Invert | ( |  | ) | const

Definition at line 97 of file matrix.cc.

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

References m.

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

## ◆ IsAffine()

constexpr bool impeller::Matrix::IsAffine | ( |  | ) | const
| inline constexpr

Definition at line 313 of file matrix.h.

313 {
314 return (m[2] == 0 && m[3] == 0 && m[6] == 0 && m[7] == 0 && m[8] == 0 &&
315 m[9] == 0 && m[10] == 1 && m[11] == 0 && m[14] == 0 && m[15] == 1);
316 }

References m.

## ◆ IsAligned()

constexpr bool impeller::Matrix::IsAligned | ( | Scalar | tolerance = `0` | ) | const
| inline constexpr

Definition at line 322 of file matrix.h.

322 {
323 int v[] = {!ScalarNearlyZero(m[0], tolerance), //
324 !ScalarNearlyZero(m[1], tolerance), //
325 !ScalarNearlyZero(m[2], tolerance), //
326 !ScalarNearlyZero(m[4], tolerance), //
327 !ScalarNearlyZero(m[5], tolerance), //
328 !ScalarNearlyZero(m[6], tolerance), //
329 !ScalarNearlyZero(m[8], tolerance), //
330 !ScalarNearlyZero(m[9], tolerance), //
331 !ScalarNearlyZero(m[10], tolerance)};
332 // Check if all three basis vectors are aligned to an axis.
333 if (v[0] + v[1] + v[2] != 1 || //
334 v[3] + v[4] + v[5] != 1 || //
335 v[6] + v[7] + v[8] != 1) {
336 return false;
337 }
338 // Ensure that none of the basis vectors overlap.
339 if (v[0] + v[3] + v[6] != 1 || //
340 v[1] + v[4] + v[7] != 1 || //
341 v[2] + v[5] + v[8] != 1) {
342 return false;
343 }
344 return true;
345 }

References m, and impeller::ScalarNearlyZero().

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

## ◆ IsIdentity()

constexpr bool impeller::Matrix::IsIdentity | ( |  | ) | const
| inline constexpr

Definition at line 347 of file matrix.h.

347 {
348 return (
349 // clang-format off
350 m[0] == 1.0f && m[1] == 0.0f && m[2] == 0.0f && m[3] == 0.0f &&
351 m[4] == 0.0f && m[5] == 1.0f && m[6] == 0.0f && m[7] == 0.0f &&
352 m[8] == 0.0f && m[9] == 0.0f && m[10] == 1.0f && m[11] == 0.0f &&
353 m[12] == 0.0f && m[13] == 0.0f && m[14] == 0.0f && m[15] == 1.0f
354 // clang-format on
355 );
356 }

References m.

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

## ◆ 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 360 of file matrix.h.

360 {
361 return (
362 // clang-format off
363 m[0] != 0.0 && m[1] == 0.0 && m[2] == 0.0 && m[3] == 0.0 &&
364 m[4] == 0.0 && m[5] != 0.0 && m[6] == 0.0 && m[7] == 0.0 &&
365 m[8] == 0.0 && m[9] == 0.0 && m[10] != 0.0 && m[11] == 0.0 &&
366 m[15] == 1.0
367 // clang-format on
368 );
369 }

References m.

Referenced by impeller::RectGeometry::CoversArea(), impeller::LineGeometry::CoversArea(), impeller::RoundRectGeometry::CoversArea(), impeller::FillPathGeometry::CoversArea(), and impeller::TextContents::Render().

## ◆ MakeColumn()

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

## ◆ MakeLookAt()

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

Definition at line 494 of file matrix.h.

496 {
497 Vector3 forward = (target - position).Normalize();
498 Vector3 right = up.Cross(forward);
499 up = forward.Cross(right);
500
501 // clang-format off
502 return {
503 right.x, up.x, forward.x, 0.0f,
504 right.y, up.y, forward.y, 0.0f,
505 right.z, up.z, forward.z, 0.0f,
506 -right.Dot(position), -up.Dot(position), -forward.Dot(position), 1.0f
507 };
508 // clang-format on
509 }

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

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

## ◆ MakeOrthographic()

template<class T >

static constexpr Matrix impeller::Matrix::MakeOrthographic | ( | TSize< T > | size | ) |
| inline static constexpr

Definition at line 459 of file matrix.h.

459 {
460 // Per assumptions about NDC documented above.
461 const auto scale =
462 MakeScale({2.0f / static_cast<Scalar>(size.width),
463 -2.0f / static_cast<Scalar>(size.height), 0.0f});
464 const auto translate = MakeTranslation({-1.0f, 1.0f, 0.5f});
465 return translate * scale;
466 }

References impeller::TSize< T >::height, MakeScale(), MakeTranslation(), 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 468 of file matrix.h.

471 {
472 Scalar height = std::tan(fov_y.radians * 0.5f);
473 Scalar width = height * aspect_ratio;
474
475 // clang-format off
476 return {
477 1.0f / width, 0.0f, 0.0f, 0.0f,
478 0.0f, 1.0f / height, 0.0f, 0.0f,
479 0.0f, 0.0f, z_far / (z_far - z_near), 1.0f,
480 0.0f, 0.0f, -(z_far * z_near) / (z_far - z_near), 0.0f,
481 };
482 // clang-format on
483 }

References impeller::Radians::radians.

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

## ◆ MakePerspective() [2/2]

template<class T >

static constexpr Matrix impeller::Matrix::MakePerspective | ( | Radians | fov_y,
|  | TSize< T > | size,
|  | Scalar | z_near,
|  | Scalar | z_far
| ) |  |
| inline static constexpr

Definition at line 486 of file matrix.h.

489 {
490 return MakePerspective(fov_y, static_cast<Scalar>(size.width) / size.height,
491 z_near, z_far);
492 }

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 126 of file matrix.h.

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

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

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

## ◆ MakeRotation() [2/2]

static Matrix impeller::Matrix::MakeRotation | ( | Scalar | radians,
|  | const Vector4 & | r
| ) |  |
| inline static

Definition at line 151 of file matrix.h.

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

References Matrix(), impeller::Vector4::Normalize(), impeller::Vector4::x, impeller::Vector4::y, and impeller::Vector4::z.

## ◆ MakeRotationX()

static Matrix impeller::Matrix::MakeRotationX | ( | Radians | r | ) |
| inline static

Definition at line 182 of file matrix.h.

182 {
183 const Scalar cosine = cos(r.radians);
184 const Scalar sine = sin(r.radians);
185 // clang-format off
186 return Matrix(
187 1.0f, 0.0f, 0.0f, 0.0f,
188 0.0f, cosine, sine, 0.0f,
189 0.0f, -sine, cosine, 0.0f,
190 0.0f, 0.0f, 0.0f, 1.0f
191 );
192 // clang-format on
193 }

References Matrix(), and impeller::Radians::radians.

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

## ◆ MakeRotationY()

static Matrix impeller::Matrix::MakeRotationY | ( | Radians | r | ) |
| inline static

Definition at line 195 of file matrix.h.

195 {
196 const Scalar cosine = cos(r.radians);
197 const Scalar sine = sin(r.radians);
198
199 // clang-format off
200 return Matrix(
201 cosine, 0.0f, -sine, 0.0f,
202 0.0f, 1.0f, 0.0f, 0.0f,
203 sine, 0.0f, cosine, 0.0f,
204 0.0f, 0.0f, 0.0f, 1.0f
205 );
206 // clang-format on
207 }

References Matrix(), and impeller::Radians::radians.

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

## ◆ MakeRotationZ()

static Matrix impeller::Matrix::MakeRotationZ | ( | Radians | r | ) |
| inline static

Definition at line 209 of file matrix.h.

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

References Matrix(), and impeller::Radians::radians.

Referenced by 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::testing::TEST().

## ◆ MakeScale() [1/2]

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

Definition at line 113 of file matrix.h.

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

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

## ◆ MakeScale() [2/2]

static constexpr Matrix impeller::Matrix::MakeScale | ( | const Vector3 & | s | ) |
| 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::TRect< Scalar >::GetNormalizingTransform(), impeller::Snapshot::GetUVTransform(), MakeOrthographic(), MakeScale(), impeller::scene::importer::ParseGLTF(), impeller::scene::importer::ProcessNode(), impeller::SceneContents::Render(), impeller::TextureContents::RenderToSnapshot(), impeller::TiledTextureContents::RenderToSnapshot(), impeller::Canvas::Scale(), impeller::testing::TEST(), impeller::scene::testing::TEST_P(), and impeller::testing::TEST_P().

## ◆ MakeSkew()

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

Definition at line 117 of file matrix.h.

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

References Matrix().

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

## ◆ 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::DlDispatcher::drawShadow(), impeller::Canvas::DrawTextFrame(), impeller::AtlasContents::GenerateSubAtlas(), MakeOrthographic(), impeller::PipelineBlend(), impeller::scene::importer::ProcessNode(), impeller::SolidRRectBlurContents::Render(), impeller::TiledTextureContents::RenderToSnapshot(), impeller::TextureContents::RenderToSnapshot(), impeller::Contents::RenderToSnapshot(), impeller::Picture::Snapshot(), impeller::testing::TEST(), impeller::testing::TEST_P(), impeller::scene::testing::TEST_P(), and impeller::Canvas::Translate().

## ◆ Multiply()

constexpr Matrix impeller::Matrix::Multiply | ( | const Matrix & | o | ) | const
| inline constexpr

Definition at line 256 of file matrix.h.

256 {
257 // clang-format off
258 return Matrix(
259 m[0] * o.m[0] + m[4] * o.m[1] + m[8] * o.m[2] + m[12] * o.m[3],
260 m[1] * o.m[0] + m[5] * o.m[1] + m[9] * o.m[2] + m[13] * o.m[3],
261 m[2] * o.m[0] + m[6] * o.m[1] + m[10] * o.m[2] + m[14] * o.m[3],
262 m[3] * o.m[0] + m[7] * o.m[1] + m[11] * o.m[2] + m[15] * o.m[3],
263 m[0] * o.m[4] + m[4] * o.m[5] + m[8] * o.m[6] + m[12] * o.m[7],
264 m[1] * o.m[4] + m[5] * o.m[5] + m[9] * o.m[6] + m[13] * o.m[7],
265 m[2] * o.m[4] + m[6] * o.m[5] + m[10] * o.m[6] + m[14] * o.m[7],
266 m[3] * o.m[4] + m[7] * o.m[5] + m[11] * o.m[6] + m[15] * o.m[7],
267 m[0] * o.m[8] + m[4] * o.m[9] + m[8] * o.m[10] + m[12] * o.m[11],
268 m[1] * o.m[8] + m[5] * o.m[9] + m[9] * o.m[10] + m[13] * o.m[11],
269 m[2] * o.m[8] + m[6] * o.m[9] + m[10] * o.m[10] + m[14] * o.m[11],
270 m[3] * o.m[8] + m[7] * o.m[9] + m[11] * o.m[10] + m[15] * o.m[11],
271 m[0] * o.m[12] + m[4] * o.m[13] + m[8] * o.m[14] + m[12] * o.m[15],
272 m[1] * o.m[12] + m[5] * o.m[13] + m[9] * o.m[14] + m[13] * o.m[15],
273 m[2] * o.m[12] + m[6] * o.m[13] + m[10] * o.m[14] + m[14] * o.m[15],
274 m[3] * o.m[12] + m[7] * o.m[13] + m[11] * o.m[14] + m[15] * o.m[15]);
275 // clang-format on
276 }

References m, and Matrix().

Referenced by operator*().

## ◆ operator!=()

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

Definition at line 382 of file matrix.h.

382 {
383 // clang-format off
384 return vec[0] != m.vec[0]
385 || vec[1] != m.vec[1]
386 || vec[2] != m.vec[2]
387 || vec[3] != m.vec[3];
388 // clang-format on
389 }

References m, and vec.

## ◆ operator*() [1/4]

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

Definition at line 395 of file matrix.h.

395 { return Multiply(m); }

References m, and Multiply().

## ◆ operator*() [2/4]

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

Definition at line 420 of file matrix.h.

420 {
421 Scalar w = v.x * m[3] + v.y * m[7] + m[15];
422 Point result(v.x * m[0] + v.y * m[4] + m[12],
423 v.x * m[1] + v.y * m[5] + m[13]);
424
425 // This is Skia's behavior, but it may be reasonable to allow UB for the w=0
426 // case.
427 if (w) {
428 w = 1 / w;
429 }
430 return result * w;
431 }

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 406 of file matrix.h.

406 {
407 Scalar w = v.x * m[3] + v.y * m[7] + v.z * m[11] + m[15];
408 Vector3 result(v.x * m[0] + v.y * m[4] + v.z * m[8] + m[12],
409 v.x * m[1] + v.y * m[5] + v.z * m[9] + m[13],
410 v.x * m[2] + v.y * m[6] + v.z * m[10] + m[14]);
411
412 // This is Skia's behavior, but it may be reasonable to allow UB for the w=0
413 // case.
414 if (w) {
415 w = 1 / w;
416 }
417 return result * w;
418 }

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 399 of file matrix.h.

399 {
400 return Vector4(v.x * m[0] + v.y * m[4] + v.z * m[8] + v.w * m[12],
401 v.x * m[1] + v.y * m[5] + v.z * m[9] + v.w * m[13],
402 v.x * m[2] + v.y * m[6] + v.z * m[10] + v.w * m[14],
403 v.x * m[3] + v.y * m[7] + v.z * m[11] + v.w * m[15]);
404 }

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 391 of file matrix.h.

391 { return Translate(t); }

References Translate().

## ◆ operator-()

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

Definition at line 393 of file matrix.h.

393 { return Translate(-t); }

References Translate().

## ◆ operator==()

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

Definition at line 373 of file matrix.h.

373 {
374 // clang-format off
375 return vec[0] == m.vec[0]
376 && vec[1] == m.vec[1]
377 && vec[2] == m.vec[2]
378 && vec[3] == m.vec[3];
379 // clang-format on
380 }

References m, and vec.

## ◆ Scale()

constexpr Matrix impeller::Matrix::Scale | ( | const Vector3 & | s | ) | const
| inline constexpr

Definition at line 247 of file matrix.h.

247 {
248 // clang-format off
249 return Matrix(m[0] * s.x, m[1] * s.x, m[2] * s.x, m[3] * s.x,
250 m[4] * s.y, m[5] * s.y, m[6] * s.y, m[7] * s.y,
251 m[8] * s.z, m[9] * s.z, m[10] * s.z, m[11] * s.z,
252 m[12] , m[13] , m[14] , m[15] );
253 // clang-format on
254 }

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

## ◆ Transform()

constexpr Quad impeller::Matrix::Transform | ( | const Quad & | quad | ) | const
| inline constexpr

Definition at line 449 of file matrix.h.

449 {
450 return {
451 *this * quad[0],
452 *this * quad[1],
453 *this * quad[2],
454 *this * quad[3],
455 };
456 }

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

## ◆ TransformDirection() [1/3]

constexpr Vector2 impeller::Matrix::TransformDirection | ( | const Vector2 & | v | ) | const
| inline constexpr

Definition at line 445 of file matrix.h.

445 {
446 return Vector2(v.x * m[0] + v.y * m[4], v.x * m[1] + v.y * m[5]);
447 }

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 439 of file matrix.h.

439 {
440 return Vector3(v.x * m[0] + v.y * m[4] + v.z * m[8],
441 v.x * m[1] + v.y * m[5] + v.z * m[9],
442 v.x * m[2] + v.y * m[6] + v.z * m[10]);
443 }

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 433 of file matrix.h.

433 {
434 return Vector4(v.x * m[0] + v.y * m[4] + v.z * m[8],
435 v.x * m[1] + v.y * m[5] + v.z * m[9],
436 v.x * m[2] + v.y * m[6] + v.z * m[10], v.w);
437 }

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

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

## ◆ Translate()

constexpr Matrix impeller::Matrix::Translate | ( | const Vector3 & | t | ) | const
| inline constexpr

Definition at line 235 of file matrix.h.

235 {
236 // clang-format off
237 return Matrix(m[0], m[1], m[2], m[3],
238 m[4], m[5], m[6], m[7],
239 m[8], m[9], m[10], m[11],
240 m[0] * t.x + m[4] * t.y + m[8] * t.z + m[12],
241 m[1] * t.x + m[5] * t.y + m[9] * t.z + m[13],
242 m[2] * t.x + m[6] * t.y + m[10] * t.z + m[14],
243 m[15]);
244 // clang-format on
245 }

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

Referenced by ImGui_ImplImpeller_RenderDrawData(), operator+(), and operator-().

## ◆ Transpose()

constexpr Matrix impeller::Matrix::Transpose | ( |  | ) | const
| inline constexpr

Definition at line 278 of file matrix.h.

278 {
279 // clang-format off
280 return {
281 m[0], m[4], m[8], m[12],
282 m[1], m[5], m[9], m[13],
283 m[2], m[6], m[10], m[14],
284 m[3], m[7], m[11], m[15],
285 };
286 // clang-format on
287 }

References m.

Referenced by Decompose().

## Member Data Documentation

## ◆ @13

union { ... }

## ◆ e

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

Definition at line 40 of file matrix.h.

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

## ◆ m

Scalar impeller::Matrix::m[16]

Definition at line 39 of file matrix.h.

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

## ◆ vec

Vector4 impeller::Matrix::vec[4]

Definition at line 41 of file matrix.h.

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

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

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

impeller::Matrix::m
Scalar m[16]
Definition: matrix.h:39
impeller::Matrix::Matrix
constexpr Matrix()
Definition: matrix.h:47
impeller::Scalar
float Scalar
Definition: scalar.h:18
impeller::Vector3::Combine
static constexpr Vector3 Combine(const Vector3 &a, Scalar aScale, const Vector3 &b, Scalar bScale)
Definition: vector.h:192
impeller::Vector2
Point Vector2
Definition: point.h:312
impeller::Matrix::MakeTranslation
static constexpr Matrix MakeTranslation(const Vector3 &t)
Definition: matrix.h:95
impeller::Matrix::e
Scalar e[4][4]
Definition: matrix.h:40
impeller::Matrix::vec
Vector4 vec[4]
Definition: matrix.h:41
impeller::Matrix::MakePerspective
static constexpr Matrix MakePerspective(Radians fov_y, Scalar aspect_ratio, Scalar z_near, Scalar z_far)
Definition: matrix.h:468
impeller::Matrix::Basis
constexpr Matrix Basis() const
The Matrix without its w components (without translation).
Definition: matrix.h:224
impeller::Point
TPoint< Scalar > Point
Definition: point.h:308
impeller::Matrix::Multiply
constexpr Matrix Multiply(const Matrix &o) const
Definition: matrix.h:256
impeller::Matrix::Translate
constexpr Matrix Translate(const Vector3 &t) const
Definition: matrix.h:235
impeller::ScalarNearlyZero
constexpr bool ScalarNearlyZero(Scalar x, Scalar tolerance=kEhCloseEnough)
Definition: scalar.h:25
impeller::Matrix::GetBasisZ
constexpr Vector3 GetBasisZ() const
Definition: matrix.h:301
impeller::Matrix::Invert
Matrix Invert() const
Definition: matrix.cc:97
impeller::Matrix::GetBasisY
constexpr Vector3 GetBasisY() const
Definition: matrix.h:299
impeller::Matrix::MakeScale
static constexpr Matrix MakeScale(const Vector3 &s)
Definition: matrix.h:104
impeller::Matrix::GetBasisX
constexpr Vector3 GetBasisX() const
Definition: matrix.h:297