Fixture screenshots show champion-path triangulation meshes for the root fixtures.
p2t is a constrained Delaunay tessellation library for Nim.
Start here: Public API guide.
Algorithm guides: Žalik sweep-line CDT and FlipScan constrained-edge insertion.
Nim is the superior code warrior's weapon of choice, but we provide a C ABI on the backend.
I wrote the original Poly2Tri in fits and starts from 2008 to 2009. It began as a small project on Google Code, which soon drew the attention of Thomas Åhlén. Thomas contributed the FlipScan constrained-edge insertion idea, the part of the algorithm that made the advancing-front sweep useful for real constrained polygons. I ported the library to a few languages, lost interest, and moved on.
In 2026 I found myself back in hobby coding and back on GitHub. I was surprised
to see how many Poly2Tri descendants were still around. The one that caught my
attention was fast-poly2tri, because it is exactly what its name says: fast,
hard-optimized C, with arena pointers and tuned sorting.
These days Nim is my favorite language, so I wanted to see how far a Nim version could be pushed on a single CPU thread. This repository is the result: the Poly2Tri sweep-line CDT, rebuilt around a pointer arena, pdqsort, a large-input front hash, and release-codegen tuning.
This level of optimization would have been hard for me to do alone now. I used AI assistance for code reading, instrumentation, benchmark bookkeeping, and working through the data. The code and the final engineering decisions remain my responsibility.
The final comparison uses the public import p2t API against vendored
fast-poly2tri and libtess2, with Shewchuk's Triangle available as an optional
external backend. Times are best/median microseconds per triangulation, from
five sequential nimble benchCompareAll passes. Each cell uses the pass with
the lowest best time for that fixture/engine.
Benchmark machine:
- Mac mini (
Mac16,11) - Apple M4 Pro, 12 cores (8 performance, 4 efficiency)
- 24 GB memory
- macOS 26.5 (
25F71), arm64 - Nim 2.2.10
Comparison dependencies are vendored in this repository:
fast-poly2tricommitc04c633f6e48fb4e79bd511f2c0bb46279fd5773libtess2commit8dbd6483e920311a58c9af10a10beb278efebc36
Triangle is supported as an optional external benchmark backend via
TRIANGLE_DIR, but is not vendored because its license does not belong in this
repository. When present, benchCompareAll runs Triangle's supported CDT
construction switches and reports the fastest valid Triangle result per fixture.
Earcut is intentionally excluded because it is not a constrained Delaunay triangulation algorithm.
Champion Nim configuration:
- pointer arena CDT
- pdqsort active-point sort
- front hash default-on at
FrontHashMinPoints = 512 - trusted raw path
- Tier 1 tuned release flags
Head-to-head contender builds use equivalent host-tuned release codegen where
their toolchains support it: C/C++ references are built with -O3 -DNDEBUG -flto plus the platform-native CPU flag (-mcpu=native on Apple Silicon,
-march=native on x86), and Nim benchmark binaries/wrappers receive the
matching C/link flags through the Tier 1 tuned flag bundle. Nim benchmark
binaries also use --panics:on; standalone C/C++ references have no direct
analogue for that Nim-specific lowering option.
Fixture stats:
| Fixture | Points | Holes | Champion triangles | Notes |
|---|---|---|---|---|
| fixture-test | 6 | 0 | 4 | tiny smoke fixture |
| diamond | 10 | 0 | 8 | convex baseline |
| star | 10 | 0 | 8 | concave baseline |
| dude-with-holes | 104 | 2 | 106 | sub-512 hole fixture |
| nazca-monkey | 1,204 | 0 | 1,202 | large organic outline |
| nazca-heron | 1,036 | 0 | 1,034 | large organic outline |
| organic-large | 3,340 | 287 | 3,912 | matched organic control |
Champion public-API results:
| Fixture | no-validate | trusted | raw |
|---|---|---|---|
| small-ui-quad | 0.216 / 0.231 | 0.101 / 0.124 | 0.083 / 0.099 |
| medium-icon | 3.525 / 3.712 | 2.504 / 2.726 | 2.264 / 2.401 |
| large-shape | 46.024 / 50.072 | 39.010 / 40.838 | 34.070 / 35.240 |
| fixture-test | 0.357 / 0.360 | 0.196 / 0.196 | 0.157 / 0.159 |
| diamond | 0.286 / 0.287 | 0.345 / 0.363 | 0.300 / 0.309 |
| star | 0.534 / 0.540 | 0.292 / 0.298 | 0.249 / 0.250 |
| dude-with-holes | 7.082 / 7.454 | 4.954 / 5.064 | 4.695 / 4.779 |
| nazca-monkey | 102.180 / 103.710 | 74.540 / 75.630 | 71.030 / 72.340 |
| nazca-heron | 83.240 / 85.880 | 63.270 / 63.760 | 56.860 / 59.530 |
| organic-large | 338.030 / 351.380 | 267.560 / 268.260 | 253.070 / 254.470 |
The raw column is the fastest workspace-backed p2t path. For exactly what each column times, see the final benchmark notes.
Raw-path head-to-head:
The faster fast-poly2tri float run stays in the table; the slower double
column is replaced by the per-fixture best Triangle configuration.
| Case | p2t raw | fast f32 | Triangle best | libtess2 | delta |
|---|---|---|---|---|---|
| fixture-test | 0.157 / 0.159 | 0.242 / 0.255 | 0.725 / 0.771 | 2.709 / 2.758 | +34.9% |
| diamond | 0.300 / 0.309 | 0.402 / 0.427 | 0.938 / 0.979 | 2.872 / 3.527 | +25.3% |
| star | 0.249 / 0.250 | 0.299 / 0.312 | 1.137 / 1.179 | 2.926 / 2.949 | +16.7% |
| dude-with-holes | 4.695 / 4.779 | 4.835 / 4.877 | 10.557 / 12.377 | 14.399 / 14.651 | +2.9% |
| nazca-monkey | 71.030 / 72.340 | 81.000 / 82.070 | 164.640 / 175.610 | 231.900 / 235.760 | +12.3% |
| nazca-heron | 56.860 / 59.530 | 68.730 / 72.250 | 134.870 / 140.060 | 206.570 / 211.700 | +17.3% |
| organic-large | 253.070 / 254.470 | failed | 863.350 / 883.830 | 1148.380 / 1152.980 | +70.7% vs Triangle |
fast-poly2tri asserts in MPE_EdgeEventPoints on organic-large, so there is
no valid timing for that fixture. The Nim implementation, Triangle, and libtess2
all complete it.
External contenders:
This separate table uses nimble benchExternalContenders, which is intentionally
not part of the final benchCompareAll suite. Delabella and artem-ogre/CDT are
external source checkouts; Fade2D is the public 2.17.3 SDK and runs under its
student/non-commercial research license. The delta column is p2t raw's
best-time advantage over the fastest external contender for that case.
Full reproduction commands are in the
final benchmark notes.
| Case | p2t raw | Delabella | CDT | Fade2D | delta |
|---|---|---|---|---|---|
| small-ui-quad | 0.083 / 0.099 | 0.241 / 0.255 | 1.605 / 1.749 | 2.580 / 2.911 | +65.4% vs Delabella |
| medium-icon | 2.264 / 2.401 | 67.174 / 67.445 | 30.555 / 31.165 | 290.432 / 291.244 | +92.6% vs CDT |
| large-shape | 34.070 / 35.240 | 510.266 / 579.064 | 403.342 / 429.738 | 2686.892 / 2687.568 | +91.6% vs CDT |
| fixture-test | 0.157 / 0.159 | 0.329 / 0.335 | 2.078 / 2.118 | 3.816 / 3.839 | +52.2% vs Delabella |
| diamond | 0.300 / 0.309 | 0.745 / 0.754 | 3.276 / 3.381 | 8.650 / 8.761 | +59.7% vs Delabella |
| star | 0.249 / 0.250 | 0.653 / 0.688 | 3.082 / 3.119 | 7.794 / 7.844 | +61.9% vs Delabella |
| dude-with-holes | 4.695 / 4.779 | 9.594 / 9.801 | 32.693 / 33.028 | 66.638 / 66.977 | +51.1% vs Delabella |
| nazca-monkey | 71.030 / 72.340 | 153.880 / 155.260 | 491.780 / 507.860 | 1190.120 / 1227.680 | +53.8% vs Delabella |
| nazca-heron | 56.860 / 59.530 | 118.770 / 120.610 | 409.030 / 417.270 | 943.200 / 983.560 | +52.1% vs Delabella |
| organic-large | 253.070 / 254.470 | 1125.050 / 1133.560 | 1784.250 / 1859.380 | 33969.460 / 34354.250 | +77.5% vs Delabella |
For the public fast path that materializes TessResult.triangles, see the
tessellateTrusted benchmark.
The short version: the optimized Nim path is ahead of the reference C
implementation on every fixture where fast-poly2tri completes, ahead of
Triangle, and much faster than libtess2 on this benchmark set. The large-input
front hash is a real win on organic large inputs; the sub-512 path is already
close to the useful limit, with legalization work dominating what remains.
The cleave branch contains my sandbox experiments toward beating the
single-threaded CPU sweep-line CDT with more ambitious approaches, including
threaded ideas. I made a mess of it, and I did not beat the single-threaded path.
Poly2Tri is small, direct, and efficient enough that parallelizing a challenger
is not the easy win I hoped it might be. Maybe someone else will sort out the
hard parts someday. Or not. This is a hobby project.
nimble test
nimble testLibtess2
nimble bench
nimble benchCompareAll
nimble benchLibtess2
nimble benchTrusted
nimble benchNormalizedTrusted
nimble benchExternalContenders
nimble benchParallel
nimble tidyBenchmark comparisons use vendored fast-poly2tri and libtess2 sources under
vendor/ by default. Set FAST_POLY2TRI_DIR, LIBTESS2_DIR, or
TRIANGLE_DIR to compare against external checkouts. Triangle must contain
triangle.c and triangle.h; it is intentionally external-only.
The external contenders task also stays external-only. Set DELABELLA_DIR,
CDT_DIR, and FADE2D_DIR before running nimble benchExternalContenders.
Use CC/CXX to override the C/C++ compilers. Use P2T_FLAGS for
platform-specific include, library, and runtime-linker paths needed by local
SDKs, for example -I/opt/foo/include -L/opt/foo/lib -Wl,-rpath,/opt/foo/lib.
The harness also checks getTempDir()/p2t-contenders; on Unix/macOS it checks
/tmp/p2t-contenders and /private/tmp/p2t-contenders as convenience
fallbacks for local benchmark checkouts.
The triangulation algorithm is the Poly2Tri advancing-front sweep-line CDT, combining the sweep-line Delaunay base algorithm with Thomas Åhlén's "FlipScan" constrained-edge insertion.
- Public API guide
- Žalik sweep-line CDT guide
- FlipScan constrained-edge insertion spec
- Žalik, B. (2005). An efficient sweep-line Delaunay triangulation algorithm. Computer-Aided Design, 37(10), pp. 1027–1038. doi:10.1016/j.cad.2004.10.004
- Domiter, V. and Žalik, B. (2008). Sweep-line algorithm for constrained Delaunay triangulation. International Journal of Geographical Information Science, 22(4), pp. 449–462. doi:10.1080/13658810701492241
- Shewchuk, J. R. (1996). Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. WACG 1996, LNCS 1148, Springer. PDF
BSD 3-Clause License. Copyright (c) 2009-2026 Mason Austin Green.