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rect.h
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1 // Copyright 2013 The Flutter Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style license that can be
3 // found in the LICENSE file.
4
5 #ifndef FLUTTER_IMPELLER_GEOMETRY_RECT_H_
6 #define FLUTTER_IMPELLER_GEOMETRY_RECT_H_
7
8 #include <array>
9 #include <optional>
10 #include <ostream>
11 #include <vector>
12
13 #include "fml/logging.h"
14 #include "impeller/geometry/matrix.h"
15 #include "impeller/geometry/point.h"
16 #include "impeller/geometry/saturated_math.h"
17 #include "impeller/geometry/scalar.h"
18 #include "impeller/geometry/size.h"
19
20 namespace impeller {
21
22 #define ONLY_ON_FLOAT_M(Modifiers, Return) \
23 template <typename U = T> \
24 Modifiers std::enable_if_t<std::is_floating_point_v<U>, Return>
25 #define ONLY_ON_FLOAT(Return) DL_ONLY_ON_FLOAT_M(, Return)
26
27 /// Templated struct for holding an axis-aligned rectangle.
28 ///
29 /// Rectangles are defined as 4 axis-aligned edges that might contain
30 /// space. They can be viewed as 2 X coordinates that define the
31 /// left and right edges and 2 Y coordinates that define the top and
32 /// bottom edges; or they can be viewed as an origin and horizontal
33 /// and vertical dimensions (width and height).
34 ///
35 /// When the left and right edges are equal or reversed (right <= left)
36 /// or the top and bottom edges are equal or reversed (bottom <= top),
37 /// the rectangle is considered empty. Considering the rectangle in XYWH
38 /// form, the width and/or the height would be negative or zero. Such
39 /// reversed/empty rectangles contain no space and act as such in the
40 /// methods that operate on them (Intersection, Union, IntersectsWithRect,
41 /// Contains, Cutout, etc.)
42 ///
43 /// Rectangles cannot be modified by any method and a new value can only
44 /// be stored into an existing rect using assignment. This keeps the API
45 /// clean compared to implementations that might have similar methods
46 /// that produce the answer in place, or construct a new object with
47 /// the answer, or place the result in an indicated result object.
48 ///
49 /// Methods that might fail to produce an answer will use |std::optional|
50 /// to indicate that success or failure (see |Intersection| and |CutOut|).
51 /// For convenience, |Intersection| and |Union| both have overloaded
52 /// variants that take |std::optional| arguments and treat them as if
53 /// the argument was an empty rect to allow chaining multiple such methods
54 /// and only needing to check the optional condition of the final result.
55 /// The primary methods also provide |...OrEmpty| overloaded variants that
56 /// translate an empty optional answer into a simple empty rectangle of the
57 /// same type.
58 ///
59 /// Rounding instance methods are not provided as the return value might
60 /// be wanted as another floating point rectangle or sometimes as an integer
61 /// rectangle. Instead a |RoundOut| factory, defined only for floating point
62 /// input rectangles, is provided to provide control over the result type.
63 ///
64 /// NaN and Infinity values
65 ///
66 /// Constructing an LTRB rectangle using Infinity values should work as
67 /// expected with either 0 or +Infinity returned as dimensions depending on
68 /// which side the Infinity values are on and the sign.
69 ///
70 /// Constructing an XYWH rectangle using Infinity values will usually
71 /// not work if the math requires the object to compute a right or bottom
72 /// edge from ([xy] -Infinity + [wh] +Infinity). Other combinations might
73 /// work.
74 ///
75 /// The special factory |MakeMaximum| is provided to construct a rectangle
76 /// of the indicated coordinate type that covers all finite coordinates.
77 /// It does not use infinity values, but rather the largest finite values
78 /// to avoid math that might produce a NaN value from various getters.
79 ///
80 /// Any rectangle that is constructed with, or computed to have a NaN value
81 /// will be considered the same as any empty rectangle.
82 ///
83 /// Empty Rectangle canonical results summary:
84 ///
85 /// Union will ignore any empty rects and return the other rect
86 /// Intersection will return nullopt if either rect is empty
87 /// IntersectsWithRect will return false if either rect is empty
88 /// Cutout will return the source rect if the argument is empty
89 /// Cutout will return nullopt if the source rectangle is empty
90 /// Contains(Point) will return false if the source rectangle is empty
91 /// Contains(Rect) will return false if the source rectangle is empty
92 /// Contains(Rect) will otherwise return true if the argument is empty
93 /// Specifically, EmptyRect.Contains(EmptyRect) returns false
94 ///
95 /// ---------------
96 /// Special notes on problems using the XYWH form of specifying rectangles:
97 ///
98 /// It is possible to have integer rectangles whose dimensions exceed
99 /// the maximum number that their coordinates can represent since
100 /// (MAX_INT - MIN_INT) overflows the representable positive numbers.
101 /// Floating point rectangles technically have a similar issue in that
102 /// overflow can occur, but it will be automatically converted into
103 /// either an infinity, or a finite-overflow value and still be
104 /// representable, just with little to no precision.
105 ///
106 /// Secondly, specifying a rectangle using XYWH leads to cases where the
107 /// math for (x+w) and/or (y+h) are also beyond the maximum representable
108 /// coordinates. For N-bit integer rectangles declared as XYWH, the
109 /// maximum right coordinate will require N+1 signed bits which cannot be
110 /// stored in storage that uses N-bit integers.
111 ///
112 /// Saturated math is used when constructing a rectangle from XYWH values
113 /// and when returning the dimensions of the rectangle. Constructing an
114 /// integer rectangle from values such that xy + wh is beyond the range
115 /// of the integer type will place the right or bottom edges at the maximum
116 /// value for the integer type. Similarly, constructing an integer rectangle
117 /// such that the distance from the left to the right (or top to bottom) is
118 /// greater than the range of the integer type will simply return the
119 /// maximum integer value as the dimension. Floating point rectangles are
120 /// naturally saturated by the rules of IEEE arithmetic.
121 template <class T>
122 struct TRect {
123 private:
124 using Type = T;
125
126 public:
127 constexpr TRect() : left_(0), top_(0), right_(0), bottom_(0) {}
128
129 constexpr static TRect MakeLTRB(Type left,
130 Type top,
131 Type right,
132 Type bottom) {
133 return TRect(left, top, right, bottom);
134 }
135
136 constexpr static TRect MakeXYWH(Type x, Type y, Type width, Type height) {
137 return TRect(x, y, saturated::Add(x, width), saturated::Add(y, height));
138 }
139
140 constexpr static TRect MakeOriginSize(const TPoint<Type>& origin,
141 const TSize<Type>& size) {
142 return MakeXYWH(origin.x, origin.y, size.width, size.height);
143 }
144
145 template <class U>
146 constexpr static TRect MakeSize(const TSize<U>& size) {
147 return TRect(0.0, 0.0, size.width, size.height);
148 }
149
150 template <typename U>
151 constexpr static std::optional<TRect> MakePointBounds(const U& value) {
152 return MakePointBounds(value.begin(), value.end());
153 }
154
155 template <typename PointIter>
156 constexpr static std::optional<TRect> MakePointBounds(const PointIter first,
157 const PointIter last) {
158 if (first == last) {
159 return std::nullopt;
160 }
161 auto left = first->x;
162 auto top = first->y;
163 auto right = first->x;
164 auto bottom = first->y;
165 for (auto it = first + 1; it < last; ++it) {
166 left = std::min(left, it->x);
167 top = std::min(top, it->y);
168 right = std::max(right, it->x);
169 bottom = std::max(bottom, it->y);
170 }
171 return TRect::MakeLTRB(left, top, right, bottom);
172 }
173
174 [[nodiscard]] constexpr static TRect MakeMaximum() {
175 return TRect::MakeLTRB(std::numeric_limits<Type>::lowest(),
176 std::numeric_limits<Type>::lowest(),
177 std::numeric_limits<Type>::max(),
178 std::numeric_limits<Type>::max());
179 }
180
181 [[nodiscard]] constexpr bool operator==(const TRect& r) const {
182 return left_ == r.left_ && //
183 top_ == r.top_ && //
184 right_ == r.right_ && //
185 bottom_ == r.bottom_;
186 }
187
188 [[nodiscard]] constexpr bool operator!=(const TRect& r) const {
189 return !(*this == r);
190 }
191
192 [[nodiscard]] constexpr TRect Scale(Type scale) const {
193 return TRect(left_ * scale, //
194 top_ * scale, //
195 right_ * scale, //
196 bottom_ * scale);
197 }
198
199 [[nodiscard]] constexpr TRect Scale(Type scale_x, Type scale_y) const {
200 return TRect(left_ * scale_x, //
201 top_ * scale_y, //
202 right_ * scale_x, //
203 bottom_ * scale_y);
204 }
205
206 [[nodiscard]] constexpr TRect Scale(TPoint<T> scale) const {
207 return Scale(scale.x, scale.y);
208 }
209
210 [[nodiscard]] constexpr TRect Scale(TSize<T> scale) const {
211 return Scale(scale.width, scale.height);
212 }
213
214 /// @brief Returns true iff the provided point |p| is inside the
215 /// half-open interior of this rectangle.
216 ///
217 /// For purposes of containment, a rectangle contains points
218 /// along the top and left edges but not points along the
219 /// right and bottom edges so that a point is only ever
220 /// considered inside one of two abutting rectangles.
221 [[nodiscard]] constexpr bool Contains(const TPoint<Type>& p) const {
222 return !this->IsEmpty() && //
223 p.x >= left_ && //
224 p.y >= top_ && //
225 p.x < right_ && //
226 p.y < bottom_;
227 }
228
229 /// @brief Returns true iff the provided point |p| is inside the
230 /// closed-range interior of this rectangle.
231 ///
232 /// Unlike the regular |Contains(TPoint)| method, this method
233 /// considers all points along the boundary of the rectangle
234 /// to be contained within the rectangle - useful for testing
235 /// if vertices that define a filled shape would carry the
236 /// interior of that shape outside the bounds of the rectangle.
237 /// Since both geometries are defining half-open spaces, their
238 /// defining geometry needs to consider their boundaries to
239 /// be equivalent with respect to interior and exterior.
240 [[nodiscard]] constexpr bool ContainsInclusive(const TPoint<Type>& p) const {
241 return !this->IsEmpty() && //
242 p.x >= left_ && //
243 p.y >= top_ && //
244 p.x <= right_ && //
245 p.y <= bottom_;
246 }
247
248 /// @brief Returns true iff this rectangle is not empty and it also
249 /// contains every point considered inside the provided
250 /// rectangle |o| (as determined by |Contains(TPoint)|).
251 ///
252 /// This is similar to a definition where the result is true iff
253 /// the union of the two rectangles is equal to this rectangle,
254 /// ignoring precision issues with performing those operations
255 /// and assuming that empty rectangles are never equal.
256 ///
257 /// An empty rectangle can contain no other rectangle.
258 ///
259 /// An empty rectangle is, however, contained within any
260 /// other non-empy rectangle as the set of points it contains
261 /// is an empty set and so there are no points to fail the
262 /// containment criteria.
263 [[nodiscard]] constexpr bool Contains(const TRect& o) const {
264 return !this->IsEmpty() && //
265 (o.IsEmpty() || (o.left_ >= left_ && //
266 o.top_ >= top_ && //
267 o.right_ <= right_ && //
268 o.bottom_ <= bottom_));
269 }
270
271 /// @brief Returns true if all of the fields of this floating point
272 /// rectangle are finite.
273 ///
274 /// Note that the results of |GetWidth()| and |GetHeight()| may
275 /// still be infinite due to overflow even if the fields themselves
276 /// are finite.
277 ONLY_ON_FLOAT_M([[nodiscard]] constexpr, bool)
278 IsFinite() const {
279 return std::isfinite(left_) && //
280 std::isfinite(top_) && //
281 std::isfinite(right_) && //
282 std::isfinite(bottom_);
283 }
284
285 /// @brief Returns true if either of the width or height are 0, negative,
286 /// or NaN.
287 [[nodiscard]] constexpr bool IsEmpty() const {
288 // Computing the non-empty condition and negating the result causes any
289 // NaN value to return true - i.e. is considered empty.
290 return !(left_ < right_ && top_ < bottom_);
291 }
292
293 /// @brief Returns true if width and height are equal and neither is NaN.
294 [[nodiscard]] constexpr bool IsSquare() const {
295 // empty rectangles can technically be "square", but would be
296 // misleading to most callers. Using |IsEmpty| also prevents
297 // "non-empty and non-overflowing" computations from happening
298 // to be equal to "empty and overflowing" results.
299 // (Consider LTRB(10, 15, MAX-2, MIN+2) which is empty, but both
300 // w/h subtractions equal "5").
301 return !IsEmpty() && (right_ - left_) == (bottom_ - top_);
302 }
303
304 [[nodiscard]] constexpr bool IsMaximum() const {
305 return *this == MakeMaximum();
306 }
307
308 /// @brief Returns the upper left corner of the rectangle as specified
309 /// by the left/top or x/y values when it was constructed.
310 [[nodiscard]] constexpr TPoint<Type> GetOrigin() const {
311 return {left_, top_};
312 }
313
314 /// @brief Returns the size of the rectangle which may be negative in
315 /// either width or height and may have been clipped to the
316 /// maximum integer values for integer rects whose size overflows.
317 [[nodiscard]] constexpr TSize<Type> GetSize() const {
318 return {GetWidth(), GetHeight()};
319 }
320
321 /// @brief Returns the X coordinate of the upper left corner, equivalent
322 /// to |GetOrigin().x|
323 [[nodiscard]] constexpr Type GetX() const { return left_; }
324
325 /// @brief Returns the Y coordinate of the upper left corner, equivalent
326 /// to |GetOrigin().y|
327 [[nodiscard]] constexpr Type GetY() const { return top_; }
328
329 /// @brief Returns the width of the rectangle, equivalent to
330 /// |GetSize().width|
331 [[nodiscard]] constexpr Type GetWidth() const {
332 return saturated::Sub(right_, left_);
333 }
334
335 /// @brief Returns the height of the rectangle, equivalent to
336 /// |GetSize().height|
337 [[nodiscard]] constexpr Type GetHeight() const {
338 return saturated::Sub(bottom_, top_);
339 }
340
341 [[nodiscard]] constexpr auto GetLeft() const { return left_; }
342
343 [[nodiscard]] constexpr auto GetTop() const { return top_; }
344
345 [[nodiscard]] constexpr auto GetRight() const { return right_; }
346
347 [[nodiscard]] constexpr auto GetBottom() const { return bottom_; }
348
349 [[nodiscard]] constexpr TPoint<T> GetLeftTop() const { //
350 return {left_, top_};
351 }
352
353 [[nodiscard]] constexpr TPoint<T> GetRightTop() const {
354 return {right_, top_};
355 }
356
357 [[nodiscard]] constexpr TPoint<T> GetLeftBottom() const {
358 return {left_, bottom_};
359 }
360
361 [[nodiscard]] constexpr TPoint<T> GetRightBottom() const {
362 return {right_, bottom_};
363 }
364
365 /// @brief Get the area of the rectangle, equivalent to |GetSize().Area()|
366 [[nodiscard]] constexpr T Area() const {
367 // TODO(flutter/flutter#141710) - Use saturated math to avoid overflow
368 // https://github.com/flutter/flutter/issues/141710
369 return IsEmpty() ? 0 : (right_ - left_) * (bottom_ - top_);
370 }
371
372 /// @brief Get the center point as a |Point|.
373 [[nodiscard]] constexpr Point GetCenter() const {
374 return {saturated::AverageScalar(left_, right_),
375 saturated::AverageScalar(top_, bottom_)};
376 }
377
378 [[nodiscard]] constexpr std::array<T, 4> GetLTRB() const {
379 return {left_, top_, right_, bottom_};
380 }
381
382 /// @brief Get the x, y coordinates of the origin and the width and
383 /// height of the rectangle in an array.
384 [[nodiscard]] constexpr std::array<T, 4> GetXYWH() const {
385 return {left_, top_, GetWidth(), GetHeight()};
386 }
387
388 /// @brief Get a version of this rectangle that has a non-negative size.
389 [[nodiscard]] constexpr TRect GetPositive() const {
390 if (!IsEmpty()) {
391 return *this;
392 }
393 return {
394 std::min(left_, right_),
395 std::min(top_, bottom_),
396 std::max(left_, right_),
397 std::max(top_, bottom_),
398 };
399 }
400
401 /// @brief Get the points that represent the 4 corners of this rectangle
402 /// in a Z order that is compatible with triangle strips or a set
403 /// of all zero points if the rectangle is empty.
404 /// The order is: Top left, top right, bottom left, bottom right.
405 [[nodiscard]] constexpr std::array<TPoint<T>, 4> GetPoints() const {
406 if (IsEmpty()) {
407 return {};
408 }
409 return {
410 TPoint{left_, top_},
411 TPoint{right_, top_},
412 TPoint{left_, bottom_},
413 TPoint{right_, bottom_},
414 };
415 }
416
417 [[nodiscard]] constexpr std::array<TPoint<T>, 4> GetTransformedPoints(
418 const Matrix& transform) const {
419 auto points = GetPoints();
420 for (size_t i = 0; i < points.size(); i++) {
421 points[i] = transform * points[i];
422 }
423 return points;
424 }
425
426 /// @brief Creates a new bounding box that contains this transformed
427 /// rectangle, clipped against the near clipping plane if
428 /// necessary.
429 [[nodiscard]] constexpr TRect TransformAndClipBounds(
430 const Matrix& transform) const {
431 if (!transform.HasPerspective2D()) {
432 return TransformBounds(transform);
433 }
434
435 if (IsEmpty()) {
436 return {};
437 }
438
439 auto ul = transform.TransformHomogenous({left_, top_});
440 auto ur = transform.TransformHomogenous({right_, top_});
441 auto ll = transform.TransformHomogenous({left_, bottom_});
442 auto lr = transform.TransformHomogenous({right_, bottom_});
443
444 // It can probably be proven that we only ever have 5 points at most
445 // which happens when only 1 corner is clipped and we get 2 points
446 // in return for it as we interpolate against its neighbors.
447 Point points[8];
448 int index = 0;
449
450 // Process (clip and interpolate) each point against its 2 neighbors:
451 // left, pt, right
452 index = ClipAndInsert(points, index, ll, ul, ur);
453 index = ClipAndInsert(points, index, ul, ur, lr);
454 index = ClipAndInsert(points, index, ur, lr, ll);
455 index = ClipAndInsert(points, index, lr, ll, ul);
456
457 auto bounds = TRect::MakePointBounds(points, points + index);
458 return bounds.value_or(TRect{});
459 }
460
461 /// @brief Creates a new bounding box that contains this transformed
462 /// rectangle.
463 [[nodiscard]] constexpr TRect TransformBounds(const Matrix& transform) const {
464 if (IsEmpty()) {
465 return {};
466 }
467 auto points = GetTransformedPoints(transform);
468 auto bounds = TRect::MakePointBounds(points.begin(), points.end());
469 if (bounds.has_value()) {
470 return bounds.value();
471 }
472 FML_UNREACHABLE();
473 }
474
475 /// @brief Constructs a Matrix that will map all points in the coordinate
476 /// space of the rectangle into a new normalized coordinate space
477 /// where the upper left corner of the rectangle maps to (0, 0)
478 /// and the lower right corner of the rectangle maps to (1, 1).
479 ///
480 /// Empty and non-finite rectangles will return a zero-scaling
481 /// transform that maps all points to (0, 0).
482 [[nodiscard]] constexpr Matrix GetNormalizingTransform() const {
483 if (!IsEmpty()) {
484 Scalar sx = 1.0 / GetWidth();
485 Scalar sy = 1.0 / GetHeight();
486 Scalar tx = left_ * -sx;
487 Scalar ty = top_ * -sy;
488
489 // Exclude NaN and infinities and either scale underflowing to zero
490 if (sx != 0.0 && sy != 0.0 && 0.0 * sx * sy * tx * ty == 0.0) {
491 // clang-format off
492 return Matrix( sx, 0.0f, 0.0f, 0.0f,
493 0.0f, sy, 0.0f, 0.0f,
494 0.0f, 0.0f, 1.0f, 0.0f,
495 tx, ty, 0.0f, 1.0f);
496 // clang-format on
497 }
498 }
499
500 // Map all coordinates to the origin.
501 return Matrix::MakeScale({0.0f, 0.0f, 1.0f});
502 }
503
504 [[nodiscard]] constexpr TRect Union(const TRect& o) const {
505 if (IsEmpty()) {
506 return o;
507 }
508 if (o.IsEmpty()) {
509 return *this;
510 }
511 return {
512 std::min(left_, o.left_),
513 std::min(top_, o.top_),
514 std::max(right_, o.right_),
515 std::max(bottom_, o.bottom_),
516 };
517 }
518
519 [[nodiscard]] constexpr std::optional<TRect> Intersection(
520 const TRect& o) const {
521 if (IntersectsWithRect(o)) {
522 return TRect{
523 std::max(left_, o.left_),
524 std::max(top_, o.top_),
525 std::min(right_, o.right_),
526 std::min(bottom_, o.bottom_),
527 };
528 } else {
529 return std::nullopt;
530 }
531 }
532
533 [[nodiscard]] constexpr bool IntersectsWithRect(const TRect& o) const {
534 return !IsEmpty() && //
535 !o.IsEmpty() && //
536 left_ < o.right_ && //
537 top_ < o.bottom_ && //
538 right_ > o.left_ && //
539 bottom_ > o.top_;
540 }
541
542 /// @brief Returns the new boundary rectangle that would result from this
543 /// rectangle being cut out by the specified rectangle.
544 [[nodiscard]] constexpr std::optional<TRect<T>> Cutout(const TRect& o) const {
545 if (IsEmpty()) {
546 // This test isn't just a short-circuit, it also prevents the concise
547 // math below from returning the wrong answer on empty rects.
548 // Once we know that this rectangle is not empty, the math below can
549 // only succeed in computing a value if o is also non-empty and non-nan.
550 // Otherwise, the method returns *this by default.
551 return std::nullopt;
552 }
553
554 const auto& [a_left, a_top, a_right, a_bottom] = GetLTRB(); // Source rect.
555 const auto& [b_left, b_top, b_right, b_bottom] = o.GetLTRB(); // Cutout.
556 if (b_left <= a_left && b_right >= a_right) {
557 if (b_top <= a_top && b_bottom >= a_bottom) {
558 // Full cutout.
559 return std::nullopt;
560 }
561 if (b_top <= a_top && b_bottom > a_top) {
562 // Cuts off the top.
563 return TRect::MakeLTRB(a_left, b_bottom, a_right, a_bottom);
564 }
565 if (b_bottom >= a_bottom && b_top < a_bottom) {
566 // Cuts off the bottom.
567 return TRect::MakeLTRB(a_left, a_top, a_right, b_top);
568 }
569 }
570 if (b_top <= a_top && b_bottom >= a_bottom) {
571 if (b_left <= a_left && b_right > a_left) {
572 // Cuts off the left.
573 return TRect::MakeLTRB(b_right, a_top, a_right, a_bottom);
574 }
575 if (b_right >= a_right && b_left < a_right) {
576 // Cuts off the right.
577 return TRect::MakeLTRB(a_left, a_top, b_left, a_bottom);
578 }
579 }
580
581 return *this;
582 }
583
584 [[nodiscard]] constexpr TRect CutoutOrEmpty(const TRect& o) const {
585 return Cutout(o).value_or(TRect());
586 }
587
588 /// @brief Returns a new rectangle translated by the given offset.
589 [[nodiscard]] constexpr TRect<T> Shift(T dx, T dy) const {
590 return {
591 saturated::Add(left_, dx), //
592 saturated::Add(top_, dy), //
593 saturated::Add(right_, dx), //
594 saturated::Add(bottom_, dy), //
595 };
596 }
597
598 /// @brief Returns a new rectangle translated by the given offset.
599 [[nodiscard]] constexpr TRect<T> Shift(TPoint<T> offset) const {
600 return Shift(offset.x, offset.y);
601 }
602
603 /// @brief Returns a rectangle with expanded edges. Negative expansion
604 /// results in shrinking.
605 [[nodiscard]] constexpr TRect<T> Expand(T left,
606 T top,
607 T right,
608 T bottom) const {
609 return {
610 saturated::Sub(left_, left), //
611 saturated::Sub(top_, top), //
612 saturated::Add(right_, right), //
613 saturated::Add(bottom_, bottom), //
614 };
615 }
616
617 /// @brief Returns a rectangle with expanded edges in all directions.
618 /// Negative expansion results in shrinking.
619 [[nodiscard]] constexpr TRect<T> Expand(T amount) const {
620 return {
621 saturated::Sub(left_, amount), //
622 saturated::Sub(top_, amount), //
623 saturated::Add(right_, amount), //
624 saturated::Add(bottom_, amount), //
625 };
626 }
627
628 /// @brief Returns a rectangle with expanded edges in all directions.
629 /// Negative expansion results in shrinking.
630 [[nodiscard]] constexpr TRect<T> Expand(T horizontal_amount,
631 T vertical_amount) const {
632 return {
633 saturated::Sub(left_, horizontal_amount), //
634 saturated::Sub(top_, vertical_amount), //
635 saturated::Add(right_, horizontal_amount), //
636 saturated::Add(bottom_, vertical_amount), //
637 };
638 }
639
640 /// @brief Returns a rectangle with expanded edges in all directions.
641 /// Negative expansion results in shrinking.
642 [[nodiscard]] constexpr TRect<T> Expand(TPoint<T> amount) const {
643 return Expand(amount.x, amount.y);
644 }
645
646 /// @brief Returns a rectangle with expanded edges in all directions.
647 /// Negative expansion results in shrinking.
648 [[nodiscard]] constexpr TRect<T> Expand(TSize<T> amount) const {
649 return Expand(amount.width, amount.height);
650 }
651
652 /// @brief Returns a new rectangle that represents the projection of the
653 /// source rectangle onto this rectangle. In other words, the source
654 /// rectangle is redefined in terms of the coordinate space of this
655 /// rectangle.
656 [[nodiscard]] constexpr TRect<T> Project(TRect<T> source) const {
657 if (IsEmpty()) {
658 return {};
659 }
660 return source.Shift(-left_, -top_)
661 .Scale(1.0 / static_cast<Scalar>(GetWidth()),
662 1.0 / static_cast<Scalar>(GetHeight()));
663 }
664
665 ONLY_ON_FLOAT_M([[nodiscard]] constexpr static, TRect)
666 RoundOut(const TRect<U>& r) {
667 return TRect::MakeLTRB(saturated::Cast<U, Type>(floor(r.GetLeft())),
668 saturated::Cast<U, Type>(floor(r.GetTop())),
669 saturated::Cast<U, Type>(ceil(r.GetRight())),
670 saturated::Cast<U, Type>(ceil(r.GetBottom())));
671 }
672
673 ONLY_ON_FLOAT_M([[nodiscard]] constexpr static, TRect)
674 Round(const TRect<U>& r) {
675 return TRect::MakeLTRB(saturated::Cast<U, Type>(round(r.GetLeft())),
676 saturated::Cast<U, Type>(round(r.GetTop())),
677 saturated::Cast<U, Type>(round(r.GetRight())),
678 saturated::Cast<U, Type>(round(r.GetBottom())));
679 }
680
681 [[nodiscard]] constexpr static std::optional<TRect> Union(
682 const TRect& a,
683 const std::optional<TRect> b) {
684 return b.has_value() ? a.Union(b.value()) : a;
685 }
686
687 [[nodiscard]] constexpr static std::optional<TRect> Union(
688 const std::optional<TRect> a,
689 const TRect& b) {
690 return a.has_value() ? a->Union(b) : b;
691 }
692
693 [[nodiscard]] constexpr static std::optional<TRect> Union(
694 const std::optional<TRect> a,
695 const std::optional<TRect> b) {
696 return a.has_value() ? Union(a.value(), b) : b;
697 }
698
699 [[nodiscard]] constexpr static std::optional<TRect> Intersection(
700 const TRect& a,
701 const std::optional<TRect> b) {
702 return b.has_value() ? a.Intersection(b.value()) : a;
703 }
704
705 [[nodiscard]] constexpr static std::optional<TRect> Intersection(
706 const std::optional<TRect> a,
707 const TRect& b) {
708 return a.has_value() ? a->Intersection(b) : b;
709 }
710
711 [[nodiscard]] constexpr static std::optional<TRect> Intersection(
712 const std::optional<TRect> a,
713 const std::optional<TRect> b) {
714 return a.has_value() ? Intersection(a.value(), b) : b;
715 }
716
717 private:
718 constexpr TRect(Type left, Type top, Type right, Type bottom)
719 : left_(left), top_(top), right_(right), bottom_(bottom) {}
720
721 Type left_;
722 Type top_;
723 Type right_;
724 Type bottom_;
725
726 static constexpr Scalar kMinimumHomogenous = 1.0f / (1 << 14);
727
728 // Clip p against the near clipping plane (W = kMinimumHomogenous)
729 // and interpolate a crossing point against the nearby neighbors
730 // left and right if p is clipped and either of them is not.
731 // This method can produce 0, 1, or 2 points per call depending on
732 // how many of the points are clipped.
733 // 0 - all points are clipped
734 // 1 - p is unclipped OR
735 // p is clipped and exactly one of the neighbors is not
736 // 2 - p is clipped and both neighbors are not
737 static constexpr int ClipAndInsert(Point clipped[],
738 int index,
739 const Vector3& left,
740 const Vector3& p,
741 const Vector3& right) {
742 if (p.z >= kMinimumHomogenous) {
743 clipped[index++] = {p.x / p.z, p.y / p.z};
744 } else {
745 index = InterpolateAndInsert(clipped, index, p, left);
746 index = InterpolateAndInsert(clipped, index, p, right);
747 }
748 return index;
749 }
750
751 // Interpolate (a clipped) point p against one of its neighbors
752 // and insert the point into the array where the line between them
753 // veers from clipped space to unclipped, if such a point exists.
754 static constexpr int InterpolateAndInsert(Point clipped[],
755 int index,
756 const Vector3& p,
757 const Vector3& neighbor) {
758 if (neighbor.z >= kMinimumHomogenous) {
759 auto t = (kMinimumHomogenous - p.z) / (neighbor.z - p.z);
760 clipped[index++] = {
761 (t * p.x + (1.0f - t) * neighbor.x) / kMinimumHomogenous,
762 (t * p.y + (1.0f - t) * neighbor.y) / kMinimumHomogenous,
763 };
764 }
765 return index;
766 }
767 };
768
769 using Rect = TRect<Scalar>;
770 using IRect32 = TRect<int32_t>;
771 using IRect64 = TRect<int64_t>;
772 using IRect = IRect64;
773
774 #undef ONLY_ON_FLOAT
775 #undef ONLY_ON_FLOAT_M
776
777 } // namespace impeller
778
779 namespace std {
780
781 template <class T>
782 inline std::ostream& operator<<(std::ostream& out,
783 const impeller::TRect<T>& r) {
784 out << "(" << r.GetOrigin() << ", " << r.GetSize() << ")";
785 return out;
786 }
787
788 } // namespace std
789
790 #endif // FLUTTER_IMPELLER_GEOMETRY_RECT_H_
impeller::TRect::Union
constexpr static std::optional< TRect > Union(const std::optional< TRect > a, const TRect &b)
Definition: rect.h:687
impeller::TRect::GetLTRB
constexpr std::array< T, 4 > GetLTRB() const
Definition: rect.h:378
point.h
impeller::TPoint::y
Type y
Definition: point.h:31
impeller::Scalar
float Scalar
Definition: scalar.h:18
impeller::TRect::Expand
constexpr TRect< T > Expand(T horizontal_amount, T vertical_amount) const
Returns a rectangle with expanded edges in all directions. Negative expansion results in shrinking.
Definition: rect.h:630
impeller::TRect::MakeXYWH
constexpr static TRect MakeXYWH(Type x, Type y, Type width, Type height)
Definition: rect.h:136
impeller::TRect::Expand
constexpr TRect< T > Expand(T amount) const
Returns a rectangle with expanded edges in all directions. Negative expansion results in shrinking.
Definition: rect.h:619
saturated_math.h
impeller::TRect::TransformBounds
constexpr TRect TransformBounds(const Matrix &transform) const
Creates a new bounding box that contains this transformed rectangle.
Definition: rect.h:463
impeller::TRect::IsMaximum
constexpr bool IsMaximum() const
Definition: rect.h:304
impeller::TRect::GetLeftTop
constexpr TPoint< T > GetLeftTop() const
Definition: rect.h:349
impeller::TRect::Intersection
constexpr std::optional< TRect > Intersection(const TRect &o) const
Definition: rect.h:519
impeller::TRect::Scale
constexpr TRect Scale(Type scale_x, Type scale_y) const
Definition: rect.h:199
impeller::TRect::GetNormalizingTransform
constexpr Matrix GetNormalizingTransform() const
Constructs a Matrix that will map all points in the coordinate space of the rectangle into a new norm...
Definition: rect.h:482
impeller::TRect::CutoutOrEmpty
constexpr TRect CutoutOrEmpty(const TRect &o) const
Definition: rect.h:584
impeller::TRect::Intersection
constexpr static std::optional< TRect > Intersection(const TRect &a, const std::optional< TRect > b)
Definition: rect.h:699
std::operator<<
std::ostream & operator<<(std::ostream &out, const impeller::Color &c)
Definition: color.h:961
impeller::TRect::Round
Round(const TRect< U > &r)
Definition: rect.h:674
impeller::TRect::TRect
constexpr TRect()
Definition: rect.h:127
impeller::TRect::GetCenter
constexpr Point GetCenter() const
Get the center point as a |Point|.
Definition: rect.h:373
impeller::TRect::GetX
constexpr Type GetX() const
Returns the X coordinate of the upper left corner, equivalent to |GetOrigin().x|.
Definition: rect.h:323
ONLY_ON_FLOAT_M
#define ONLY_ON_FLOAT_M(Modifiers, Return)
Definition: rect.h:22
impeller::TRect::GetHeight
constexpr Type GetHeight() const
Returns the height of the rectangle, equivalent to |GetSize().height|.
Definition: rect.h:337
impeller::TRect::GetOrigin
constexpr TPoint< Type > GetOrigin() const
Returns the upper left corner of the rectangle as specified by the left/top or x/y values when it was...
Definition: rect.h:310
impeller::TRect::GetRightTop
constexpr TPoint< T > GetRightTop() const
Definition: rect.h:353
offset
SeparatedVector2 offset
Definition: stroke_path_geometry.cc:311
impeller::TRect::Contains
constexpr bool Contains(const TRect &o) const
Returns true iff this rectangle is not empty and it also contains every point considered inside the p...
Definition: rect.h:263
impeller::TRect::operator==
constexpr bool operator==(const TRect &r) const
Definition: rect.h:181
impeller::TRect::IntersectsWithRect
constexpr bool IntersectsWithRect(const TRect &o) const
Definition: rect.h:533
impeller::TRect::GetPoints
constexpr std::array< TPoint< T >, 4 > GetPoints() const
Get the points that represent the 4 corners of this rectangle in a Z order that is compatible with tr...
Definition: rect.h:405
impeller::TRect::MakePointBounds
constexpr static std::optional< TRect > MakePointBounds(const U &value)
Definition: rect.h:151
impeller::TRect::Shift
constexpr TRect< T > Shift(T dx, T dy) const
Returns a new rectangle translated by the given offset.
Definition: rect.h:589
impeller::TRect::ContainsInclusive
constexpr bool ContainsInclusive(const TPoint< Type > &p) const
Returns true iff the provided point |p| is inside the closed-range interior of this rectangle.
Definition: rect.h:240
impeller::TRect::IsEmpty
constexpr bool IsEmpty() const
Returns true if either of the width or height are 0, negative, or NaN.
Definition: rect.h:287
impeller::TRect::RoundOut
RoundOut(const TRect< U > &r)
Definition: rect.h:666
matrix.h
impeller::TRect::Scale
constexpr TRect Scale(TSize< T > scale) const
Definition: rect.h:210
impeller::TSize
Definition: size.h:19
impeller::Point
TPoint< Scalar > Point
Definition: point.h:322
impeller::TRect::TransformAndClipBounds
constexpr TRect TransformAndClipBounds(const Matrix &transform) const
Creates a new bounding box that contains this transformed rectangle, clipped against the near clippin...
Definition: rect.h:429
impeller::TRect::GetLeft
constexpr auto GetLeft() const
Definition: rect.h:341
impeller::TRect::GetTransformedPoints
constexpr std::array< TPoint< T >, 4 > GetTransformedPoints(const Matrix &transform) const
Definition: rect.h:417
transform
Matrix transform
Definition: gaussian_blur_filter_contents.cc:231
impeller::TRect::GetWidth
constexpr Type GetWidth() const
Returns the width of the rectangle, equivalent to |GetSize().width|.
Definition: rect.h:331
impeller::TRect::GetLeftBottom
constexpr TPoint< T > GetLeftBottom() const
Definition: rect.h:357
impeller::TRect::IsSquare
constexpr bool IsSquare() const
Returns true if width and height are equal and neither is NaN.
Definition: rect.h:294
impeller::TRect::MakeOriginSize
constexpr static TRect MakeOriginSize(const TPoint< Type > &origin, const TSize< Type > &size)
Definition: rect.h:140
impeller::TRect::Scale
constexpr TRect Scale(Type scale) const
Definition: rect.h:192
impeller::TRect::MakePointBounds
constexpr static std::optional< TRect > MakePointBounds(const PointIter first, const PointIter last)
Definition: rect.h:156
impeller::TRect::Shift
constexpr TRect< T > Shift(TPoint< T > offset) const
Returns a new rectangle translated by the given offset.
Definition: rect.h:599
impeller::TRect::Scale
constexpr TRect Scale(TPoint< T > scale) const
Definition: rect.h:206
impeller::TSize::width
Type width
Definition: size.h:22
impeller::TRect::Contains
constexpr bool Contains(const TPoint< Type > &p) const
Returns true iff the provided point |p| is inside the half-open interior of this rectangle.
Definition: rect.h:221
impeller::TPoint::x
Type x
Definition: point.h:30
impeller::TRect::IsFinite
IsFinite() const
Returns true if all of the fields of this floating point rectangle are finite.
Definition: rect.h:278
scalar.h
impeller::TRect::Expand
constexpr TRect< T > Expand(TPoint< T > amount) const
Returns a rectangle with expanded edges in all directions. Negative expansion results in shrinking.
Definition: rect.h:642
impeller::TRect::Expand
constexpr TRect< T > Expand(TSize< T > amount) const
Returns a rectangle with expanded edges in all directions. Negative expansion results in shrinking.
Definition: rect.h:648
impeller::TRect::Cutout
constexpr std::optional< TRect< T > > Cutout(const TRect &o) const
Returns the new boundary rectangle that would result from this rectangle being cut out by the specifi...
Definition: rect.h:544
impeller::TRect::GetSize
constexpr TSize< Type > GetSize() const
Returns the size of the rectangle which may be negative in either width or height and may have been c...
Definition: rect.h:317
impeller::TRect::GetRight
constexpr auto GetRight() const
Definition: rect.h:345
impeller::TRect::MakeSize
constexpr static TRect MakeSize(const TSize< U > &size)
Definition: rect.h:146
std
Definition: comparable.h:95
impeller::TRect::Project
constexpr TRect< T > Project(TRect< T > source) const
Returns a new rectangle that represents the projection of the source rectangle onto this rectangle....
Definition: rect.h:656
impeller::TPoint
Definition: point.h:27
impeller::TRect::MakeMaximum
constexpr static TRect MakeMaximum()
Definition: rect.h:174
impeller::saturated::b
SI b
Definition: saturated_math.h:87
impeller::IRect64
TRect< int64_t > IRect64
Definition: rect.h:771
scale
const Scalar scale
Definition: stroke_path_geometry.cc:308
impeller::TRect::Union
constexpr TRect Union(const TRect &o) const
Definition: rect.h:504
impeller::TRect::Area
constexpr T Area() const
Get the area of the rectangle, equivalent to |GetSize().Area()|.
Definition: rect.h:366
impeller::TRect::GetBottom
constexpr auto GetBottom() const
Definition: rect.h:347
impeller::TSize::height
Type height
Definition: size.h:23
impeller::TRect::Union
constexpr static std::optional< TRect > Union(const std::optional< TRect > a, const std::optional< TRect > b)
Definition: rect.h:693
impeller::TRect::MakeLTRB
constexpr static TRect MakeLTRB(Type left, Type top, Type right, Type bottom)
Definition: rect.h:129
impeller::TRect::GetPositive
constexpr TRect GetPositive() const
Get a version of this rectangle that has a non-negative size.
Definition: rect.h:389
impeller::TRect::GetRightBottom
constexpr TPoint< T > GetRightBottom() const
Definition: rect.h:361
impeller::TRect::Intersection
constexpr static std::optional< TRect > Intersection(const std::optional< TRect > a, const TRect &b)
Definition: rect.h:705
impeller::TRect::GetY
constexpr Type GetY() const
Returns the Y coordinate of the upper left corner, equivalent to |GetOrigin().y|.
Definition: rect.h:327
impeller
Definition: aiks_blend_unittests.cc:18
impeller::TRect::GetXYWH
constexpr std::array< T, 4 > GetXYWH() const
Get the x, y coordinates of the origin and the width and height of the rectangle in an array.
Definition: rect.h:384
impeller::Matrix::MakeScale
static constexpr Matrix MakeScale(const Vector3 &s)
Definition: matrix.h:104
impeller::TRect::GetTop
constexpr auto GetTop() const
Definition: rect.h:343
impeller::TRect
Definition: rect.h:122
impeller::Matrix
A 4x4 matrix using column-major storage.
Definition: matrix.h:37
size.h
impeller::TRect::Expand
constexpr TRect< T > Expand(T left, T top, T right, T bottom) const
Returns a rectangle with expanded edges. Negative expansion results in shrinking.
Definition: rect.h:605
impeller::TRect::Union
constexpr static std::optional< TRect > Union(const TRect &a, const std::optional< TRect > b)
Definition: rect.h:681
impeller::TRect::Intersection
constexpr static std::optional< TRect > Intersection(const std::optional< TRect > a, const std::optional< TRect > b)
Definition: rect.h:711
impeller::TRect::operator!=
constexpr bool operator!=(const TRect &r) const
Definition: rect.h:188