| 1 | // Copyright 2018 the Kurbo Authors |
| 2 | // SPDX-License-Identifier: Apache-2.0 OR MIT |
| 3 | |
| 4 | //! Lines. |
| 5 | |
| 6 | use core::ops::{Add, Mul, Range, Sub}; |
| 7 | |
| 8 | use arrayvec::ArrayVec; |
| 9 | |
| 10 | use crate::{ |
| 11 | Affine, Nearest, ParamCurve, ParamCurveArclen, ParamCurveArea, ParamCurveCurvature, |
| 12 | ParamCurveDeriv, ParamCurveExtrema, ParamCurveNearest, PathEl, Point, Rect, Shape, Vec2, |
| 13 | DEFAULT_ACCURACY, MAX_EXTREMA, |
| 14 | }; |
| 15 | |
| 16 | /// A single line. |
| 17 | #[derive (Clone, Copy, Debug, PartialEq)] |
| 18 | #[cfg_attr (feature = "schemars" , derive(schemars::JsonSchema))] |
| 19 | #[cfg_attr (feature = "serde" , derive(serde::Serialize, serde::Deserialize))] |
| 20 | pub struct Line { |
| 21 | /// The line's start point. |
| 22 | pub p0: Point, |
| 23 | /// The line's end point. |
| 24 | pub p1: Point, |
| 25 | } |
| 26 | |
| 27 | impl Line { |
| 28 | /// Create a new line. |
| 29 | #[inline ] |
| 30 | pub fn new(p0: impl Into<Point>, p1: impl Into<Point>) -> Line { |
| 31 | Line { |
| 32 | p0: p0.into(), |
| 33 | p1: p1.into(), |
| 34 | } |
| 35 | } |
| 36 | |
| 37 | /// Returns a copy of this `Line` with the end points swapped so that it |
| 38 | /// points in the opposite direction. |
| 39 | #[must_use ] |
| 40 | #[inline ] |
| 41 | pub fn reversed(&self) -> Line { |
| 42 | Self { |
| 43 | p0: self.p1, |
| 44 | p1: self.p0, |
| 45 | } |
| 46 | } |
| 47 | |
| 48 | /// The length of the line. |
| 49 | #[inline ] |
| 50 | pub fn length(self) -> f64 { |
| 51 | self.arclen(DEFAULT_ACCURACY) |
| 52 | } |
| 53 | |
| 54 | /// The midpoint of the line. |
| 55 | /// |
| 56 | /// This is the same as calling [`Point::midpoint`] with |
| 57 | /// the endpoints of this line. |
| 58 | #[must_use ] |
| 59 | #[inline ] |
| 60 | pub fn midpoint(&self) -> Point { |
| 61 | self.p0.midpoint(self.p1) |
| 62 | } |
| 63 | |
| 64 | /// Computes the point where two lines, if extended to infinity, would cross. |
| 65 | pub fn crossing_point(self, other: Line) -> Option<Point> { |
| 66 | let ab = self.p1 - self.p0; |
| 67 | let cd = other.p1 - other.p0; |
| 68 | let pcd = ab.cross(cd); |
| 69 | if pcd == 0.0 { |
| 70 | return None; |
| 71 | } |
| 72 | let h = ab.cross(self.p0 - other.p0) / pcd; |
| 73 | Some(other.p0 + cd * h) |
| 74 | } |
| 75 | |
| 76 | /// Is this line `finite`? |
| 77 | /// |
| 78 | /// [finite]: f64::is_finite |
| 79 | #[inline ] |
| 80 | pub fn is_finite(self) -> bool { |
| 81 | self.p0.is_finite() && self.p1.is_finite() |
| 82 | } |
| 83 | |
| 84 | /// Is this line `NaN`? |
| 85 | /// |
| 86 | /// [NaN]: f64::is_nan |
| 87 | #[inline ] |
| 88 | pub fn is_nan(self) -> bool { |
| 89 | self.p0.is_nan() || self.p1.is_nan() |
| 90 | } |
| 91 | } |
| 92 | |
| 93 | impl From<(Point, Point)> for Line { |
| 94 | fn from((from: Point, to: Point): (Point, Point)) -> Self { |
| 95 | Line::new(p0:from, p1:to) |
| 96 | } |
| 97 | } |
| 98 | |
| 99 | impl From<(Point, Vec2)> for Line { |
| 100 | fn from((origin: Point, displacement: Vec2): (Point, Vec2)) -> Self { |
| 101 | Line::new(p0:origin, p1:origin + displacement) |
| 102 | } |
| 103 | } |
| 104 | |
| 105 | impl ParamCurve for Line { |
| 106 | #[inline ] |
| 107 | fn eval(&self, t: f64) -> Point { |
| 108 | self.p0.lerp(self.p1, t) |
| 109 | } |
| 110 | |
| 111 | #[inline ] |
| 112 | fn subsegment(&self, range: Range<f64>) -> Line { |
| 113 | Line { |
| 114 | p0: self.eval(range.start), |
| 115 | p1: self.eval(range.end), |
| 116 | } |
| 117 | } |
| 118 | |
| 119 | #[inline ] |
| 120 | fn start(&self) -> Point { |
| 121 | self.p0 |
| 122 | } |
| 123 | |
| 124 | #[inline ] |
| 125 | fn end(&self) -> Point { |
| 126 | self.p1 |
| 127 | } |
| 128 | } |
| 129 | |
| 130 | impl ParamCurveDeriv for Line { |
| 131 | type DerivResult = ConstPoint; |
| 132 | |
| 133 | #[inline ] |
| 134 | fn deriv(&self) -> ConstPoint { |
| 135 | ConstPoint((self.p1 - self.p0).to_point()) |
| 136 | } |
| 137 | } |
| 138 | |
| 139 | impl ParamCurveArclen for Line { |
| 140 | #[inline ] |
| 141 | fn arclen(&self, _accuracy: f64) -> f64 { |
| 142 | (self.p1 - self.p0).hypot() |
| 143 | } |
| 144 | |
| 145 | #[inline ] |
| 146 | fn inv_arclen(&self, arclen: f64, _accuracy: f64) -> f64 { |
| 147 | arclen / (self.p1 - self.p0).hypot() |
| 148 | } |
| 149 | } |
| 150 | |
| 151 | impl ParamCurveArea for Line { |
| 152 | #[inline ] |
| 153 | fn signed_area(&self) -> f64 { |
| 154 | self.p0.to_vec2().cross(self.p1.to_vec2()) * 0.5 |
| 155 | } |
| 156 | } |
| 157 | |
| 158 | impl ParamCurveNearest for Line { |
| 159 | fn nearest(&self, p: Point, _accuracy: f64) -> Nearest { |
| 160 | let d: Vec2 = self.p1 - self.p0; |
| 161 | let dotp: f64 = d.dot(p - self.p0); |
| 162 | let d_squared: f64 = d.dot(d); |
| 163 | let (t: f64, distance_sq: f64) = if dotp <= 0.0 { |
| 164 | (0.0, (p - self.p0).hypot2()) |
| 165 | } else if dotp >= d_squared { |
| 166 | (1.0, (p - self.p1).hypot2()) |
| 167 | } else { |
| 168 | let t: f64 = dotp / d_squared; |
| 169 | let dist: f64 = (p - self.eval(t)).hypot2(); |
| 170 | (t, dist) |
| 171 | }; |
| 172 | Nearest { distance_sq, t } |
| 173 | } |
| 174 | } |
| 175 | |
| 176 | impl ParamCurveCurvature for Line { |
| 177 | #[inline ] |
| 178 | fn curvature(&self, _t: f64) -> f64 { |
| 179 | 0.0 |
| 180 | } |
| 181 | } |
| 182 | |
| 183 | impl ParamCurveExtrema for Line { |
| 184 | #[inline ] |
| 185 | fn extrema(&self) -> ArrayVec<f64, MAX_EXTREMA> { |
| 186 | ArrayVec::new() |
| 187 | } |
| 188 | } |
| 189 | |
| 190 | /// A trivial "curve" that is just a constant. |
| 191 | #[derive (Clone, Copy, Debug)] |
| 192 | #[cfg_attr (feature = "schemars" , derive(schemars::JsonSchema))] |
| 193 | #[cfg_attr (feature = "serde" , derive(serde::Serialize, serde::Deserialize))] |
| 194 | pub struct ConstPoint(Point); |
| 195 | |
| 196 | impl ConstPoint { |
| 197 | /// Is this point [finite]? |
| 198 | /// |
| 199 | /// [finite]: f64::is_finite |
| 200 | #[inline ] |
| 201 | pub fn is_finite(self) -> bool { |
| 202 | self.0.is_finite() |
| 203 | } |
| 204 | |
| 205 | /// Is this point [NaN]? |
| 206 | /// |
| 207 | /// [NaN]: f64::is_nan |
| 208 | #[inline ] |
| 209 | pub fn is_nan(self) -> bool { |
| 210 | self.0.is_nan() |
| 211 | } |
| 212 | } |
| 213 | |
| 214 | impl ParamCurve for ConstPoint { |
| 215 | #[inline ] |
| 216 | fn eval(&self, _t: f64) -> Point { |
| 217 | self.0 |
| 218 | } |
| 219 | |
| 220 | #[inline ] |
| 221 | fn subsegment(&self, _range: Range<f64>) -> ConstPoint { |
| 222 | *self |
| 223 | } |
| 224 | } |
| 225 | |
| 226 | impl ParamCurveDeriv for ConstPoint { |
| 227 | type DerivResult = ConstPoint; |
| 228 | |
| 229 | #[inline ] |
| 230 | fn deriv(&self) -> ConstPoint { |
| 231 | ConstPoint(Point::new(x:0.0, y:0.0)) |
| 232 | } |
| 233 | } |
| 234 | |
| 235 | impl ParamCurveArclen for ConstPoint { |
| 236 | #[inline ] |
| 237 | fn arclen(&self, _accuracy: f64) -> f64 { |
| 238 | 0.0 |
| 239 | } |
| 240 | |
| 241 | #[inline ] |
| 242 | fn inv_arclen(&self, _arclen: f64, _accuracy: f64) -> f64 { |
| 243 | 0.0 |
| 244 | } |
| 245 | } |
| 246 | |
| 247 | impl Mul<Line> for Affine { |
| 248 | type Output = Line; |
| 249 | |
| 250 | #[inline ] |
| 251 | fn mul(self, other: Line) -> Line { |
| 252 | Line { |
| 253 | p0: self * other.p0, |
| 254 | p1: self * other.p1, |
| 255 | } |
| 256 | } |
| 257 | } |
| 258 | |
| 259 | impl Add<Vec2> for Line { |
| 260 | type Output = Line; |
| 261 | |
| 262 | #[inline ] |
| 263 | fn add(self, v: Vec2) -> Line { |
| 264 | Line::new(self.p0 + v, self.p1 + v) |
| 265 | } |
| 266 | } |
| 267 | |
| 268 | impl Sub<Vec2> for Line { |
| 269 | type Output = Line; |
| 270 | |
| 271 | #[inline ] |
| 272 | fn sub(self, v: Vec2) -> Line { |
| 273 | Line::new(self.p0 - v, self.p1 - v) |
| 274 | } |
| 275 | } |
| 276 | |
| 277 | /// An iterator yielding the path for a single line. |
| 278 | #[doc (hidden)] |
| 279 | pub struct LinePathIter { |
| 280 | line: Line, |
| 281 | ix: usize, |
| 282 | } |
| 283 | |
| 284 | impl Shape for Line { |
| 285 | type PathElementsIter<'iter> = LinePathIter; |
| 286 | |
| 287 | #[inline ] |
| 288 | fn path_elements(&self, _tolerance: f64) -> LinePathIter { |
| 289 | LinePathIter { line: *self, ix: 0 } |
| 290 | } |
| 291 | |
| 292 | /// Returning zero here is consistent with the contract (area is |
| 293 | /// only meaningful for closed shapes), but an argument can be made |
| 294 | /// that the contract should be tightened to include the Green's |
| 295 | /// theorem contribution. |
| 296 | fn area(&self) -> f64 { |
| 297 | 0.0 |
| 298 | } |
| 299 | |
| 300 | #[inline ] |
| 301 | fn perimeter(&self, _accuracy: f64) -> f64 { |
| 302 | (self.p1 - self.p0).hypot() |
| 303 | } |
| 304 | |
| 305 | /// Same consideration as `area`. |
| 306 | fn winding(&self, _pt: Point) -> i32 { |
| 307 | 0 |
| 308 | } |
| 309 | |
| 310 | #[inline ] |
| 311 | fn bounding_box(&self) -> Rect { |
| 312 | Rect::from_points(self.p0, self.p1) |
| 313 | } |
| 314 | |
| 315 | #[inline ] |
| 316 | fn as_line(&self) -> Option<Line> { |
| 317 | Some(*self) |
| 318 | } |
| 319 | } |
| 320 | |
| 321 | impl Iterator for LinePathIter { |
| 322 | type Item = PathEl; |
| 323 | |
| 324 | fn next(&mut self) -> Option<PathEl> { |
| 325 | self.ix += 1; |
| 326 | match self.ix { |
| 327 | 1 => Some(PathEl::MoveTo(self.line.p0)), |
| 328 | 2 => Some(PathEl::LineTo(self.line.p1)), |
| 329 | _ => None, |
| 330 | } |
| 331 | } |
| 332 | } |
| 333 | |
| 334 | #[cfg (test)] |
| 335 | mod tests { |
| 336 | use crate::{Line, ParamCurveArclen, Point}; |
| 337 | |
| 338 | #[test ] |
| 339 | fn line_reversed() { |
| 340 | let l = Line::new((0.0, 0.0), (1.0, 1.0)); |
| 341 | let f = l.reversed(); |
| 342 | |
| 343 | assert_eq!(l.p0, f.p1); |
| 344 | assert_eq!(l.p1, f.p0); |
| 345 | |
| 346 | // Reversing it again should result in the original line |
| 347 | assert_eq!(l, f.reversed()); |
| 348 | } |
| 349 | |
| 350 | #[test ] |
| 351 | fn line_arclen() { |
| 352 | let l = Line::new((0.0, 0.0), (1.0, 1.0)); |
| 353 | let true_len = 2.0f64.sqrt(); |
| 354 | let epsilon = 1e-9; |
| 355 | assert!(l.arclen(epsilon) - true_len < epsilon); |
| 356 | |
| 357 | let t = l.inv_arclen(true_len / 3.0, epsilon); |
| 358 | assert!((t - 1.0 / 3.0).abs() < epsilon); |
| 359 | } |
| 360 | |
| 361 | #[test ] |
| 362 | fn line_midpoint() { |
| 363 | let l = Line::new((0.0, 0.0), (2.0, 4.0)); |
| 364 | assert_eq!(l.midpoint(), Point::new(1.0, 2.0)); |
| 365 | } |
| 366 | |
| 367 | #[test ] |
| 368 | fn line_is_finite() { |
| 369 | assert!((Line { |
| 370 | p0: Point { x: 0., y: 0. }, |
| 371 | p1: Point { x: 1., y: 1. } |
| 372 | }) |
| 373 | .is_finite()); |
| 374 | |
| 375 | assert!(!(Line { |
| 376 | p0: Point { x: 0., y: 0. }, |
| 377 | p1: Point { |
| 378 | x: f64::INFINITY, |
| 379 | y: 1. |
| 380 | } |
| 381 | }) |
| 382 | .is_finite()); |
| 383 | |
| 384 | assert!(!(Line { |
| 385 | p0: Point { x: 0., y: 0. }, |
| 386 | p1: Point { |
| 387 | x: 0., |
| 388 | y: f64::INFINITY |
| 389 | } |
| 390 | }) |
| 391 | .is_finite()); |
| 392 | } |
| 393 | } |
| 394 | |