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LibGfx: Approximate elliptical arcs with cubic beziers

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Unlike all other primitives elliptical arcs are non-trivial to
manipulate, it's tricky to correctly apply a Gfx::AffineTransform to
them. Prior to this change, Path::copy_transformed() was still
incorrectly applying transforms such as flips and skews to arcs.

This patch very closely approximates arcs with cubic beziers (I can not
visually spot any differences), which can then be easily and correctly
transformed in all cases.

Most of the maths here was taken from:
https://mortoray.com/rendering-an-svg-elliptical-arc-as-bezier-curves/
(which came from https://www.joecridge.me/content/pdf/bezier-arcs.pdf,
now a dead link).
This commit is contained in:
MacDue 2023-07-15 15:59:33 +01:00 • committed by Andreas Kling
parent 2a1bf63f9e
commit 1bc7b0320e
4 changed files with 54 additions and 101 deletions
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91
Userland/Libraries/LibGfx/Path.cpp
View file

@ -14,6 +14,54 @@
namespace Gfx {
void Path::approximate_elliptical_arc_with_cubic_beziers(FloatPoint center, FloatSize radii, float x_axis_rotation, float theta, float theta_delta)
{
float sin_x_rotation;
float cos_x_rotation;
AK::sincos(x_axis_rotation, sin_x_rotation, cos_x_rotation);
auto arc_point_and_derivative = [&](float t, FloatPoint& point, FloatPoint& derivative) {
float sin_angle;
float cos_angle;
AK::sincos(t, sin_angle, cos_angle);
point = FloatPoint {
center.x()
+ radii.width() * cos_x_rotation * cos_angle
- radii.height() * sin_x_rotation * sin_angle,
center.y()
+ radii.width() * sin_x_rotation * cos_angle
+ radii.height() * cos_x_rotation * sin_angle,
};
derivative = FloatPoint {
-radii.width() * cos_x_rotation * sin_angle
- radii.height() * sin_x_rotation * cos_angle,
-radii.width() * sin_x_rotation * sin_angle
+ radii.height() * cos_x_rotation * cos_angle,
};
};
auto approximate_arc_between = [&](float start_angle, float end_angle) {
auto t = AK::tan((end_angle - start_angle) / 2);
auto alpha = AK::sin(end_angle - start_angle) * ((AK::sqrt(4 + 3 * t * t) - 1) / 3);
FloatPoint p1, d1;
FloatPoint p2, d2;
arc_point_and_derivative(start_angle, p1, d1);
arc_point_and_derivative(end_angle, p2, d2);
auto q1 = p1 + d1.scaled(alpha, alpha);
auto q2 = p2 - d2.scaled(alpha, alpha);
cubic_bezier_curve_to(q1, q2, p2);
};
// FIXME: Come up with a more mathematically sound step size (using some error calculation).
auto step = theta_delta;
int step_count = 1;
while (fabs(step) > AK::Pi<float> / 4) {
step /= 2;
step_count *= 2;
}
float prev = theta;
float t = prev + step;
for (int i = 0; i < step_count; i++, prev = t, t += step)
approximate_arc_between(prev, t);
}
void Path::elliptical_arc_to(FloatPoint point, FloatSize radii, float x_axis_rotation, bool large_arc, bool sweep)
{
auto next_point = point;
@ -105,15 +153,12 @@ void Path::elliptical_arc_to(FloatPoint point, FloatSize radii, float x_axis_rot
theta_delta += 2 * AK::Pi<double>;
}
elliptical_arc_to(
next_point,
approximate_elliptical_arc_with_cubic_beziers(
{ cx, cy },
{ rx, ry },
x_axis_rotation,
theta_1,
theta_delta,
large_arc,
sweep);
theta_delta);
}
void Path::close()
@ -170,7 +215,6 @@ void Path::close_all_subpaths()
case Segment::Type::LineTo:
case Segment::Type::QuadraticBezierCurveTo:
case Segment::Type::CubicBezierCurveTo:
case Segment::Type::EllipticalArcTo:
if (is_first_point_in_subpath) {
start_of_subpath = cursor;
is_first_point_in_subpath = false;
@ -205,9 +249,6 @@ DeprecatedString Path::to_deprecated_string() const
case Segment::Type::CubicBezierCurveTo:
builder.append("CubicBezierCurveTo"sv);
break;
case Segment::Type::EllipticalArcTo:
builder.append("EllipticalArcTo"sv);
break;
case Segment::Type::Invalid:
builder.append("Invalid"sv);
break;
@ -225,16 +266,6 @@ DeprecatedString Path::to_deprecated_string() const
builder.append(", "sv);
builder.append(static_cast<CubicBezierCurveSegment const&>(*segment).through_1().to_deprecated_string());
break;
case Segment::Type::EllipticalArcTo: {
auto& arc = static_cast<EllipticalArcSegment const&>(*segment);
builder.appendff(", {}, {}, {}, {}, {}",
arc.radii().to_deprecated_string().characters(),
arc.center().to_deprecated_string().characters(),
arc.x_axis_rotation(),
arc.theta_1(),
arc.theta_delta());
break;
}
default:
break;
}
@ -304,14 +335,6 @@ void Path::segmentize_path()
cursor = segment->point();
break;
}
case Segment::Type::EllipticalArcTo: {
auto& arc = static_cast<EllipticalArcSegment const&>(*segment);
Painter::for_each_line_segment_on_elliptical_arc(cursor, arc.point(), arc.center(), arc.radii(), arc.x_axis_rotation(), arc.theta_1(), arc.theta_delta(), [&](FloatPoint p0, FloatPoint p1) {
add_line(p0, p1);
});
cursor = segment->point();
break;
}
case Segment::Type::Invalid:
VERIFY_NOT_REACHED();
}
@ -346,20 +369,6 @@ Path Path::copy_transformed(Gfx::AffineTransform const& transform) const
result.cubic_bezier_curve_to(transform.map(cubic_segment.through_0()), transform.map(cubic_segment.through_1()), transform.map(segment->point()));
break;
}
case Segment::Type::EllipticalArcTo: {
auto const& arc_segment = static_cast<EllipticalArcSegment const&>(*segment);
auto det_negative = transform.determinant() < 0;
result.elliptical_arc_to(
transform.map(segment->point()),
transform.map(arc_segment.center()),
transform.map(arc_segment.radii()),
arc_segment.x_axis_rotation() + transform.rotation(),
det_negative ? AK::Pi<float> * 2 - arc_segment.theta_1() : arc_segment.theta_1(),
det_negative ? -arc_segment.theta_delta() : arc_segment.theta_delta(),
arc_segment.large_arc(),
det_negative ? !arc_segment.sweep() : arc_segment.sweep());
break;
}
case Segment::Type::Invalid:
VERIFY_NOT_REACHED();
}