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Summary: ### Overview The current C++ code for `pytorch3d.ops.ball_query()` performs floating point multiplication for every coordinate of every pair of points (up until the maximum number of neighbor points is reached). This PR modifies the code (for both CPU and CUDA versions) to implement idea presented [here](https://stackoverflow.com/a/3939525): a `D`-cube around the `D`-ball is first constructed, and any point pairs falling outside the cube are skipped, without explicitly computing the squared distances. This change is especially useful for when the dimension `D` and the number of points `P2` are large and the radius is much smaller than the overall volume of space occupied by the point clouds; as much as **~2.5x speedup** (CPU case; ~1.8x speedup in CUDA case) is observed when `D = 10` and `radius = 0.01`. In all benchmark cases, points were uniform randomly distributed inside a unit `D`-cube. The benchmark code used was different from `tests/benchmarks/bm_ball_query.py` (only the forward part is benchmarked, larger input sizes were used) and is stored in `tests/benchmarks/bm_ball_query_large.py`. ### Average time comparisons <img width="360" height="270" alt="cpu-03-0 01-avg" src="https://github.com/user-attachments/assets/6cc79893-7921-44af-9366-1766c3caf142" /> <img width="360" height="270" alt="cuda-03-0 01-avg" src="https://github.com/user-attachments/assets/5151647d-0273-40a3-aac6-8b9399ede18a" /> <img width="360" height="270" alt="cpu-03-0 10-avg" src="https://github.com/user-attachments/assets/a87bc150-a5eb-47cd-a4ba-83c2ec81edaf" /> <img width="360" height="270" alt="cuda-03-0 10-avg" src="https://github.com/user-attachments/assets/e3699a9f-dfd3-4dd3-b3c9-619296186d43" /> <img width="360" height="270" alt="cpu-10-0 01-avg" src="https://github.com/user-attachments/assets/5ec8c32d-8e4d-4ced-a94e-1b816b1cb0f8" /> <img width="360" height="270" alt="cuda-10-0 01-avg" src="https://github.com/user-attachments/assets/168a3dfc-777a-4fb3-8023-1ac8c13985b8" /> <img width="360" height="270" alt="cpu-10-0 10-avg" src="https://github.com/user-attachments/assets/43a57fd6-1e01-4c5e-87a9-8ef604ef5fa0" /> <img width="360" height="270" alt="cuda-10-0 10-avg" src="https://github.com/user-attachments/assets/a7c7cc69-f273-493e-95b8-3ba2bb2e32da" /> ### Peak time comparisons <img width="360" height="270" alt="cpu-03-0 01-peak" src="https://github.com/user-attachments/assets/5bbbea3f-ef9b-490d-ab0d-ce551711d74f" /> <img width="360" height="270" alt="cuda-03-0 01-peak" src="https://github.com/user-attachments/assets/30b5ab9b-45cb-4057-b69f-bda6e76bd1dc" /> <img width="360" height="270" alt="cpu-03-0 10-peak" src="https://github.com/user-attachments/assets/db69c333-e5ac-4305-8a86-a26a8a9fe80d" /> <img width="360" height="270" alt="cuda-03-0 10-peak" src="https://github.com/user-attachments/assets/82549656-1f12-409e-8160-dd4c4c9d14f7" /> <img width="360" height="270" alt="cpu-10-0 01-peak" src="https://github.com/user-attachments/assets/d0be8ef1-535e-47bc-b773-b87fad625bf0" /> <img width="360" height="270" alt="cuda-10-0 01-peak" src="https://github.com/user-attachments/assets/e308e66e-ae30-400f-8ad2-015517f6e1af" /> <img width="360" height="270" alt="cpu-10-0 10-peak" src="https://github.com/user-attachments/assets/c9b5bf59-9cc2-465c-ad5d-d4e23bdd138a" /> <img width="360" height="270" alt="cuda-10-0 10-peak" src="https://github.com/user-attachments/assets/311354d4-b488-400c-a1dc-c85a21917aa9" /> ### Full benchmark logs [benchmark-before-change.txt](https://github.com/user-attachments/files/22978300/benchmark-before-change.txt) [benchmark-after-change.txt](https://github.com/user-attachments/files/22978299/benchmark-after-change.txt) Pull Request resolved: https://github.com/facebookresearch/pytorch3d/pull/2006 Reviewed By: shapovalov Differential Revision: D85356394 Pulled By: bottler fbshipit-source-id: 9b3ce5fc87bb73d4323cc5b4190fc38ae42f41b2