From 58ca374fab6dd90c4d7415bdcc98add002274894 Mon Sep 17 00:00:00 2001 From: Arne Dußin Date: Sat, 21 Nov 2020 11:23:16 +0100 Subject: Move polygon functions into own mod The math module was starting to be mostly polygon files and functions, so those got their own subfolder to make the math module less of a mess. --- src/math/polygon/mod.rs | 177 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 177 insertions(+) create mode 100644 src/math/polygon/mod.rs (limited to 'src/math/polygon/mod.rs') diff --git a/src/math/polygon/mod.rs b/src/math/polygon/mod.rs new file mode 100644 index 0000000..4530857 --- /dev/null +++ b/src/math/polygon/mod.rs @@ -0,0 +1,177 @@ +//! Contains functions and structures to help with operations on polygons. + +pub mod polygon_graph; +pub mod triangulate; + +pub use polygon_graph::*; +pub use triangulate::*; + +use super::Vec2; +use nalgebra::{ClosedDiv, ClosedMul, ClosedSub, RealField, Scalar}; +use num_traits::Zero; +use std::ops::Neg; + +#[derive(Debug)] +// TODO: Support polygons with holes +pub struct Polygon { + pub corners: Vec>, +} + +impl Polygon { + pub fn new(corners: Vec>) -> Self { + Self { corners } + } + + /// Check whether a point is inside a polygon or not. If a point lies on an edge, it also + /// counts as inside the polygon. + pub fn contains_point(&self, p: Vec2) -> bool + where + T: Zero + ClosedSub + ClosedMul + ClosedDiv + Neg + PartialOrd, + { + let n = self.corners.len(); + + let a = self.corners[n - 1]; + let mut b = self.corners[n - 2]; + let mut ax; + let mut ay = a.y - p.y; + let mut bx = b.x - p.x; + let mut by = b.y - p.y; + + let mut lup = by > ay; + for i in 0..n { + // ax = bx; + ay = by; + b = self.corners[i]; + bx = b.x - p.x; + by = b.y - p.y; + + if ay == by { + continue; + } + lup = by > ay; + } + + let mut depth = 0; + for i in 0..n { + ax = bx; + ay = by; + let b = &self.corners[i]; + bx = b.x - p.x; + by = b.y - p.y; + + if ay < T::zero() && by < T::zero() { + // both "up" or both "down" + continue; + } + if ay > T::zero() && by > T::zero() { + // both "up" or both "down" + continue; + } + if ax < T::zero() && bx < T::zero() { + // both points on the left + continue; + } + + if ay == by && (if ax < bx { ax } else { bx }) <= T::zero() { + return true; + } + if ay == by { + continue; + } + + let lx = ax + (((bx - ax) * -ay) / (by - ay)); + if lx == T::zero() { + // point on edge + return true; + } + if lx > T::zero() { + depth += 1; + } + if ay == T::zero() && lup && by > ay { + // hit vertex, both up + depth -= 1; + } + if ay == T::zero() && !lup && by < ay { + // hit vertex, both down + depth -= 1; + } + + lup = by > ay; + } + + (depth & 1) == 1 + } + + /// Join this polygon with another, ensuring the area of the two stays the same, but the + /// overlap is not doubled, but instead joined into one. + /// Returns the Polygons themselves, if there is no overlap + pub fn unite(self, other: Polygon) -> Vec> + where + T: RealField, + { + let mut graph = PolygonGraph::from_polygon(&self); + graph.add_all(&other); + + // TODO: Make bounding box support multiple polygons + vec![graph.bounding_polygon()] + } +} + +#[cfg(test)] +mod test { + use super::*; + + #[test] + fn polygon_contains() { + let polygon = Polygon::new(vec![ + Vec2::new(0., 0.), + Vec2::new(-1., 1.), + Vec2::new(0., 2.), + Vec2::new(1., 3.), + Vec2::new(3., 1.5), + Vec2::new(2., 0.), + Vec2::new(1., 1.), + ]); + + assert!(!polygon.contains_point(Vec2::new(1., -2.))); + assert!(!polygon.contains_point(Vec2::new(-1., 0.5))); + assert!(polygon.contains_point(Vec2::new(0., 0.5))); + assert!(polygon.contains_point(Vec2::new(0.5, 1.))); + assert!(polygon.contains_point(Vec2::new(0.5, 1.5))); + assert!(!polygon.contains_point(Vec2::new(-2., 1.9))); + assert!(!polygon.contains_point(Vec2::new(0., 3.))); + assert!(polygon.contains_point(Vec2::new(1., 3.))); + } + + #[test] + fn polygon_union() { + let first = Polygon::new(vec![ + Vec2::new(-2., 1.), + Vec2::new(-0.5, 2.5), + Vec2::new(2., 2.), + Vec2::new(0.5, 1.5), + Vec2::new(1., 0.), + Vec2::new(-0.5, 1.), + ]); + + let second = Polygon::new(vec![ + Vec2::new(0., 0.), + Vec2::new(-2., 2.), + Vec2::new(3., 2.), + Vec2::new(1.5, 0.), + ]); + + let union = first.unite(second); + assert_eq!(union.len(), 1); + let union = &union[0]; + + println!("Union of the two polygons: {:?}", union); + + assert_eq!(union.corners.len(), 11); + assert!(union + .corners + .iter() + .find(|&p| p.x == 0. && p.y == 0.) + .is_some()); + } +} -- cgit v1.2.3-70-g09d2 From abf55d8d46fc7d5cfccc9f778da6fca10b33d0cd Mon Sep 17 00:00:00 2001 From: Arne Dußin Date: Sat, 21 Nov 2020 20:55:47 +0100 Subject: Move containment of points/ lines into trait --- src/gui/tool_sidebar.rs | 4 +- src/math/line_segment.rs | 6 +-- src/math/mod.rs | 10 +++++ src/math/polygon/mod.rs | 53 ++++++++++++---------- src/math/rect.rs | 112 +++++++++++++++++++++++----------------------- src/tool/deletion_tool.rs | 6 +-- 6 files changed, 105 insertions(+), 86 deletions(-) (limited to 'src/math/polygon/mod.rs') diff --git a/src/gui/tool_sidebar.rs b/src/gui/tool_sidebar.rs index 46b53ea..7674c47 100644 --- a/src/gui/tool_sidebar.rs +++ b/src/gui/tool_sidebar.rs @@ -1,4 +1,4 @@ -use crate::math::{Rect, Vec2}; +use crate::math::{Rect, Surface, Vec2}; use crate::tool::ToolType; use crate::Editor; use raylib::core::texture::Texture2D; @@ -28,7 +28,7 @@ impl ToolSidebar { /// Check if the mouse is currently being captured by this GUI-element. In that case, /// everything else that might want to access the mouse will be blocked. pub fn mouse_captured(screen_height: u16, mouse_pos: Vec2) -> bool { - Self::panel_rect(screen_height).contains(mouse_pos) + Self::panel_rect(screen_height).contains_point(&mouse_pos) } pub fn draw(&self, screen_height: u16, rld: &mut impl RaylibDrawGui, editor: &mut Editor) { diff --git a/src/math/line_segment.rs b/src/math/line_segment.rs index 244b0af..94f58b2 100644 --- a/src/math/line_segment.rs +++ b/src/math/line_segment.rs @@ -1,4 +1,4 @@ -use super::{Rect, TripletOrientation, Vec2}; +use super::{Rect, Surface, TripletOrientation, Vec2}; use alga::general::{ClosedDiv, ClosedMul, ClosedSub}; use nalgebra::{RealField, Scalar}; use num_traits::Zero; @@ -118,8 +118,8 @@ impl LineSegment { * the segments. We know it's on the lines, so checking with the lines bounding box is * faster than checking where on the line exactly it would be. */ - if Rect::bounding_rect(line_a.start, line_a.end).contains(out) - && Rect::bounding_rect(line_b.start, line_b.end).contains(out) + if Rect::bounding_rect(line_a.start, line_a.end).contains_point(&out) + && Rect::bounding_rect(line_b.start, line_b.end).contains_point(&out) { Some(out) } else { diff --git a/src/math/mod.rs b/src/math/mod.rs index e72a7a4..6f83c98 100644 --- a/src/math/mod.rs +++ b/src/math/mod.rs @@ -10,8 +10,18 @@ pub use self::rect::*; pub use self::triangle::*; pub use self::vec2::*; +use nalgebra::Scalar; use std::cmp::Ordering; +/// Trait that describes an area in the vector space on the field of T +pub trait Surface { + /// Checks if a point lies on this surface. + fn contains_point(&self, point: &Vec2) -> bool; + + /// Checks if a line segment is entirely contained by this surface. + fn contains_line_segment(&self, line_segment: &LineSegment) -> bool; +} + /// Round a floating point number to the nearest step given by the step argument. For instance, if /// the step is 0.5, then all numbers from 0.0 to 0.24999... will be 0., while all numbers from /// 0.25 to 0.74999... will be 0.5 and so on. diff --git a/src/math/polygon/mod.rs b/src/math/polygon/mod.rs index 4530857..d351ec7 100644 --- a/src/math/polygon/mod.rs +++ b/src/math/polygon/mod.rs @@ -6,7 +6,7 @@ pub mod triangulate; pub use polygon_graph::*; pub use triangulate::*; -use super::Vec2; +use super::{LineSegment, Surface, Vec2}; use nalgebra::{ClosedDiv, ClosedMul, ClosedSub, RealField, Scalar}; use num_traits::Zero; use std::ops::Neg; @@ -24,10 +24,27 @@ impl Polygon { /// Check whether a point is inside a polygon or not. If a point lies on an edge, it also /// counts as inside the polygon. - pub fn contains_point(&self, p: Vec2) -> bool + + /// Join this polygon with another, ensuring the area of the two stays the same, but the + /// overlap is not doubled, but instead joined into one. + /// Returns the Polygons themselves, if there is no overlap + pub fn unite(self, other: Polygon) -> Vec> where - T: Zero + ClosedSub + ClosedMul + ClosedDiv + Neg + PartialOrd, + T: RealField, { + let mut graph = PolygonGraph::from_polygon(&self); + graph.add_all(&other); + + // TODO: Make bounding box support multiple polygons + vec![graph.bounding_polygon()] + } +} + +impl< + T: Scalar + Copy + ClosedSub + ClosedMul + ClosedDiv + Neg + PartialOrd + Zero, + > Surface for Polygon +{ + fn contains_point(&self, p: &Vec2) -> bool { let n = self.corners.len(); let a = self.corners[n - 1]; @@ -102,18 +119,8 @@ impl Polygon { (depth & 1) == 1 } - /// Join this polygon with another, ensuring the area of the two stays the same, but the - /// overlap is not doubled, but instead joined into one. - /// Returns the Polygons themselves, if there is no overlap - pub fn unite(self, other: Polygon) -> Vec> - where - T: RealField, - { - let mut graph = PolygonGraph::from_polygon(&self); - graph.add_all(&other); - - // TODO: Make bounding box support multiple polygons - vec![graph.bounding_polygon()] + fn contains_line_segment(&self, line_segment: &LineSegment) -> bool { + unimplemented!() } } @@ -133,14 +140,14 @@ mod test { Vec2::new(1., 1.), ]); - assert!(!polygon.contains_point(Vec2::new(1., -2.))); - assert!(!polygon.contains_point(Vec2::new(-1., 0.5))); - assert!(polygon.contains_point(Vec2::new(0., 0.5))); - assert!(polygon.contains_point(Vec2::new(0.5, 1.))); - assert!(polygon.contains_point(Vec2::new(0.5, 1.5))); - assert!(!polygon.contains_point(Vec2::new(-2., 1.9))); - assert!(!polygon.contains_point(Vec2::new(0., 3.))); - assert!(polygon.contains_point(Vec2::new(1., 3.))); + assert!(!polygon.contains_point(&Vec2::new(1., -2.))); + assert!(!polygon.contains_point(&Vec2::new(-1., 0.5))); + assert!(polygon.contains_point(&Vec2::new(0., 0.5))); + assert!(polygon.contains_point(&Vec2::new(0.5, 1.))); + assert!(polygon.contains_point(&Vec2::new(0.5, 1.5))); + assert!(!polygon.contains_point(&Vec2::new(-2., 1.9))); + assert!(!polygon.contains_point(&Vec2::new(0., 3.))); + assert!(polygon.contains_point(&Vec2::new(1., 3.))); } #[test] diff --git a/src/math/rect.rs b/src/math/rect.rs index 6988b2c..876e728 100644 --- a/src/math/rect.rs +++ b/src/math/rect.rs @@ -1,6 +1,6 @@ -use super::Vec2; +use super::{LineSegment, Surface, Vec2}; //use alga::general::{Additive, Identity}; -use nalgebra::{RealField, Scalar}; +use nalgebra::{ClosedAdd, RealField, Scalar}; use num_traits::identities::Zero; use serde::{Deserialize, Serialize}; use std::ops::{Add, AddAssign, Sub}; @@ -18,48 +18,6 @@ pub struct Rect { pub h: T, } -// This is sad, but also sadly necessary :/ -impl + Scalar + Copy> Into for Rect { - fn into(self) -> raylib::ffi::Rectangle { - raylib::ffi::Rectangle { - x: self.x.into(), - y: self.y.into(), - width: self.w.into(), - height: self.h.into(), - } - } -} -impl + Scalar + Copy> From for Rect { - fn from(r: raylib::ffi::Rectangle) -> Self { - Self { - x: T::from(r.x), - y: T::from(r.y), - w: T::from(r.width), - h: T::from(r.height), - } - } -} -impl + Scalar + Copy> Into for Rect { - fn into(self) -> raylib::math::Rectangle { - raylib::math::Rectangle { - x: self.x.into(), - y: self.y.into(), - width: self.w.into(), - height: self.h.into(), - } - } -} -impl + Scalar + Copy> From for Rect { - fn from(r: raylib::math::Rectangle) -> Self { - Self { - x: T::from(r.x), - y: T::from(r.y), - w: T::from(r.width), - h: T::from(r.height), - } - } -} - impl Rect { pub fn new(x: T, y: T, w: T, h: T) -> Self { Self { x, y, w, h } @@ -105,17 +63,6 @@ impl Rect { || this.y + this.h < other.y) } - /// Check if the point is inside this Rect and return true if so. - pub fn contains(&self, point: Vec2) -> bool - where - T: PartialOrd + Add, - { - point.x >= self.x - && point.x <= self.x + self.w - && point.y >= self.y - && point.y <= self.y + self.h - } - /// Returns true if the entire rect is contained inside this rectangle. pub fn contains_rect(&self, rect: Rect) -> bool where @@ -181,6 +128,61 @@ impl Rect { } } +impl Surface for Rect { + fn contains_point(&self, point: &Vec2) -> bool { + point.x >= self.x + && point.x <= self.x + self.w + && point.y >= self.y + && point.y <= self.y + self.h + } + + fn contains_line_segment(&self, line_segment: &LineSegment) -> bool { + self.contains_point(&line_segment.start) && self.contains_point(&line_segment.end) + } +} + +// This is sad, but also sadly necessary :/ +impl + Scalar + Copy> Into for Rect { + fn into(self) -> raylib::ffi::Rectangle { + raylib::ffi::Rectangle { + x: self.x.into(), + y: self.y.into(), + width: self.w.into(), + height: self.h.into(), + } + } +} +impl + Scalar + Copy> From for Rect { + fn from(r: raylib::ffi::Rectangle) -> Self { + Self { + x: T::from(r.x), + y: T::from(r.y), + w: T::from(r.width), + h: T::from(r.height), + } + } +} +impl + Scalar + Copy> Into for Rect { + fn into(self) -> raylib::math::Rectangle { + raylib::math::Rectangle { + x: self.x.into(), + y: self.y.into(), + width: self.w.into(), + height: self.h.into(), + } + } +} +impl + Scalar + Copy> From for Rect { + fn from(r: raylib::math::Rectangle) -> Self { + Self { + x: T::from(r.x), + y: T::from(r.y), + w: T::from(r.width), + h: T::from(r.height), + } + } +} + #[cfg(test)] mod test { use super::*; diff --git a/src/tool/deletion_tool.rs b/src/tool/deletion_tool.rs index c313574..5031f5d 100644 --- a/src/tool/deletion_tool.rs +++ b/src/tool/deletion_tool.rs @@ -2,7 +2,7 @@ use super::Tool; use crate::button::Button; use crate::config::{DeletionToolKeybindings, ToolKeybindings}; use crate::map_data::MapData; -use crate::math::{Rect, Vec2}; +use crate::math::{Rect, Surface, Vec2}; use crate::transform::Transform; use raylib::core::drawing::{RaylibDraw, RaylibDrawHandle}; use raylib::ffi::Color; @@ -28,10 +28,10 @@ impl DeletionTool { .retain(|&room| !rect.contains_rect(room)); map_data .walls_mut() - .retain(|&(pos1, pos2)| !rect.contains(pos1) || !rect.contains(pos2)); + .retain(|&(pos1, pos2)| !rect.contains_point(&pos1) || !rect.contains_point(&pos2)); map_data .icons_mut() - .retain(|icon| !rect.contains(icon.position)); + .retain(|icon| !rect.contains_point(&icon.position)); } } -- cgit v1.2.3-70-g09d2 From 1363c7713d19bd733a97dff5727827cf7684a27b Mon Sep 17 00:00:00 2001 From: Arne Dußin Date: Mon, 23 Nov 2020 21:06:56 +0100 Subject: Add ear clipping algorithm --- src/math/polygon/mod.rs | 93 +++++++++++++++++++++++++++++++- src/math/polygon/triangulate.rs | 114 ++++++++++++++++++++++++++++++++++++++-- 2 files changed, 201 insertions(+), 6 deletions(-) (limited to 'src/math/polygon/mod.rs') diff --git a/src/math/polygon/mod.rs b/src/math/polygon/mod.rs index d351ec7..baa1e6d 100644 --- a/src/math/polygon/mod.rs +++ b/src/math/polygon/mod.rs @@ -6,7 +6,8 @@ pub mod triangulate; pub use polygon_graph::*; pub use triangulate::*; -use super::{LineSegment, Surface, Vec2}; +use super::{LineSegment, Surface, TripletOrientation, Vec2}; +use crate::math; use nalgebra::{ClosedDiv, ClosedMul, ClosedSub, RealField, Scalar}; use num_traits::Zero; use std::ops::Neg; @@ -120,7 +121,51 @@ impl< } fn contains_line_segment(&self, line_segment: &LineSegment) -> bool { - unimplemented!() + /* In case at least one of the points is not contained by the polygon, the line cannot lie + * inside of the polygon in its entirety. + */ + if !self.contains_point(&line_segment.start) || !self.contains_point(&line_segment.end) { + return false; + } + + /* Both end-points are inside the polygon. */ + + /* Check the intersections of the line segment with all polygon edges and see if it is + * piercing through any of them. + */ + for c in 0..self.corners.len() { + let next = (c + 1) % self.corners.len(); + let current_edge = LineSegment::new(self.corners[c], self.corners[next]); + + if LineSegment::intersect(&line_segment, ¤t_edge) { + let orientation_start = math::triplet_orientation( + current_edge.start, + current_edge.end, + line_segment.start, + ); + let orientation_end = math::triplet_orientation( + current_edge.start, + current_edge.end, + line_segment.end, + ); + match (orientation_start, orientation_end) { + /* If at least one of the points is on the edge, make sure, the line points + * inside of the polygon, not to the outside. + */ + (TripletOrientation::Collinear, o) | (o, TripletOrientation::Collinear) => { + if o == TripletOrientation::Clockwise { + return false; + } + } + /* Start and endpoint are on different sides of the edge, therefore the line + * must be partially outside. + */ + _ => return false, + } + } + } + + true } } @@ -150,6 +195,50 @@ mod test { assert!(polygon.contains_point(&Vec2::new(1., 3.))); } + #[test] + fn contains_line_segment() { + let polygon = Polygon::new(vec![ + Vec2::new(0., 0.), + Vec2::new(0., 4.5), + Vec2::new(6.5, 4.5), + Vec2::new(5.5, 0.), + Vec2::new(5.5, 3.), + Vec2::new(1.5, 3.), + Vec2::new(1.5, 1.), + Vec2::new(2., 0.5), + Vec2::new(4., 2.), + Vec2::new(4., 0.), + ]); + + /* NOTE: From now on, inside means inside the polygon, but might be on an edge or on a + * corner point, really inside means inside and not on an edge. + */ + + // Start point really inside, end point really inside. Line not completely inside. + assert!(!polygon + .contains_line_segment(&LineSegment::new(Vec2::new(2.5, 0.5), Vec2::new(0.5, 2.5)))); + + // Start point on edge, end point on corner, line completely outside. + assert!(!polygon + .contains_line_segment(&LineSegment::new(Vec2::new(1.5, 2.), Vec2::new(4., 2.)))); + + // Start point on edge, end point on edge, line inside. + assert!(polygon + .contains_line_segment(&LineSegment::new(Vec2::new(3.5, 3.), Vec2::new(3.5, 4.5)))); + + // Start point on corner, end point on corner, line inside. + assert!(polygon + .contains_line_segment(&LineSegment::new(Vec2::new(5.5, 3.), Vec2::new(6.5, 4.5)))); + + // Start point really inside, end point on edge. Line not inside. + assert!(!polygon + .contains_line_segment(&LineSegment::new(Vec2::new(3.5, 0.5), Vec2::new(5.5, 0.5)))); + + // Start point and endpoint outside. Line completely outside. + assert!(!polygon + .contains_line_segment(&LineSegment::new(Vec2::new(7.0, 0.), Vec2::new(7.5, 1.)))); + } + #[test] fn polygon_union() { let first = Polygon::new(vec![ diff --git a/src/math/polygon/triangulate.rs b/src/math/polygon/triangulate.rs index 4860518..096a1c6 100644 --- a/src/math/polygon/triangulate.rs +++ b/src/math/polygon/triangulate.rs @@ -1,13 +1,119 @@ //! Module for turning a polygon into a number of non-overlapping triangles. use super::Polygon; -use crate::math::Triangle; -use nalgebra::Scalar; +use crate::math::{self, LineSegment, Surface, Triangle}; +use nalgebra::{RealField, Scalar}; + +/// Type that saves the flags that match a corner in a space efficient manner. +type Flags = u8; + +/// Tells the algorithm that this corner of the polygon is an ear. An ear means the adjacent corners +/// form a triangle with this corner of which the area is entirely contained by the polygon itself. +const FLAG_EAR: Flags = 0b0000_0001; +/// Tells the algorithm that this corner is convex, meaning its internal angle is less than Pi. +/// Useful, because this is a necessary condition for earness. False if the vertex is reflex. +// TODO: The convex flag is a remnant from the previous algorithm, but currently it's not being +// used. Consider removing it entirely. +const FLAG_CONVEX: Flags = 0b0000_0010; + +fn flag_corner(polygon: &Polygon, corner: usize) -> Flags +where + T: RealField, +{ + // First, check if it is convex. If it is not, it can also not be an ear. + let prev = (corner + polygon.corners.len() - 1) % polygon.corners.len(); + let next = (corner + 1) % polygon.corners.len(); + + /* Since the angle is also in counterclockwise direction, like the polygon itself, the corner + * is convex if and only if the angle is **not**. + */ + if math::triplet_angle( + polygon.corners[prev], + polygon.corners[corner], + polygon.corners[next], + ) < T::pi() + { + // The corner is reflex. + return 0b0; + } + + // The corner is convex, check if it is also an ear. + if polygon.contains_line_segment(&LineSegment::new( + polygon.corners[prev], + polygon.corners[next], + )) { + // Corner is an ear. + FLAG_EAR | FLAG_CONVEX + } else { + // Corner is not an ear. + FLAG_CONVEX + } +} /// Uses earclipping algorithm (see https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf) /// to find an explanation of what exactly is happening. /// Currently only handles simple polygons, but once the polygon struct supports holes must be /// extended to also support those. -pub fn triangulate(_polygon: &Polygon) -> Vec> { - unimplemented!() +pub fn triangulate(mut polygon: Polygon) -> Vec> +where + T: RealField, +{ + assert!(polygon.corners.len() >= 3); + /* Information about the corner of the polygon. See the flags constant for information about + * what the bits mean. + */ + let mut flags = Vec::with_capacity(polygon.corners.len()); + for c in 0..polygon.corners.len() { + flags.push(flag_corner(&polygon, c)); + } + + let mut triangles = Vec::with_capacity(polygon.corners.len() - 2); + // Clip ears until there's only the last triangle left. + /* NOTE: This could be changed to > 2 and the last triangle would be pushed inside the loop, + * because it is also detected as an ear, however this is more logical to the original idea + * imo. + */ + while polygon.corners.len() > 3 { + // Find the ear with the highest index. + let ear = flags + .iter() + .rposition(|&x| (x & FLAG_EAR) != 0) + .expect("Polygon has more than three vertices, but no ear."); + + // Add the ear's triangle to the list. + { + let prev = (ear + polygon.corners.len() - 1) % polygon.corners.len(); + let next = (ear + 1) % polygon.corners.len(); + triangles.push(Triangle::new( + polygon.corners[prev], + polygon.corners[ear], + polygon.corners[next], + )); + + // Remove the ear from the polygon and the flag list. + polygon.corners.remove(ear); + flags.remove(ear); + } + + // Reassess the status of the two adjacent points. Notice that since the ear was removed, + // their array positions have changed. + let prev = if ear == 0 || ear == polygon.corners.len() { + polygon.corners.len() - 1 + } else { + ear - 1 + }; + let next = if ear == polygon.corners.len() { 0 } else { ear }; + + flags[prev] = flag_corner(&polygon, prev); + flags[next] = flag_corner(&polygon, next); + } + + // Push the remaining triangle into the list. + triangles.push(Triangle::new( + polygon.corners[0], + polygon.corners[1], + polygon.corners[2], + )); + + triangles } -- cgit v1.2.3-70-g09d2 From a6c141908ddb94a0ebb3a1ac95d3f8444e13e3b5 Mon Sep 17 00:00:00 2001 From: Arne Dußin Date: Mon, 23 Nov 2020 22:40:12 +0100 Subject: Fix corner case not being handled Previously, the algorithm to check, if a line-segment is inside a polygon did not have a special case for when the start or end of the segment is on a polygon corner. In case this corner is reflexive, checking against one line between this corner and an adjacent one may not be enough. --- src/math/polygon/mod.rs | 64 +++++++++++++++++++++++++++++++++++++++++++++++-- src/math/triangle.rs | 35 +++++++++++++++++++++++++++ 2 files changed, 97 insertions(+), 2 deletions(-) (limited to 'src/math/polygon/mod.rs') diff --git a/src/math/polygon/mod.rs b/src/math/polygon/mod.rs index baa1e6d..e19e097 100644 --- a/src/math/polygon/mod.rs +++ b/src/math/polygon/mod.rs @@ -130,11 +130,60 @@ impl< /* Both end-points are inside the polygon. */ + /* In case the an endpoint of the line segment is equal to a corner of the polygon, it's + * not enough to merely check one edge, since if the corner is reflex, the segment may + * still be inside, eventhough its similar to the outwards pointing normal of one edge, but + * may be to the inside of the other edge. + */ + let mut start_looks_inside = false; + let mut end_looks_inside = false; + /* Helper function that checks if a point p, when starting from the given corner c is in a + * direction so that considering both edges that are connected to c, the point is in the + * direction of the inside of the polygon. + */ + let corner_vec_pointing_inside = |p: Vec2, c: usize| { + let prev = (c + self.corners.len() - 1) % self.corners.len(); + let next = (c + 1) % self.corners.len(); + + let last_edge_orientation = + math::triplet_orientation(self.corners[prev], self.corners[c], p); + let current_edge_orientation = + math::triplet_orientation(self.corners[c], self.corners[next], p); + + if last_edge_orientation == TripletOrientation::Clockwise + && current_edge_orientation == TripletOrientation::Clockwise + { + false + } else { + true + } + }; + + for c in 0..self.corners.len() { + if line_segment.start == self.corners[c] { + start_looks_inside = corner_vec_pointing_inside(line_segment.end, c); + if !start_looks_inside { + return false; + } + } + if line_segment.end == self.corners[c] { + end_looks_inside = corner_vec_pointing_inside(line_segment.start, c); + if !end_looks_inside { + return false; + } + } + } + + if start_looks_inside && end_looks_inside { + return true; + } + /* Check the intersections of the line segment with all polygon edges and see if it is * piercing through any of them. */ for c in 0..self.corners.len() { let next = (c + 1) % self.corners.len(); + let current_edge = LineSegment::new(self.corners[c], self.corners[next]); if LineSegment::intersect(&line_segment, ¤t_edge) { @@ -152,8 +201,13 @@ impl< /* If at least one of the points is on the edge, make sure, the line points * inside of the polygon, not to the outside. */ - (TripletOrientation::Collinear, o) | (o, TripletOrientation::Collinear) => { - if o == TripletOrientation::Clockwise { + (TripletOrientation::Collinear, o) => { + if !start_looks_inside && o == TripletOrientation::Clockwise { + return false; + } + } + (o, TripletOrientation::Collinear) => { + if !end_looks_inside && o == TripletOrientation::Clockwise { return false; } } @@ -237,6 +291,12 @@ mod test { // Start point and endpoint outside. Line completely outside. assert!(!polygon .contains_line_segment(&LineSegment::new(Vec2::new(7.0, 0.), Vec2::new(7.5, 1.)))); + + // Start point on vertex, pointing in same dir as one of the adjacent edge normals, + // completely inside. + assert!( + polygon.contains_line_segment(&LineSegment::new(Vec2::new(2., 0.5), Vec2::new(4., 0.))) + ); } #[test] diff --git a/src/math/triangle.rs b/src/math/triangle.rs index 5cf16e5..35bdcec 100644 --- a/src/math/triangle.rs +++ b/src/math/triangle.rs @@ -4,6 +4,7 @@ use nalgebra::{RealField, Scalar}; use num_traits::Zero; /// Represents a triangle +#[derive(Debug)] pub struct Triangle { /// The three corners of the triangle. Internally, it is made sure that the corners are always /// ordered in a counterclockwise manner, to make operations like contains simpler. @@ -80,6 +81,25 @@ impl Into<[Vec2; 3]> for Triangle { } } +impl PartialEq for Triangle { + fn eq(&self, other: &Self) -> bool { + // The indexes of the elements are not important, so try all shifting options. + for shift in 0..=2 { + if self + .corners + .iter() + .enumerate() + .find(|(i, &c)| c != other.corners[(i + shift) % 3]) + .is_none() + { + return true; + } + } + + false + } +} + #[derive(PartialEq, Eq)] pub(crate) enum TripletOrientation { Clockwise, @@ -186,6 +206,21 @@ mod test { assert!(!triangle.contains_point(Vec2::new(-2., -2.))); } + #[test] + fn equality() { + let a = Vec2::new(0., 0.); + let b = Vec2::new(-1., -1.); + let c = Vec2::new(-2., 0.); + let d = Vec2::new(-3., 0.); + + let cmp = Triangle::new(a, b, c); + + assert_eq!(Triangle::new(a, b, c), cmp); + assert_eq!(Triangle::new(c, b, a), cmp); + assert_eq!(Triangle::new(b, a, c), cmp); + assert!(Triangle::new(a, b, d) != cmp); + } + #[test] fn triplet_angle() { assert_eq!( -- cgit v1.2.3-70-g09d2 From 3b0c99351da92410bbfaba233e40376b767cb64e Mon Sep 17 00:00:00 2001 From: Arne Dußin Date: Mon, 23 Nov 2020 23:25:45 +0100 Subject: Add triangulation function --- src/math/polygon/mod.rs | 33 ++++++++++++++++++++------------- src/math/polygon/triangulate.rs | 30 ++++++++++++++++++++++++++++++ 2 files changed, 50 insertions(+), 13 deletions(-) (limited to 'src/math/polygon/mod.rs') diff --git a/src/math/polygon/mod.rs b/src/math/polygon/mod.rs index e19e097..cc89169 100644 --- a/src/math/polygon/mod.rs +++ b/src/math/polygon/mod.rs @@ -42,7 +42,15 @@ impl Polygon { } impl< - T: Scalar + Copy + ClosedSub + ClosedMul + ClosedDiv + Neg + PartialOrd + Zero, + T: Scalar + + Copy + + ClosedSub + + ClosedMul + + ClosedDiv + + Neg + + PartialOrd + + RealField + + Zero, > Surface for Polygon { fn contains_point(&self, p: &Vec2) -> bool { @@ -145,18 +153,11 @@ impl< let prev = (c + self.corners.len() - 1) % self.corners.len(); let next = (c + 1) % self.corners.len(); - let last_edge_orientation = - math::triplet_orientation(self.corners[prev], self.corners[c], p); - let current_edge_orientation = - math::triplet_orientation(self.corners[c], self.corners[next], p); - - if last_edge_orientation == TripletOrientation::Clockwise - && current_edge_orientation == TripletOrientation::Clockwise - { - false - } else { - true - } + let edge_angle = + math::triplet_angle(self.corners[prev], self.corners[c], self.corners[next]); + let vec_angle = math::triplet_angle(self.corners[prev], self.corners[c], p); + + vec_angle == T::zero() || vec_angle >= edge_angle }; for c in 0..self.corners.len() { @@ -297,6 +298,12 @@ mod test { assert!( polygon.contains_line_segment(&LineSegment::new(Vec2::new(2., 0.5), Vec2::new(4., 0.))) ); + + // Start and end point on vertex, not pointing in the dir of adjacent edge normals, + // not completely inside. + assert!( + !polygon.contains_line_segment(&LineSegment::new(Vec2::new(4., 2.), Vec2::new(0., 0.))) + ); } #[test] diff --git a/src/math/polygon/triangulate.rs b/src/math/polygon/triangulate.rs index 096a1c6..78dfa03 100644 --- a/src/math/polygon/triangulate.rs +++ b/src/math/polygon/triangulate.rs @@ -117,3 +117,33 @@ where triangles } + +#[cfg(test)] +mod test { + use super::*; + use crate::math::Vec2; + + #[test] + fn triangulate() { + let polygon = Polygon::new(vec![ + Vec2::new(0., 0.), + Vec2::new(0., 4.5), + Vec2::new(6.5, 4.5), + Vec2::new(5.5, 0.), + Vec2::new(5.5, 3.), + Vec2::new(1.5, 3.), + Vec2::new(1.5, 1.), + Vec2::new(2., 0.5), + Vec2::new(4., 2.), + Vec2::new(4., 0.), + ]); + + let triangles = super::triangulate(polygon); + + assert_eq!(triangles.len(), 8); + assert_eq!( + triangles[0], + (Triangle::new(Vec2::new(2., 0.5), Vec2::new(4., 2.), Vec2::new(4., 0.))) + ); + } +} -- cgit v1.2.3-70-g09d2