14 if (ratio_left == 0 && ratio_right == 0) {
15 return (left + right) / 2;
17 return (left * ratio_right + right * ratio_left) / (ratio_left + ratio_right);
23 return Point{std::isnan(in.x) ? default_size.width : in.
x,
24 std::isnan(in.y) ? default_size.height : in.y};
42 constexpr
Scalar kPrecomputedVariables[][2] = {
43 {2.00000000, 1.13276676},
44 {2.18349805, 1.20311921},
45 {2.33888662, 1.28698796},
46 {2.48660575, 1.36351941},
47 {2.62226596, 1.44717976},
48 {2.75148990, 1.53385819},
49 {3.36298265, 1.98288283},
50 {4.08649929, 2.23811846},
51 {4.85481134, 2.47563463},
52 {5.62945551, 2.72948597},
53 {6.43023796, 2.98020421}};
55 constexpr
Scalar kMinRatio = 2.00;
61 constexpr
Scalar kFirstStepInverse = 10;
62 constexpr
Scalar kFirstMaxRatio = 2.50;
63 constexpr
Scalar kFirstNumRecords = 6;
65 constexpr
Scalar kSecondStepInverse = 2;
66 constexpr
Scalar kSecondMaxRatio = 5.00;
68 constexpr
Scalar kThirdNSlope = 1.559599389;
69 constexpr
Scalar kThirdKxjSlope = 0.522807185;
71 constexpr
size_t kNumRecords =
72 sizeof(kPrecomputedVariables) /
sizeof(kPrecomputedVariables[0]);
75 std::array<Scalar, 2> ComputeNAndXj(
Scalar ratio) {
76 if (ratio > kSecondMaxRatio) {
77 Scalar n = kThirdNSlope * (ratio - kSecondMaxRatio) +
78 kPrecomputedVariables[kNumRecords - 1][0];
79 Scalar k_xJ = kThirdKxjSlope * (ratio - kSecondMaxRatio) +
80 kPrecomputedVariables[kNumRecords - 1][1];
81 return {n, 1 - 1 / k_xJ};
83 ratio = std::clamp(ratio, kMinRatio, kSecondMaxRatio);
85 if (ratio < kFirstMaxRatio) {
86 steps = (ratio - kMinRatio) * kFirstStepInverse;
89 (ratio - kFirstMaxRatio) * kSecondStepInverse + kFirstNumRecords - 1;
92 size_t left = std::clamp<size_t>(
static_cast<size_t>(std::floor(steps)), 0,
94 Scalar frac = steps - left;
96 Scalar n = (1 - frac) * kPrecomputedVariables[left][0] +
97 frac * kPrecomputedVariables[left + 1][0];
98 Scalar k_xJ = (1 - frac) * kPrecomputedVariables[left][1] +
99 frac * kPrecomputedVariables[left + 1][1];
100 return {n, 1 - 1 / k_xJ};
121 Scalar distance_am = a_to_b.GetLength() / 2;
122 Scalar distance_cm = sqrt(r * r - distance_am * distance_am);
123 return m - distance_cm * c_to_m.Normalize();
128 RoundSuperellipseParam::Octant ComputeOctant(
Point center,
151 return RoundSuperellipseParam::Octant{
157 .circle_start = {a, a},
161 Scalar ratio = a * 2 / radius;
164 auto precomputed_vars = ComputeNAndXj(ratio);
165 Scalar n = precomputed_vars[0];
166 Scalar xJ = precomputed_vars[1] * a;
167 Scalar yJ = pow(1 - pow(precomputed_vars[1], n), 1 / n) * a;
168 Scalar max_theta = asinf(pow(precomputed_vars[1], n / 2));
170 Scalar tan_phiJ = pow(xJ / yJ, n - 1);
171 Scalar d = (xJ - tan_phiJ * yJ) / (1 - tan_phiJ);
172 Scalar R = (a - d - g) * sqrt(2);
174 Point pointM{a - g, a - g};
176 Point circle_center =
177 radius == 0 ? pointM : FindCircleCenter(pointJ, pointM, R);
178 Radians circle_max_angle =
179 radius == 0 ? Radians(0)
180 : (pointM - circle_center).AngleTo(pointJ - circle_center);
182 return RoundSuperellipseParam::Octant{
187 .se_max_theta = max_theta,
189 .circle_start = pointJ,
190 .circle_center = circle_center,
191 .circle_max_angle = circle_max_angle,
204 RoundSuperellipseParam::Quadrant ComputeQuadrant(
Point center,
208 Point corner_vector = corner - center;
215 Scalar norm_radius = radii.MinDimension();
216 Size forward_scale = norm_radius == 0 ?
Size{1, 1} : radii / norm_radius;
217 Point norm_half_size = corner_vector.
Abs() / forward_scale;
219 ReplanceNaNWithDefault(corner_vector / norm_half_size, sign);
226 Scalar c = norm_half_size.x - norm_half_size.y;
228 return RoundSuperellipseParam::Quadrant{
230 .signed_scale = signed_scale,
231 .top = ComputeOctant(
Point{0, -c}, norm_half_size.
x, norm_radius),
232 .right = ComputeOctant(
Point{c, 0}, norm_half_size.
y, norm_radius),
249 bool OctantContains(
const RoundSuperellipseParam::Octant& param,
252 if (p.x < 0 || p.y < 0 || p.y < p.x) {
256 if (p.x <= param.circle_start.x) {
257 Point p_se = p / param.se_a;
258 return powf(p_se.x, param.se_n) + powf(p_se.y, param.se_n) <= 1;
261 param.circle_start.GetDistanceSquared(param.circle_center);
262 Point p_circle = p - param.circle_center;
280 bool CornerContains(
const RoundSuperellipseParam::Quadrant& param,
282 bool check_quadrant =
true) {
283 Point norm_point = (p - param.offset) / param.signed_scale;
284 if (check_quadrant) {
285 if (norm_point.x < 0 || norm_point.y < 0) {
289 norm_point = norm_point.
Abs();
291 if (param.top.se_n < 2 || param.right.se_n < 2) {
294 Scalar x_delta = param.right.offset.x + param.right.se_a - norm_point.x;
295 Scalar y_delta = param.top.offset.y + param.top.se_a - norm_point.y;
296 bool x_within = x_delta > 0 || (x_delta == 0 && param.signed_scale.x < 0);
297 bool y_within = y_delta > 0 || (y_delta == 0 && param.signed_scale.y < 0);
298 return x_within && y_within;
300 return OctantContains(param.top, norm_point - param.top.offset) &&
301 OctantContains(param.right, Flip(norm_point - param.right.offset));
304 class RoundSuperellipseBuilder {
306 explicit RoundSuperellipseBuilder(PathReceiver& receiver)
307 : receiver_(receiver) {}
318 void AddQuadrant(
const RoundSuperellipseParam::Quadrant& param,
323 if (param.top.se_n < 2 || param.right.se_n < 2) {
324 receiver_.LineTo(
transform * (param.top.offset +
325 Point(param.top.se_a, param.top.se_a)));
328 (param.right.offset +
Point(param.right.se_a, 0)));
331 (param.top.offset +
Point(0, param.top.se_a)));
336 AddOctant(param.top,
false,
false,
transform);
337 AddOctant(param.right,
true,
true,
transform);
339 AddOctant(param.right,
false,
true,
transform);
340 AddOctant(param.top,
true,
false,
transform);
345 std::array<Point, 4> SuperellipseArcPoints(
346 const RoundSuperellipseParam::Octant& param) {
348 const Point&
end = param.circle_start;
349 constexpr
Point start_tangent = {1, 0};
350 Point circle_start_vector = param.circle_start - param.circle_center;
352 Point{-circle_start_vector.
y, circle_start_vector.x}.Normalize();
354 std::array<Scalar, 2> factors = SuperellipseBezierFactors(param.se_n);
356 return std::array<Point, 4>{
357 start,
start + start_tangent * factors[0] * param.se_a,
358 end + end_tangent * factors[1] * param.se_a,
end};
361 std::array<Point, 4> CircularArcPoints(
362 const RoundSuperellipseParam::Octant& param) {
363 Point start_vector = param.circle_start - param.circle_center;
365 start_vector.
Rotate(Radians(-param.circle_max_angle.radians));
366 Point circle_end = param.circle_center + end_vector;
367 Point start_tangent =
Point{start_vector.
y, -start_vector.x}.Normalize();
368 Point end_tangent =
Point{-end_vector.
y, end_vector.x}.Normalize();
369 Scalar bezier_factor = std::tan(param.circle_max_angle.radians / 4) * 4 / 3;
370 Scalar radius = start_vector.GetLength();
372 return std::array<Point, 4>{
374 param.circle_start + start_tangent * bezier_factor * radius,
375 circle_end + end_tangent * bezier_factor * radius, circle_end};
389 void AddOctant(
const RoundSuperellipseParam::Octant& param,
392 const Matrix& external_transform) {
399 auto circle_points = CircularArcPoints(param);
400 auto se_points = SuperellipseArcPoints(param);
405 receiver_.CubicTo(
transform * circle_points[1],
409 receiver_.CubicTo(
transform * circle_points[2],
424 std::array<Scalar, 2> SuperellipseBezierFactors(
Scalar n) {
425 constexpr
Scalar kPrecomputedVariables[][2] = {
426 {0.01339448, 0.05994973},
427 {0.13664115, 0.13592082},
428 {0.24545546, 0.14099516},
429 {0.32353151, 0.12808021},
430 {0.39093068, 0.11726264},
431 {0.44847800, 0.10808278},
432 {0.49817452, 0.10026175},
433 {0.54105583, 0.09344429},
434 {0.57812578, 0.08748984},
435 {0.61050961, 0.08224722},
436 {0.63903989, 0.07759639},
437 {0.66416338, 0.07346530},
438 {0.68675338, 0.06974996},
439 {0.70678034, 0.06529512}};
440 constexpr
size_t kNumRecords =
441 sizeof(kPrecomputedVariables) /
sizeof(kPrecomputedVariables[0]);
442 constexpr
Scalar kStep = 1.00f;
443 constexpr
Scalar kMinN = 2.00f;
444 constexpr
Scalar kMaxN = kMinN + (kNumRecords - 1) * kStep;
448 return {1.07f - expf(1.307649835) * powf(n, -0.8568516731),
449 -0.01f + expf(-0.9287690322) * powf(n, -0.6120901398)};
452 Scalar steps = std::clamp<Scalar>((n - kMinN) / kStep, 0, kNumRecords - 1);
453 size_t left = std::clamp<size_t>(
static_cast<size_t>(std::floor(steps)), 0,
455 Scalar frac = steps - left;
457 return std::array<Scalar, 2>{(1 - frac) * kPrecomputedVariables[left][0] +
458 frac * kPrecomputedVariables[left + 1][0],
459 (1 - frac) * kPrecomputedVariables[left][1] +
460 frac * kPrecomputedVariables[left + 1][1]};
463 PathReceiver& receiver_;
467 static constexpr Matrix kFlip = Matrix(
468 0.0f, 1.0f, 0.0f, 0.0f,
469 1.0f, 0.0f, 0.0f, 0.0f,
470 0.0f, 0.0f, 1.0f, 0.0f,
471 0.0f, 0.0f, 0.0f, 1.0f);
482 {radius, radius}, {-1, 1}),
483 .all_corners_same =
true,
496 .all_corners_same =
true,
514 ComputeQuadrant(
Point{bottom_split, right_split},
517 ComputeQuadrant(
Point{bottom_split, left_split},
522 .all_corners_same =
false,
527 RoundSuperellipseBuilder builder(path_receiver);
543 builder.AddQuadrant(
top_left,
true);
547 path_receiver.
Close();
Collection of functions to receive path segments from the underlying path representation via the DlPa...
virtual void LineTo(const Point &p2)=0
virtual void MoveTo(const Point &p2, bool will_be_closed)=0
static bool CornerContains(const Point &p, const Point &corner, const Point &direction, const Size &radii)
static constexpr Matrix MakeTranslation(const Vector3 &t)
static constexpr Matrix MakeTranslateScale(const Vector3 &s, const Vector3 &t)
static RoundSuperellipseParam MakeBoundsRadii(const Rect &bounds, const RoundingRadii &radii)
void Dispatch(PathReceiver &receiver) const
bool Contains(const Point &point) const
static constexpr Scalar kGapFactor
static RoundSuperellipseParam MakeBoundsRadius(const Rect &bounds, Scalar radius)
constexpr bool AreAllCornersSame(Scalar tolerance=kEhCloseEnough) const
constexpr TPoint Abs() const
constexpr TPoint Rotate(const Radians &angle) const
constexpr Type GetDistanceSquared(const TPoint &p) const
constexpr auto GetBottom() const
constexpr auto GetTop() const
constexpr auto GetLeft() const
constexpr auto GetRight() const
constexpr TPoint< T > GetLeftBottom() const
constexpr TPoint< T > GetRightTop() const
constexpr TPoint< T > GetRightBottom() const
constexpr Point GetCenter() const
Get the center point as a |Point|.
constexpr TPoint< T > GetLeftTop() const
constexpr TSize Abs() const
constexpr bool IsEmpty() const
Returns true if either of the width or height are 0, negative, or NaN.