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earcut: new industrial-strength polygon triangulation library

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Signed-off-by: Stephen Gutekanst <stephen@hexops.com>
This commit is contained in:
Stephen Gutekanst 2022-10-30 05:44:16 -07:00
parent 839d60c940
commit 09fa494359
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* text=auto eol=lf
upstream/** linguist-vendored

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github: slimsag

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Please send your change to [the main repository](https://github.com/hexops/mach/tree/main/libs/earcut) instead, sorry for the trouble!
This helps us avoid some complex merge conflicts we run into when changes are made to both repositories and history needs to be reconciled. Keeping PRs in just that repository enables us to use `git subtree` to trivially keep the two repositories in sync.
Once your PR is merged over there, it'll automatically sync to this repository.

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name: CI
on:
- push
- pull_request
jobs:
x86_64-linux:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Setup Zig
run: |
sudo apt install xz-utils
sudo sh -c 'wget -c https://ziglang.org/builds/zig-linux-x86_64-0.10.0-dev.4476+0f0076666.tar.xz -O - | tar -xJ --strip-components=1 -C /usr/local/bin'
- name: x86_64-linux -> aarch64-macos
run: zig build test -Dtarget=aarch64-macos.12-none
- name: test
run: |
zig build test
x86_64-windows:
runs-on: windows-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Install Git
run: choco install git
- name: Setup Zig
run: |
$ProgressPreference = 'SilentlyContinue'
Invoke-WebRequest -Uri "https://ziglang.org/builds/zig-windows-x86_64-0.10.0-dev.4476+0f0076666.zip" -OutFile "C:\zig.zip"
cd C:\
7z x zig.zip
Add-Content $env:GITHUB_PATH "C:\zig-windows-x86_64-0.10.0-dev.4476+0f0076666\"
- name: test
run: zig build test
x86_64-macos:
runs-on: macos-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Setup Zig
run: |
brew install xz
sudo sh -c 'wget -c https://ziglang.org/builds/zig-macos-x86_64-0.10.0-dev.4476+0f0076666.tar.xz -O - | tar -xJ --strip-components=1 -C /usr/local/bin'
- name: test
run: zig build test

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# This file is for zig-specific build artifacts.
# If you have OS-specific or editor-specific files to ignore,
# such as *.swp or .DS_Store, put those in your global
# ~/.gitignore and put this in your ~/.gitconfig:
#
# [core]
# excludesfile = ~/.gitignore
#
# Cheers!
# -andrewrk
zig-cache/
zig-out/
/release/
/debug/
/build/
/build-*/
/docgen_tmp/

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Copyright 2021, Hexops Contributors (given via the Git commit history).
All documentation, image, sound, font, and 2D/3D model files are CC-BY-4.0 licensed unless
otherwise noted. You may get a copy of this license at https://creativecommons.org/licenses/by/4.0
Files in a directory with a separate LICENSE file may contain files under different license terms,
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All other files are licensed under the Apache License, Version 2.0 (see LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
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All files in the project without exclusions may not be copied, modified, or distributed except
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# mach/earcut: industrial-strength polygon triangulation
Turning polygons into triangle meshes is a challenging problem, with numerous edge-cases. Popular libraries that try to solve this problem include libtess2, libtess3, and poly2tri (including the MetricPanda poly2tri variant.) Some of these libraries are better than others, but all of them suffer from performance and correctness issues-often failing on some very simple polygon inputs.
State-of-the-art research into polygon tesselation includes [CMU researcher Jonathan Shewchuk's outstanding 'Triangle' library](https://www.cs.cmu.edu/~quake/triangle.html), which is probably the most industrial-strength and correct polygon tesselator in existence today. Despite widespread adoption in some open source projects, [it is proprietary](https://gist.github.com/slimsag/7e38961c7f9dfc2dcf8eea17b41f919e) and not legally suitable for inclusion in open source software.
The second most industrial-strength tesselation library in existence today is from [a company called Mapbox](https://github.com/mapbox/earcut), and is [at the core of their map rendering](https://docs.mapbox.com/mapbox-gl-js/example/) technology. `mach/earcut` is a port of their library to Zig. It is open-source and permissively licensed, and based on ideas from [FIST: Fast Industrial-Strength Triangulation of Polygons](http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html) by Martin Held and [Triangulation by Ear Clipping](http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf) by David Eberly - and optimized by [z-order curve](http://en.wikipedia.org/wiki/Z-order_curve) hashing.
It can handle holes, twisted polygons, degeneracies and self-intersections. While it doesn't _guarantee_ correctness of triangulation, it attempts to always produce acceptable results for practical data. In effect, it is good for *turning polygons into triangles for visualization*.
It is [faster and more correct](https://github.com/mapbox/earcut#why-another-triangulation-library) than other libraries such as libtess, poly2tri, and others.
This Zig implementation is a direct port, and should theoretically be equally correct - and possibly faster than the mapbox version.
(This repository is a separate copy of the same library in the [main Mach repository](https://github.com/hexops/mach), and is automatically kept in sync, so that anyone can use this library in their own project if they like!)
## Getting started
### Adding dependency
In a `libs` subdirectory of the root of your project:
```sh
git clone https://github.com/hexops/mach-earcut
```
Then in your `build.zig` add:
```zig
...
const earcut = @import("libs/mach-earcut/build.zig");
pub fn build(b: *Builder) void {
...
exe.addPackage(earcut.pkg);
}
```
For usage, see `src/main.zig` `test "basic"`.
## Join the community
Join the Mach community [on Discord](https://discord.gg/XNG3NZgCqp) or [Matrix](https://matrix.to/#/#hexops:matrix.org) to discuss this project, ask questions, get help, etc.
## Issues
Issues are tracked in the [main Mach repository](https://github.com/hexops/mach/issues?q=is%3Aissue+is%3Aopen+label%3Aearcut).
## Contributing
Contributions are very welcome. Pull requests must be sent to [the main repository](https://github.com/hexops/mach/tree/main/earcut) to avoid some complex merge conflicts we'd get by accepting contributions in both repositories. Once the changes are merged there, they'll get sync'd to this repository automatically.
## Version
We currently reflect [this version](https://github.com/mapbox/earcut/tree/ae33a9fc9731c76519e66081995387e08d48eb65) of the upstream library.

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const std = @import("std");
pub fn build(b: *std.build.Builder) void {
const mode = b.standardReleaseOptions();
const lib = b.addStaticLibrary("earcut", "src/main.zig");
lib.setBuildMode(mode);
lib.install();
var main_tests = b.addTest("src/main.zig");
main_tests.setBuildMode(mode);
const test_step = b.step("test", "Run library tests");
test_step.dependOn(&main_tests.step);
_ = pkg;
}
pub const pkg = std.build.Pkg{
.name = "earcut",
.source = .{ .path = thisDir() ++ "/src/main.zig" },
};
fn thisDir() []const u8 {
return std.fs.path.dirname(@src().file) orelse ".";
}

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const std = @import("std");
const testing = std.testing;
const sign = std.math.sign;
const min = std.math.min;
const max = std.math.max;
const inf = std.math.inf;
const Allocator = std.mem.Allocator;
/// Returns a polygon processor, which can reuse its internal buffers to process multiple polygons
/// (call reset between process calls.) The type T denotes e.g. f16, f32, or f64 vertices.
pub fn Processor(comptime T: type) type {
return struct {
/// Resulting triangle indices once process() has finished.
triangles: std.ArrayListUnmanaged(u32) = .{},
/// Internal node buffer.
nodes: std.ArrayListUnmanaged(Node) = .{},
pub fn deinit(processor: *@This(), allocator: Allocator) void {
processor.triangles.deinit(allocator);
// TODO: since nodes list is unused currently, this results in a big leak.
processor.nodes.deinit(allocator);
}
pub fn process(processor: *@This(), allocator: Allocator, data: []const T, hole_indices: ?[]const u32, dim: u3) error{OutOfMemory}!void {
processor.triangles.clearRetainingCapacity();
processor.nodes.clearRetainingCapacity();
var has_holes = hole_indices != null and hole_indices.?.len > 0;
var outer_len: u32 = if (has_holes) hole_indices.?[0] * dim else @intCast(u32, data.len);
var outer_node = try processor.linkedList(allocator, data, 0, outer_len, dim, true);
if (outer_node == null or outer_node.?.next == outer_node.?.prev) return;
var min_x: T = undefined;
var min_y: T = undefined;
var max_x: T = undefined;
var max_y: T = undefined;
var x: T = undefined;
var y: T = undefined;
var inv_size: T = 0;
if (has_holes) outer_node = try processor.eliminateHoles(allocator, data, hole_indices.?, outer_node, dim);
// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
if (data.len > 80 * @intCast(usize, dim)) {
min_x = data[0];
max_x = data[0];
min_y = data[1];
max_y = data[1];
var i = dim;
while (i < outer_len) : (i += dim) {
x = data[i];
y = data[i + 1];
if (x < min_x) min_x = x;
if (y < min_y) min_y = y;
if (x > max_x) max_x = x;
if (y > max_y) max_y = y;
}
// min_x, min_y and inv_size are later used to transform coords into integers for z-order calculation
inv_size = max(max_x - min_x, max_y - min_y);
inv_size = if (inv_size != 0) 32767 / inv_size else 0;
}
if (outer_node) |e| try processor.earcutLinked(allocator, e, &processor.triangles, dim, min_x, min_y, inv_size, 0);
}
/// create a circular doubly linked list from polygon points in the specified winding order
fn linkedList(processor: *@This(), allocator: Allocator, data: []const T, start: u32, end: u32, dim: u3, clockwise: bool) error{OutOfMemory}!?*Node {
var i: u32 = undefined;
var last: ?*Node = null;
if (clockwise == (signedArea(data, start, end, dim) > 0)) {
i = start;
while (i < end) : (i += dim) last = try processor.insertNode(allocator, i, data[i], data[i + 1], last);
} else {
i = end - dim;
while (i >= start) : (i -= dim) {
last = try processor.insertNode(allocator, i, data[i], data[i + 1], last);
if (i == 0) break;
}
}
if (last != null and equals(last.?, last.?.next.?)) {
removeNode(last.?);
last = last.?.next.?;
}
return last;
}
/// eliminate colinear or duplicate points
fn filterPoints(start: ?*Node, end_in: ?*Node) ?*Node {
if (start == null) return start;
var end = if (end_in) |e| e else start;
var p = start;
var again = false;
while (true) {
again = false;
if (!p.?.steiner and (equals(p.?, p.?.next.?) or area(p.?.prev.?, p.?, p.?.next.?) == 0)) {
removeNode(p.?);
p = p.?.prev;
end = p.?.prev;
if (p == p.?.next) break;
again = true;
} else {
p = p.?.next;
}
if (again or p != end) break;
}
return end;
}
/// main ear slicing loop which triangulates a polygon (given as a linked list)
fn earcutLinked(processor: *@This(), allocator: Allocator, ear_in: *Node, triangles: *std.ArrayListUnmanaged(u32), dim: u3, min_x: T, min_y: T, inv_size: T, pass: u2) error{OutOfMemory}!void {
// interlink polygon nodes in z-order
if (pass == 0 and inv_size != 0) indexCurve(ear_in, min_x, min_y, inv_size);
var ear: ?*Node = ear_in;
var stop = ear;
var prev: ?*Node = null;
var next: ?*Node = null;
// iterate through ears, slicing them one by one
while (ear.?.prev != ear.?.next) {
prev = ear.?.prev;
next = ear.?.next;
if (if (inv_size != 0) isEarHashed(ear.?, min_x, min_y, inv_size) else isEar(ear.?)) {
// cut off the triangle
try triangles.append(allocator, prev.?.i / dim | 0);
try triangles.append(allocator, ear.?.i / dim | 0);
try triangles.append(allocator, next.?.i / dim | 0);
removeNode(ear.?);
// skipping the next vertex leads to less sliver triangles
ear = next.?.next;
stop = next.?.next;
continue;
}
ear = next;
// if we looped through the whole remaining polygon and can't find any more ears
if (ear == stop) {
// try filtering points and slicing again
if (pass == 0) {
if (filterPoints(ear, null)) |e| try processor.earcutLinked(allocator, e, triangles, dim, min_x, min_y, inv_size, 1);
// if this didn't work, try curing all small self-intersections locally
} else if (pass == 1) {
ear = try cureLocalIntersections(allocator, filterPoints(ear, null).?, triangles, dim);
if (ear) |e| try processor.earcutLinked(allocator, e, triangles, dim, min_x, min_y, inv_size, 2);
// as a last resort, try splitting the remaining polygon into two
} else if (pass == 2) {
try processor.splitEarcut(allocator, ear.?, triangles, dim, min_x, min_y, inv_size);
}
break;
}
}
}
/// check whether a polygon node forms a valid ear with adjacent nodes
fn isEar(ear: *Node) bool {
var a = ear.prev.?;
var b = ear;
var c = ear.next.?;
if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
// now make sure we don't have other points inside the potential ear
var ax = a.x;
var bx = b.x;
var cx = c.x;
var ay = a.y;
var by = b.y;
var cy = c.y;
// triangle bbox; min & max are calculated like this for speed
var x0 = if (ax < bx) (if (ax < cx) ax else cx) else (if (bx < cx) bx else cx);
var y0 = if (ay < by) (if (ay < cy) ay else cy) else (if (by < cy) by else cy);
var x1 = if (ax > bx) (if (ax > cx) ax else cx) else (if (bx > cx) bx else cx);
var y1 = if (ay > by) (if (ay > cy) ay else cy) else (if (by > cy) by else cy);
var p = c.next;
while (p != a) {
if (p.?.x >= x0 and p.?.x <= x1 and p.?.y >= y0 and p.?.y <= y1 and
pointInTriangle(ax, ay, bx, by, cx, cy, p.?.x, p.?.y) and
area(p.?.prev.?, p.?, p.?.next.?) >= 0) return false;
p = p.?.next;
}
return true;
}
fn isEarHashed(ear: *Node, min_x: T, min_y: T, inv_size: T) bool {
var a = ear.prev.?;
var b = ear;
var c = ear.next.?;
if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
var ax = a.x;
var bx = b.x;
var cx = c.x;
var ay = a.y;
var by = b.y;
var cy = c.y;
// triangle bbox; min & max are calculated like this for speed
var x0 = if (ax < bx) (if (ax < cx) ax else cx) else (if (bx < cx) bx else cx);
var y0 = if (ay < by) (if (ay < cy) ay else cy) else (if (by < cy) by else cy);
var x1 = if (ax > bx) (if (ax > cx) ax else cx) else (if (bx > cx) bx else cx);
var y1 = if (ay > by) (if (ay > cy) ay else cy) else (if (by > cy) by else cy);
// z-order range for the current triangle bbox;
var min_z = zOrder(x0, y0, min_x, min_y, inv_size);
var max_z = zOrder(x1, y1, min_x, min_y, inv_size);
var p = ear.prev_z;
var n = ear.next_z;
// look for points inside the triangle in both directions
while (p != null and p.?.z >= min_z and n != null and n.?.z <= max_z) {
if (p.?.x >= x0 and p.?.x <= x1 and p.?.y >= y0 and p.?.y <= y1 and p != a and p != c and
pointInTriangle(ax, ay, bx, by, cx, cy, p.?.x, p.?.y) and area(p.?.prev.?, p.?, p.?.next.?) >= 0) return false;
p = p.?.prev_z;
if (n.?.x >= x0 and n.?.x <= x1 and n.?.y >= y0 and n.?.y <= y1 and n != a and n != c and
pointInTriangle(ax, ay, bx, by, cx, cy, n.?.x, n.?.y) and area(n.?.prev.?, n.?, n.?.next.?) >= 0) return false;
n = n.?.next_z;
}
// look for remaining points in decreasing z-order
while (p != null and p.?.z >= min_z) {
if (p.?.x >= x0 and p.?.x <= x1 and p.?.y >= y0 and p.?.y <= y1 and p != a and p != c and
pointInTriangle(ax, ay, bx, by, cx, cy, p.?.x, p.?.y) and area(p.?.prev.?, p.?, p.?.next.?) >= 0) return false;
p = p.?.prev_z;
}
// look for remaining points in increasing z-order
while (n != null and n.?.z <= max_z) {
if (n.?.x >= x0 and n.?.x <= x1 and n.?.y >= y0 and n.?.y <= y1 and n != a and n != c and
pointInTriangle(ax, ay, bx, by, cx, cy, n.?.x, n.?.y) and area(n.?.prev.?, n.?, n.?.next.?) >= 0) return false;
n = n.?.next_z;
}
return true;
}
/// go through all polygon nodes and cure small local self-intersections
fn cureLocalIntersections(allocator: Allocator, start_in: *Node, triangles: *std.ArrayListUnmanaged(u32), dim: u3) error{OutOfMemory}!?*Node {
var start = start_in;
var p = start;
while (true) {
var a = p.prev.?;
var b = p.next.?.next.?;
if (!equals(a, b) and intersects(a, p, p.next.?, b) and locallyInside(a, b) and locallyInside(b, a)) {
try triangles.append(allocator, a.i / dim | 0);
try triangles.append(allocator, p.i / dim | 0);
try triangles.append(allocator, b.i / dim | 0);
// remove two nodes involved
removeNode(p);
removeNode(p.next.?);
p = b;
start = b;
}
p = p.next.?;
if (p != start) break;
}
return filterPoints(p, null);
}
/// try splitting polygon into two and triangulate them independently
fn splitEarcut(processor: *@This(), allocator: Allocator, start: *Node, triangles: *std.ArrayListUnmanaged(u32), dim: u3, min_x: T, min_y: T, inv_size: T) error{OutOfMemory}!void {
// look for a valid diagonal that divides the polygon into two
var a = start;
while (true) {
var b = a.next.?.next;
while (b != a.prev) {
if (a.i != b.?.i and isValidDiagonal(a, b.?)) {
// split the polygon in two by the diagonal
var c = try processor.splitPolygon(allocator, a, b.?);
// filter colinear points around the cuts
a = filterPoints(a, a.next).?;
c = filterPoints(c, c.next).?;
// run earcut on each half
try processor.earcutLinked(allocator, a, triangles, dim, min_x, min_y, inv_size, 0);
try processor.earcutLinked(allocator, c, triangles, dim, min_x, min_y, inv_size, 0);
return;
}
b = b.?.next.?;
}
a = a.next.?;
if (a != start) break;
}
}
/// link every hole into the outer loop, producing a single-ring polygon without holes
fn eliminateHoles(processor: *@This(), allocator: Allocator, data: []const T, hole_indices: []const u32, outer_node_in: ?*Node, dim: u3) error{OutOfMemory}!?*Node {
var queue = std.ArrayListUnmanaged(*Node){};
defer queue.deinit(allocator);
var start: u32 = undefined;
var end: u32 = undefined;
var i: u32 = 0;
var len = hole_indices.len;
while (i < len) : (i += 1) {
start = hole_indices[i] * dim;
end = if (i < len - 1) hole_indices[i + 1] * dim else @intCast(u32, data.len);
const list = try processor.linkedList(allocator, data, start, end, dim, false);
if (list == list.?.next) list.?.steiner = true;
try queue.append(allocator, getLeftmost(list.?));
}
std.sort.sort(*Node, queue.items, {}, compareX);
// process holes from left to right
i = 0;
var outer_node = outer_node_in;
while (i < queue.items.len) : (i += 1) {
outer_node = try processor.eliminateHole(allocator, queue.items[i], outer_node.?);
}
return outer_node;
}
fn compareX(context: void, lhs: *Node, rhs: *Node) bool {
_ = context;
return (lhs.x - rhs.x) < 0;
}
/// find a bridge between vertices that connects hole with an outer ring and and link it
fn eliminateHole(processor: *@This(), allocator: Allocator, hole: *Node, outer_node: *Node) error{OutOfMemory}!?*Node {
var bridge = findHoleBridge(hole, outer_node);
if (bridge == null) {
return outer_node;
}
var bridge_reverse = try processor.splitPolygon(allocator, bridge.?, hole);
// filter collinear points around the cuts
_ = filterPoints(bridge_reverse, bridge_reverse.next); // TODO: is this ineffective?
return filterPoints(bridge, bridge.?.next);
}
/// David Eberly's algorithm for finding a bridge between hole and outer polygon
fn findHoleBridge(hole: *Node, outer_node: *Node) ?*Node {
var p = outer_node;
var hx = hole.x;
var hy = hole.y;
var qx = -inf(T);
var m: ?*Node = null;
// find a segment intersected by a ray from the hole's leftmost point to the left;
// segment's endpoint with lesser x will be potential connection point
while (true) {
if (hy <= p.y and hy >= p.next.?.y and p.next.?.y != p.y) {
var x = p.x + (hy - p.y) * (p.next.?.x - p.x) / (p.next.?.y - p.y);
if (x <= hx and x > qx) {
qx = x;
m = if (p.x < p.next.?.x) p else p.next.?;
if (x == hx) return m; // hole touches outer segment; pick leftmost endpoint
}
}
p = p.next.?;
if (p != outer_node) break;
}
if (m == null) return null;
// look for points inside the triangle of hole point, segment intersection and endpoint;
// if there are no points found, we have a valid connection;
// otherwise choose the point of the minimum angle with the ray as connection point
var stop = m;
var mx = m.?.x;
var my = m.?.y;
var tan_min = inf(T);
var tan: T = 0;
p = m.?;
while (true) {
if (hx >= p.x and p.x >= mx and hx != p.x and
pointInTriangle(if (hy < my) hx else qx, hy, mx, my, if (hy < my) qx else hx, hy, p.x, p.y))
{
tan = @fabs(hy - p.y) / (hx - p.x); // tangential
if (locallyInside(p, hole) and
(tan < tan_min or (tan == tan_min and (p.x > m.?.x or (p.x == m.?.x and sectorContainsSector(m.?, p))))))
{
m = p;
tan_min = tan;
}
}
p = p.next.?;
if (p != stop) break;
}
return m;
}
/// whether sector in vertex m contains sector in vertex p in the same coordinates
fn sectorContainsSector(m: *Node, p: *Node) bool {
return area(m.prev.?, m, p.prev.?) < 0 and area(p.next.?, m, m.next.?) < 0;
}
/// interlink polygon nodes in z-order
fn indexCurve(start: *Node, min_x: T, min_y: T, inv_size: T) void {
var p = start;
while (true) {
if (p.z == 0) p.z = zOrder(p.x, p.y, min_x, min_y, inv_size);
p.prev_z = p.prev;
p.next_z = p.next;
p = p.next.?;
if (p != start) break;
}
p.prev_z.?.next_z = null;
p.prev_z = null;
_ = sortLinked(p);
}
/// Simon Tatham's linked list merge sort algorithm
/// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
fn sortLinked(list_in: *Node) ?*Node {
var list: ?*Node = list_in;
var i: usize = undefined;
var p: ?*Node = null;
var q: ?*Node = null;
var e: ?*Node = null;
var tail: ?*Node = null;
var num_merges: usize = 0;
var p_size: usize = 0;
var q_size: usize = 0;
var in_size: usize = 1;
while (true) {
p = list;
list = null;
tail = null;
num_merges = 0;
while (p != null) {
num_merges += 1;
q = p;
p_size = 0;
i = 0;
while (i < in_size) : (i += 1) {
p_size += 1;
q = q.?.next_z;
if (q == null) break;
}
q_size = in_size;
while (p_size > 0 or (q_size > 0 and q != null)) {
if (p_size != 0 and (q_size == 0 or q == null or p.?.z <= q.?.z)) {
e = p;
p = p.?.next_z;
p_size -= 1;
} else {
e = q;
q = q.?.next_z;
q_size -= 1;
}
if (tail != null) tail.?.next_z = e else list = e;
e.?.prev_z = tail;
tail = e;
}
p = q;
}
tail.?.next_z = null;
in_size *= 2;
if (num_merges > 1) break;
}
return list;
}
/// z-order of a point given coords and inverse of the longer side of data bbox
fn zOrder(x_in: T, y_in: T, min_x: T, min_y: T, inv_size: T) T {
// coords are transformed into non-negative 15-bit integer range
var x = @floatToInt(i32, (x_in - min_x) * inv_size) | 0;
var y = @floatToInt(i32, (y_in - min_y) * inv_size) | 0;
x = (x | (x << 8)) & 0x00FF00FF;
x = (x | (x << 4)) & 0x0F0F0F0F;
x = (x | (x << 2)) & 0x33333333;
x = (x | (x << 1)) & 0x55555555;
y = (y | (y << 8)) & 0x00FF00FF;
y = (y | (y << 4)) & 0x0F0F0F0F;
y = (y | (y << 2)) & 0x33333333;
y = (y | (y << 1)) & 0x55555555;
return @intToFloat(T, x | (y << 1));
}
/// find the leftmost node of a polygon ring
fn getLeftmost(start: *Node) *Node {
var p = start;
var leftmost = start;
while (true) {
if (p.x < leftmost.x or (p.x == leftmost.x and p.y < leftmost.y)) leftmost = p;
p = p.next.?;
if (p != start) break;
}
return leftmost;
}
/// check if a point lies within a convex triangle
fn pointInTriangle(ax: T, ay: T, bx: T, by: T, cx: T, cy: T, px: T, py: T) bool {
return (cx - px) * (ay - py) >= (ax - px) * (cy - py) and
(ax - px) * (by - py) >= (bx - px) * (ay - py) and
(bx - px) * (cy - py) >= (cx - px) * (by - py);
}
/// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
fn isValidDiagonal(a: *Node, b: *Node) bool {
return a.next.?.i != b.i and a.prev.?.i != b.i and !intersectsPolygon(a, b) and // dones't intersect other edges
(locallyInside(a, b) and locallyInside(b, a) and middleInside(a, b) and // locally visible
(area(a.prev.?, a, b.prev.?) != 0 or area(a, b.prev.?, b) != 0) or // does not create opposite-facing sectors
equals(a, b) and area(a.prev.?, a, a.next.?) > 0 and area(b.prev.?, b, b.next.?) > 0); // special zero-length case
}
/// signed area of a triangle
fn area(p: *Node, q: *Node, r: *Node) T {
return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
}
/// check if two points are equal
fn equals(p1: *Node, p2: *Node) bool {
return p1.x == p2.x and p1.y == p2.y;
}
/// check if two segments intersect
fn intersects(p1: *Node, q1: *Node, p2: *Node, q2: *Node) bool {
var o1 = sign(area(p1, q1, p2));
var o2 = sign(area(p1, q1, q2));
var o3 = sign(area(p2, q2, p1));
var o4 = sign(area(p2, q2, q1));
if (o1 != o2 and o3 != o4) return true; // general case
if (o1 == 0 and onSegment(p1, p2, q1)) return true; // p1, q1 and p2 are collinear and p2 lies on p1q1
if (o2 == 0 and onSegment(p1, q2, q1)) return true; // p1, q1 and q2 are collinear and q2 lies on p1q1
if (o3 == 0 and onSegment(p2, p1, q2)) return true; // p2, q2 and p1 are collinear and p1 lies on p2q2
if (o4 == 0 and onSegment(p2, q1, q2)) return true; // p2, q2 and q1 are collinear and q1 lies on p2q2
return false;
}
/// for collinear points p, q, r, check if point q lies on segment pr
fn onSegment(p: *Node, q: *Node, r: *Node) bool {
return q.x <= max(p.x, r.x) and q.x >= min(p.x, r.x) and q.y <= max(p.y, r.y) and q.y >= min(p.y, r.y);
}
/// check if a polygon diagonal intersects any polygon segments
fn intersectsPolygon(a: *Node, b: *Node) bool {
var p = a;
while (true) {
if (p.i != a.i and p.next.?.i != a.i and p.i != b.i and p.next.?.i != b.i and
intersects(p, p.next.?, a, b)) return true;
p = p.next.?;
if (p != a) break;
}
return false;
}
/// check if a polygon diagonal is locally inside the polygon
fn locallyInside(a: *Node, b: *Node) bool {
return if (area(a.prev.?, a, a.next.?) < 0)
area(a, b, a.next.?) >= 0 and area(a, a.prev.?, b) >= 0
else
area(a, b, a.prev.?) < 0 or area(a, a.next.?, b) < 0;
}
/// check if the middle point of a polygon diagonal is inside the polygon
fn middleInside(a: *Node, b: *Node) bool {
var p = a;
var inside = false;
var px = (a.x + b.x) / 2.0;
var py = (a.y + b.y) / 2.0;
while (true) {
if (((p.y > py) != (p.next.?.y > py)) and p.next.?.y != p.y and
(px < (p.next.?.x - p.x) * (py - p.y) / (p.next.?.y - p.y) + p.x))
inside = !inside;
p = p.next.?;
if (p != a) break;
}
return inside;
}
/// link two polygon vertices with a bridge; if the vertices belong the same ring, it splits
/// polygon into two; if one belongs to the outer ring and another to a hole, it merges it
/// into a single ring.
fn splitPolygon(processor: *@This(), allocator: Allocator, a: *Node, b: *Node) error{OutOfMemory}!*Node {
var a2 = try processor.initNode(allocator, a.i, a.x, a.y);
var b2 = try processor.initNode(allocator, b.i, b.x, b.y);
var an = a.next;
var bp = b.prev;
a.next = b;
b.prev = a;
a2.next = an;
an.?.prev = a2;
b2.next = a2;
a2.prev = b2;
bp.?.next = b2;
b2.prev = bp;
return b2;
}
/// create a node and optionally link it with previous one (in a circular doubly linked list)
fn insertNode(processor: *@This(), allocator: Allocator, i: u32, x: T, y: T, last: ?*Node) error{OutOfMemory}!*Node {
var p = try processor.initNode(allocator, i, x, y);
if (last != null) {
p.next = last.?.next;
p.prev = last.?;
last.?.next.?.prev = p;
last.?.next = p;
} else {
p.prev = p;
p.next = p;
}
return p;
}
fn removeNode(p: *Node) void {
p.next.?.prev = p.prev;
p.prev.?.next = p.next;
if (p.prev_z) |prev_z| prev_z.next_z = p.next_z;
if (p.next_z) |next_z| next_z.prev_z = p.prev_z;
}
fn initNode(processor: *@This(), allocator: Allocator, i: u32, x: T, y: T) error{OutOfMemory}!*Node {
// TODO: make use of processor.nodes list for allocation.
_ = processor;
var n = try allocator.create(Node);
n.* = .{
.i = i,
.x = x,
.y = y,
};
return n;
}
const Node = struct {
i: u32, // vertex index in coordinates array
// vertex coordinates
x: T,
y: T,
// previous and next vertex nodes in a polygon ring
prev: ?*Node = null,
next: ?*Node = null,
// z-order curve value
z: T = 0,
// previous and next nodes in z-order
prev_z: ?*Node = null,
next_z: ?*Node = null,
// indicates whether this is a steiner point
steiner: bool = false,
};
fn signedArea(data: []const T, start: u32, end: u32, dim: u3) T {
var sum: T = 0;
var j = end - dim;
var i = start;
while (i < end) : (i += dim) {
sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
j = i;
}
return sum;
}
};
}
test {
std.testing.refAllDeclsRecursive(@This());
}
test "basic" {
const allocator = testing.allocator;
var processor = Processor(f32){};
defer processor.deinit(allocator);
const data = &[_]f32{
0, 0, // left, bottom
0, 1, // left, top
1, 1, // right, top
1, 0, // right, bottom
};
const hole_indices: ?[]u32 = null;
const dimensions = 2;
try processor.process(allocator, data, hole_indices, dimensions);
const tri = processor.triangles.items;
try testing.expectEqual(@as(usize, 6), tri.len);
try testing.expectEqualSlices(f32, &.{ 0, 1 }, data[tri[0] * dimensions .. (tri[0] * dimensions) + 2]); // left, top
try testing.expectEqualSlices(f32, &.{ 0, 0 }, data[tri[1] * dimensions .. (tri[1] * dimensions) + 2]); // left, bottom
try testing.expectEqualSlices(f32, &.{ 1, 0 }, data[tri[2] * dimensions .. (tri[2] * dimensions) + 2]); // right, bottom
try testing.expectEqualSlices(f32, &.{ 1, 0 }, data[tri[3] * dimensions .. (tri[3] * dimensions) + 2]); // right, bottom
try testing.expectEqualSlices(f32, &.{ 1, 1 }, data[tri[4] * dimensions .. (tri[4] * dimensions) + 2]); // right, top
try testing.expectEqualSlices(f32, &.{ 0, 1 }, data[tri[5] * dimensions .. (tri[5] * dimensions) + 2]); // left, top
}