1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
|
use super::*;
/// A bezier path.
#[derive(Debug, Default, Clone, Eq, PartialEq)]
pub struct Path(pub Vec<PathElement>);
/// An element in a bezier path.
#[derive(Debug, Clone, Eq, PartialEq)]
pub enum PathElement {
MoveTo(Point),
LineTo(Point),
CubicTo(Point, Point, Point),
ClosePath,
}
impl Path {
/// Create an empty path.
pub const fn new() -> Self {
Self(vec![])
}
/// Create a path that describes a rectangle.
pub fn rect(size: Size) -> Self {
let z = Length::zero();
let point = Point::new;
let mut path = Self::new();
path.move_to(point(z, z));
path.line_to(point(size.x, z));
path.line_to(point(size.x, size.y));
path.line_to(point(z, size.y));
path.close_path();
path
}
/// Create a path that approximates an axis-aligned ellipse.
pub fn ellipse(size: Size) -> Self {
// https://stackoverflow.com/a/2007782
let z = Length::zero();
let rx = size.x / 2.0;
let ry = size.y / 2.0;
let m = 0.551784;
let mx = m * rx;
let my = m * ry;
let point = |x, y| Point::new(x + rx, y + ry);
let mut path = Self::new();
path.move_to(point(-rx, z));
path.cubic_to(point(-rx, -my), point(-mx, -ry), point(z, -ry));
path.cubic_to(point(mx, -ry), point(rx, -my), point(rx, z));
path.cubic_to(point(rx, my), point(mx, ry), point(z, ry));
path.cubic_to(point(-mx, ry), point(-rx, my), point(-rx, z));
path
}
/// Push a [`MoveTo`](PathElement::MoveTo) element.
pub fn move_to(&mut self, p: Point) {
self.0.push(PathElement::MoveTo(p));
}
/// Push a [`LineTo`](PathElement::LineTo) element.
pub fn line_to(&mut self, p: Point) {
self.0.push(PathElement::LineTo(p));
}
/// Push a [`CubicTo`](PathElement::CubicTo) element.
pub fn cubic_to(&mut self, p1: Point, p2: Point, p3: Point) {
self.0.push(PathElement::CubicTo(p1, p2, p3));
}
/// Push a [`ClosePath`](PathElement::ClosePath) element.
pub fn close_path(&mut self) {
self.0.push(PathElement::ClosePath);
}
}
/// Get the control points for a bezier curve that describes a circular arc
/// of this angle with the given radius.
pub fn bezier_arc(
angle: Angle,
radius: Length,
rotate: bool,
mirror_x: bool,
mirror_y: bool,
) -> [Point; 4] {
let end = Point::new(angle.cos() * radius - radius, angle.sin() * radius);
let center = Point::new(-radius, Length::zero());
let mut ts = if mirror_y {
Transform::mirror_y()
} else {
Transform::identity()
};
if mirror_x {
ts = ts.pre_concat(Transform::mirror_x());
}
if rotate {
ts = ts.pre_concat(Transform::rotate(Angle::deg(90.0)));
}
let a = center * -1.0;
let b = end - center;
let q1 = a.x.to_raw() * a.x.to_raw() + a.y.to_raw() * a.y.to_raw();
let q2 = q1 + a.x.to_raw() * b.x.to_raw() + a.y.to_raw() * b.y.to_raw();
let k2 = (4.0 / 3.0) * ((2.0 * q1 * q2).sqrt() - q2)
/ (a.x.to_raw() * b.y.to_raw() - a.y.to_raw() * b.x.to_raw());
let control_1 = Point::new(center.x + a.x - k2 * a.y, center.y + a.y + k2 * a.x);
let control_2 = Point::new(center.x + b.x + k2 * b.y, center.y + b.y - k2 * b.x);
[
Point::zero(),
control_1.transform(ts),
control_2.transform(ts),
end.transform(ts),
]
}
|
