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| // | ||
| // Line.swift | ||
| // Euclid | ||
| // | ||
| // Created by Nick Lockwood on 20/11/2019. | ||
| // Copyright © 2018 Nick Lockwood. All rights reserved. | ||
| // | ||
| // Distributed under the permissive MIT license | ||
| // Get the latest version from here: | ||
| // | ||
| // https://github.com/nicklockwood/Euclid | ||
| // | ||
| // Permission is hereby granted, free of charge, to any person obtaining a copy | ||
| // of this software and associated documentation files (the "Software"), to deal | ||
| // in the Software without restriction, including without limitation the rights | ||
| // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
| // copies of the Software, and to permit persons to whom the Software is | ||
| // furnished to do so, subject to the following conditions: | ||
| // | ||
| // The above copyright notice and this permission notice shall be included in all | ||
| // copies or substantial portions of the Software. | ||
| // | ||
| // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
| // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
| // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
| // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
| // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
| // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
| // SOFTWARE. | ||
| // | ||
|
|
||
| import Foundation | ||
|
|
||
| public struct LineSegment : Hashable { | ||
| public init(_ point1: Vector, _ point2: Vector) { | ||
| self.point1 = point1 | ||
| self.point2 = point2 | ||
| } | ||
|
|
||
| public var point1: Vector { | ||
| didSet { point1 = point1.quantized() } | ||
| } | ||
|
|
||
| public var point2: Vector { | ||
| didSet { point2 = point2.quantized() } | ||
| } | ||
|
|
||
| public var direction : Vector { | ||
| let diff = point2 - point1 | ||
| return diff.normalized() | ||
| } | ||
|
|
||
| public func intersects(with: LineSegment) -> Bool { | ||
| if ((self.direction.z == 0) && (with.direction.z == 0) && (self.point1.z == with.point1.z)) { | ||
| return lineSegmentsIntersect(self.point1, self.point2, with.point1, with.point2) | ||
| } else if ((self.direction.y == 0) && (with.direction.y == 0) && (self.point1.y == with.point1.y)) { | ||
| // Switch dimensions and then solve | ||
| let p0 = Vector(self.point1.x, self.point1.z, 0) | ||
| let p1 = Vector(self.point2.x, self.point2.z, 0) | ||
| let p2 = Vector(with.point1.x, with.point1.z, 0) | ||
| let p3 = Vector(with.point2.x, with.point2.z, 0) | ||
| return lineSegmentsIntersect(p0, p1, p2, p3) | ||
| } else if ((self.direction.x == 0) && (with.direction.x == 0) && (self.point1.x == with.point1.x)) { | ||
| // Switch dimensions and then solve | ||
| let p0 = Vector(self.point1.y, self.point1.z, 0) | ||
| let p1 = Vector(self.point2.y, self.point2.z, 0) | ||
| let p2 = Vector(with.point1.y, with.point1.z, 0) | ||
| let p3 = Vector(with.point2.y, with.point2.z, 0) | ||
| return lineSegmentsIntersect(p0, p1, p2, p3) | ||
| } else { | ||
| // TOOO: Generalize to 3D | ||
| return false; | ||
| } | ||
| } | ||
| } | ||
|
|
||
| public struct Line : Hashable { | ||
| public init(point: Vector, direction: Vector) { | ||
| self.point = point | ||
| self.direction = direction | ||
| } | ||
|
|
||
| public init(from: LineSegment) { | ||
| self.point = from.point1 | ||
| self.direction = from.direction | ||
| } | ||
|
|
||
| public var point: Vector { | ||
| didSet { point = point.quantized() } | ||
| } | ||
|
|
||
| public var direction: Vector { | ||
| didSet { direction = direction.normalized() } | ||
| } | ||
|
|
||
| public func distance(to: Vector) -> Double { | ||
| // See "Vector formulation" at https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line | ||
| let aMinusP = self.point - to | ||
| let v = aMinusP - (self.direction * aMinusP.dot(self.direction)) | ||
| return v.length | ||
| } | ||
|
|
||
| public func intersection(with: Line) -> Vector? { | ||
| if ((self.direction.z == 0) && (with.direction.z == 0) && (self.point.z == with.point.z)) { | ||
| return lineIntersection(self.point, self.point + self.direction, with.point, with.point + with.direction) | ||
| } else if ((self.direction.y == 0) && (with.direction.y == 0) && (self.point.y == with.point.y)) { | ||
| // Switch dimensions and then solve | ||
| let p0 = Vector(self.point.x, self.point.z, self.point.y) | ||
| let p1 = p0 + Vector(self.direction.x, self.direction.z, 0) | ||
| let p2 = Vector(with.point.x, with.point.z, with.point.y) | ||
| let p3 = p2 + Vector(with.direction.x, with.direction.z, 0) | ||
| let solution = lineIntersection(p0, p1, p2, p3) | ||
| if (solution != nil) { | ||
| return Vector(solution!.x, solution!.z, solution!.y) | ||
| } else { | ||
| return nil; | ||
| } | ||
| } else if ((self.direction.x == 0) && (with.direction.x == 0) && (self.point.x == with.point.x)) { | ||
| // Switch dimensions and then solve | ||
| let p0 = Vector(self.point.y, self.point.z, self.point.x) | ||
| let p1 = p0 + Vector(self.direction.y, self.direction.z, 0) | ||
| let p2 = Vector(with.point.y, with.point.z, with.point.x) | ||
| let p3 = p2 + Vector(with.direction.y, with.direction.z, 0) | ||
| let solution = lineIntersection(p0, p1, p2, p3) | ||
| if (solution != nil) { | ||
| return Vector(solution!.z, solution!.x, solution!.y) | ||
| } else { | ||
| return nil; | ||
| } | ||
| } else { | ||
| // TOOO: Generalize to 3D | ||
| return nil; | ||
| } | ||
| } | ||
| } | ||
|
|
||
| // MARK: Private utility functions | ||
|
|
||
| // Get the intersection point between two lines | ||
| // TODO: extend this to work in 3D | ||
| // TODO: improve this using https://en.wikipedia.org/wiki/Line–line_intersection | ||
| private func lineIntersection(_ p0: Vector, _ p1: Vector, | ||
| _ p2: Vector, _ p3: Vector) -> Vector? { | ||
| let x1 = p0.x, y1 = p0.y | ||
| let x2 = p1.x, y2 = p1.y | ||
| let x3 = p2.x, y3 = p2.y | ||
| let x4 = p3.x, y4 = p3.y | ||
|
|
||
| let x1y2 = x1 * y2, y1x2 = y1 * x2 | ||
| let x1y2minusy1x2 = x1y2 - y1x2 | ||
|
|
||
| let x3minusx4 = x3 - x4 | ||
| let x1minusx2 = x1 - x2 | ||
|
|
||
| let x3y4 = x3 * y4, y3x4 = y3 * x4 | ||
| let x3y4minusy3x4 = x3y4 - y3x4 | ||
|
|
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| let y3minusy4 = y3 - y4 | ||
| let y1minusy2 = y1 - y2 | ||
|
|
||
| let d = x1minusx2 * y3minusy4 - y1minusy2 * x3minusx4 | ||
| if abs(d) < epsilon { | ||
| return nil // lines are parallel | ||
| } | ||
| let ix = (x1y2minusy1x2 * x3minusx4 - x1minusx2 * x3y4minusy3x4) / d | ||
| let iy = (x1y2minusy1x2 * y3minusy4 - y1minusy2 * x3y4minusy3x4) / d | ||
|
|
||
| return Vector(ix, iy, p0.z).quantized() | ||
| } | ||
|
|
||
| // TODO: extend this to work in 3D | ||
| private func lineSegmentsIntersect(_ p0: Vector, _ p1: Vector, | ||
| _ p2: Vector, _ p3: Vector) -> Bool { | ||
| guard let pi = lineIntersection(p0, p1, p2, p3) else { | ||
| return false // lines are parallel | ||
| } | ||
| // TODO: is there a cheaper way to do this? | ||
| if pi.x < min(p0.x, p1.x) || pi.x > max(p0.x, p1.x) || | ||
| pi.x < min(p2.x, p3.x) || pi.x > max(p2.x, p3.x) || | ||
| pi.y < min(p0.y, p1.y) || pi.y > max(p0.y, p1.y) || | ||
| pi.y < min(p2.y, p3.y) || pi.y > max(p2.y, p3.y) { | ||
| return false | ||
| } | ||
| return true | ||
| } |
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