1use crate::BackendCoord;
2
3// Compute the tanginal and normal vectors of the given straight line.
4fn get_dir_vector(from: BackendCoord, to: BackendCoord, flag: bool) -> ((f64, f64), (f64, f64)) {
5 let v: (i64, i64) = (i64::from(to.0 - from.0), i64::from(to.1 - from.1));
6 let l: f64 = ((v.0 * v.0 + v.1 * v.1) as f64).sqrt();
7
8 let v: (f64, f64) = (v.0 as f64 / l, v.1 as f64 / l);
9
10 if flag {
11 (v, (v.1, -v.0))
12 } else {
13 (v, (-v.1, v.0))
14 }
15}
16
17// Compute the polygonized vertex of the given angle
18// d is the distance between the polygon edge and the actual line.
19// d can be negative, this will emit a vertex on the other side of the line.
20fn compute_polygon_vertex(triple: &[BackendCoord; 3], d: f64, buf: &mut Vec<BackendCoord>) {
21 buf.clear();
22
23 // Compute the tanginal and normal vectors of the given straight line.
24 let (a_t, a_n) = get_dir_vector(triple[0], triple[1], false);
25 let (b_t, b_n) = get_dir_vector(triple[2], triple[1], true);
26
27 // Compute a point that is d away from the line for line a and line b.
28 let a_p = (
29 f64::from(triple[1].0) + d * a_n.0,
30 f64::from(triple[1].1) + d * a_n.1,
31 );
32 let b_p = (
33 f64::from(triple[1].0) + d * b_n.0,
34 f64::from(triple[1].1) + d * b_n.1,
35 );
36
37 // Check if 3 points are colinear, up to precision. If so, just emit the point.
38 if (a_t.1 * b_t.0 - a_t.0 * b_t.1).abs() <= f64::EPSILON {
39 buf.push((a_p.0 as i32, a_p.1 as i32));
40 return;
41 }
42
43 // So we are actually computing the intersection of two lines:
44 // a_p + u * a_t and b_p + v * b_t.
45 // We can solve the following vector equation:
46 // u * a_t + a_p = v * b_t + b_p
47 //
48 // which is actually a equation system:
49 // u * a_t.0 - v * b_t.0 = b_p.0 - a_p.0
50 // u * a_t.1 - v * b_t.1 = b_p.1 - a_p.1
51
52 // The following vars are coefficients of the linear equation system.
53 // a0*u + b0*v = c0
54 // a1*u + b1*v = c1
55 // in which x and y are the coordinates that two polygon edges intersect.
56
57 let a0 = a_t.0;
58 let b0 = -b_t.0;
59 let c0 = b_p.0 - a_p.0;
60 let a1 = a_t.1;
61 let b1 = -b_t.1;
62 let c1 = b_p.1 - a_p.1;
63
64 // Since the points are not collinear, the determinant is not 0, and we can get a intersection point.
65 let u = (c0 * b1 - c1 * b0) / (a0 * b1 - a1 * b0);
66 let x = a_p.0 + u * a_t.0;
67 let y = a_p.1 + u * a_t.1;
68
69 let cross_product = a_t.0 * b_t.1 - a_t.1 * b_t.0;
70 if (cross_product < 0.0 && d < 0.0) || (cross_product > 0.0 && d > 0.0) {
71 // Then we are at the outer side of the angle, so we need to consider a cap.
72 let dist_square = (x - triple[1].0 as f64).powi(2) + (y - triple[1].1 as f64).powi(2);
73 // If the point is too far away from the line, we need to cap it.
74 if dist_square > d * d * 16.0 {
75 buf.push((a_p.0.round() as i32, a_p.1.round() as i32));
76 buf.push((b_p.0.round() as i32, b_p.1.round() as i32));
77 return;
78 }
79 }
80
81 buf.push((x.round() as i32, y.round() as i32));
82}
83
84fn traverse_vertices<'a>(
85 mut vertices: impl Iterator<Item = &'a BackendCoord>,
86 width: u32,
87 mut op: impl FnMut(BackendCoord),
88) {
89 let mut a = vertices.next().unwrap();
90 let mut b = vertices.next().unwrap();
91
92 while a == b {
93 a = b;
94 if let Some(new_b) = vertices.next() {
95 b = new_b;
96 } else {
97 return;
98 }
99 }
100
101 let (_, n) = get_dir_vector(*a, *b, false);
102
103 op((
104 (f64::from(a.0) + n.0 * f64::from(width) / 2.0).round() as i32,
105 (f64::from(a.1) + n.1 * f64::from(width) / 2.0).round() as i32,
106 ));
107
108 let mut recent = [(0, 0), *a, *b];
109 let mut vertex_buf = Vec::with_capacity(3);
110
111 for p in vertices {
112 if *p == recent[2] {
113 continue;
114 }
115 recent.swap(0, 1);
116 recent.swap(1, 2);
117 recent[2] = *p;
118 compute_polygon_vertex(&recent, f64::from(width) / 2.0, &mut vertex_buf);
119 vertex_buf.iter().cloned().for_each(&mut op);
120 }
121
122 let b = recent[1];
123 let a = recent[2];
124
125 let (_, n) = get_dir_vector(a, b, true);
126
127 op((
128 (f64::from(a.0) + n.0 * f64::from(width) / 2.0).round() as i32,
129 (f64::from(a.1) + n.1 * f64::from(width) / 2.0).round() as i32,
130 ));
131}
132
133/// Covert a path with >1px stroke width into polygon.
134pub fn polygonize(vertices: &[BackendCoord], stroke_width: u32) -> Vec<BackendCoord> {
135 if vertices.len() < 2 {
136 return vec![];
137 }
138
139 let mut ret: Vec<(i32, i32)> = vec![];
140
141 traverse_vertices(vertices.iter(), stroke_width, |v: (i32, i32)| ret.push(v));
142 traverse_vertices(vertices.iter().rev(), stroke_width, |v: (i32, i32)| ret.push(v));
143
144 ret
145}
146
147#[cfg(test)]
148mod test {
149 use super::*;
150
151 /// Test for regression with respect to https://github.com/plotters-rs/plotters/issues/562
152 #[test]
153 fn test_no_inf_in_compute_polygon_vertex() {
154 let path = [(335, 386), (338, 326), (340, 286)];
155 let mut buf = Vec::new();
156 compute_polygon_vertex(&path, 2.0, buf.as_mut());
157 assert!(!buf.is_empty());
158 let nani32 = f64::INFINITY as i32;
159 assert!(!buf.iter().any(|&v| v.0 == nani32 || v.1 == nani32));
160 }
161
162 /// Correct 90 degree turn to the right
163 #[test]
164 fn standard_corner() {
165 let path = [(10, 10), (20, 10), (20, 20)];
166 let mut buf = Vec::new();
167 compute_polygon_vertex(&path, 2.0, buf.as_mut());
168 assert!(!buf.is_empty());
169 let buf2 = vec![(18, 12)];
170 assert_eq!(buf, buf2);
171 }
172}
173