[WIP] Trapezoidal Decomposition Prototype for Discussion #658

tigercosmos · 2025-12-26T14:12:35Z

The PR is a prototype of trapezoidal decomposition for the further support of polygon operations.

tigercosmos

@yungyuc Could you take a look and discuss if the current PR approach is correct? I want to add trapezoidal decomposition with further support of polygon boolean operations. However, after studying a while, I am still confusing what to do next.

tigercosmos · 2025-12-26T14:13:26Z

cpp/modmesh/universe/polygon.hpp

+    struct Trapezoid
+    {
+        value_type top_y; ///< Y-coordinate of the top horizontal edge
+        value_type bottom_y; ///< Y-coordinate of the bottom horizontal edge
+        segment_type left_edge; ///< Left boundary segment of the trapezoid
+        segment_type right_edge; ///< Right boundary segment of the trapezoid
+        size_t source_polygon; ///< ID of the polygon this trapezoid came from
+    };


Struct for trapazoid

Trapezoid should be taken outside to be a normal class (with the name Trapezoid3d, class declaration, private data with prefix, and accessors). It will be so useful that you may just create TrapezoidPad using this PR.

Got it. Thanks.

tigercosmos · 2025-12-26T14:16:36Z

cpp/modmesh/universe/polygon.hpp

+     * @throws std::out_of_range if polygon_id is invalid
+     * @throws std::invalid_argument if polygon has fewer than 3 nodes
+     */
+    std::vector<Trapezoid> const & decompose_polygon(size_t polygon_id);


The API for trapazoidal decomposition.

Create a helper class TrapezoidalDecomposition (or a more accurate name you like), and rename PolygonPad::decompose_polygon() to PolygonPad::decompose_to_trapezoid() for accurate semantics. Call the helper class from decompose_to_trapezoid().

tigercosmos · 2025-12-26T14:18:01Z

cpp/modmesh/universe/polygon.hpp

+     * @param p2 Second polygon
+     * @return Vector of polygons forming the union
+     */
+    std::vector<polygon_type> boolean_union(polygon_type const & p1, polygon_type const & p2);


The part I am not sure. Do we want to have operation APIs in the PolygonPad? The operation is between polygon and polygon, or polygon pad or polygon pad?

Good point. Area Boolean is set Boolean, so it operates between sets, so PolygonPad and PolygonPad.

Our goal is volumetric Boolean, but we need to make the area Boolean very clear before moving forward.

Create helper classes AreaBooleanUnion, AreaBooleanIntersection, and AreaBooleanDifference for the 3 operations you are prototyping here.

Use naive implementation at this point. Add unit tests to make sure they have Python interface and do not crash. Leave TODO comments in the tests saying results are not confirmed to be correct and the correctness is left for a follow-up PR.

This is good progress.

I see. Thanks!

yungyuc

Did you use any AI tool to help? I am curious about it. If you did please specify.

This is good progress. Points to address:

Make a normal (non-nested) Trapezoid3d and TrapezoidPad.
Do not use hash table and do not use hash table to vectors.
Create a helper class TrapezoidalDecomposition (or a more accurate name you like).
Rename PolygonPad::decompose_polygon() to PolygonPad::decompose_to_trapezoid() for accurate semantics.
Create helper classes AreaBooleanUnion, AreaBooleanIntersection, and AreaBooleanDifference for the 3 operations.
For the area Boolean, add unit tests to make sure they have Python interface and do not crash. Leave TODO comments in the tests saying results are not confirmed to be correct and the correctness is left for a follow-up PR.

yungyuc · 2025-12-27T01:38:43Z

cpp/modmesh/universe/polygon.hpp

+    struct Trapezoid
+    {
+        value_type top_y; ///< Y-coordinate of the top horizontal edge
+        value_type bottom_y; ///< Y-coordinate of the bottom horizontal edge
+        segment_type left_edge; ///< Left boundary segment of the trapezoid
+        segment_type right_edge; ///< Right boundary segment of the trapezoid
+        size_t source_polygon; ///< ID of the polygon this trapezoid came from
+    };


Trapezoid should be taken outside to be a normal class (with the name Trapezoid3d, class declaration, private data with prefix, and accessors). It will be so useful that you may just create TrapezoidPad using this PR.

yungyuc · 2025-12-27T01:40:55Z

cpp/modmesh/universe/polygon.hpp

-    //  - Point location query structure
-    //  - Integration with node lists for synchronization
+    /// Cache of trapezoidal decompositions, keyed by polygon ID. Computed lazily on first access.
+    std::unordered_map<size_t, std::vector<Trapezoid>> m_decompositions;


Do not use hash table. Hash table is the last resort when (1) you run out of ideas or (2) you run out of time.

A has table to vector is even worth: tons of dynamic memory allocation. It is bound to be slow.

This is why you need TrapezoidPad.

yungyuc · 2025-12-27T01:45:02Z

cpp/modmesh/universe/polygon.hpp

+     * @throws std::out_of_range if polygon_id is invalid
+     * @throws std::invalid_argument if polygon has fewer than 3 nodes
+     */
+    std::vector<Trapezoid> const & decompose_polygon(size_t polygon_id);


Create a helper class TrapezoidalDecomposition (or a more accurate name you like), and rename PolygonPad::decompose_polygon() to PolygonPad::decompose_to_trapezoid() for accurate semantics. Call the helper class from decompose_to_trapezoid().

yungyuc · 2025-12-27T01:48:36Z

cpp/modmesh/universe/polygon.hpp

+     * @param p2 Second polygon
+     * @return Vector of polygons forming the union
+     */
+    std::vector<polygon_type> boolean_union(polygon_type const & p1, polygon_type const & p2);


Good point. Area Boolean is set Boolean, so it operates between sets, so PolygonPad and PolygonPad.

Our goal is volumetric Boolean, but we need to make the area Boolean very clear before moving forward.

yungyuc · 2025-12-27T01:51:28Z

cpp/modmesh/universe/polygon.hpp

+     * @param p2 Second polygon
+     * @return Vector of polygons forming the union
+     */
+    std::vector<polygon_type> boolean_union(polygon_type const & p1, polygon_type const & p2);


Create helper classes AreaBooleanUnion, AreaBooleanIntersection, and AreaBooleanDifference for the 3 operations you are prototyping here.

Use naive implementation at this point. Add unit tests to make sure they have Python interface and do not crash. Leave TODO comments in the tests saying results are not confirmed to be correct and the correctness is left for a follow-up PR.

This is good progress.

tigercosmos · 2025-12-31T13:41:40Z

@yungyuc Yes, I used AI and spent around 5–6 hours exploring how to implement the trapezoidal decomposition. In the end, I wasn’t happy with the outcome and wasn’t confident about the design direction. I removed most of the implementation, kept what seemed to be the most reasonable interface, and opened this PR for discussion.

yungyuc · 2026-01-01T03:24:19Z

@yungyuc Yes, I used AI and spent around 5–6 hours exploring how to implement the trapezoidal decomposition. In the end, I wasn’t happy with the outcome and wasn’t confident about the design direction. I removed most of the implementation, kept what seemed to be the most reasonable interface, and opened this PR for discussion.

6 hours on the trapezoidal algorithm are not too many, but spending time to study it and then prototype incrementally will be more productive. Dividing tasks is an art that we cannot count on tools already.

trapezoidal decomposition prototype

d9acf55

tigercosmos marked this pull request as draft December 26, 2025 14:12

tigercosmos commented Dec 26, 2025

View reviewed changes

yungyuc assigned tigercosmos Dec 27, 2025

yungyuc added the geometry Geometry entities and manipulation label Dec 27, 2025

yungyuc requested changes Dec 27, 2025

View reviewed changes

[WIP] Trapezoidal Decomposition Prototype for Discussion #658

Are you sure you want to change the base?

[WIP] Trapezoidal Decomposition Prototype for Discussion #658

Uh oh!

Conversation

tigercosmos commented Dec 26, 2025

Uh oh!

tigercosmos left a comment

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

yungyuc left a comment • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

tigercosmos commented Dec 31, 2025

Uh oh!

yungyuc commented Jan 1, 2026

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

2 participants

yungyuc left a comment •

edited

Loading