project_points — 3D render op

Data kinds: pointskeypoints

Call: import fullseye as fs; fs.ledger.project_points(points, K, R=None, t=None) (to call the implementation directly, import match3d; match3d.project_points(points, K, R=None, t=None); from the registry, ops3d.get("project_points"))

Return value through the ledger: fullseye.ledger.project_points(...) returns **only the declared out type keypoints** (the underlying function also returns auxiliary values). When you need what was dropped, use fullseye.ledger.project_points.raw(...) or call match3d.project_points directly.

• Underlying return: (uv (N,2), depth (N,)) → uv

Usage

3-D point set (N,3) → image coordinates (u,v) and depth. Pinhole (the forward direction of depth_to_points).

> The detailed description below is the original text — the summary and the headings are translated.

K=カメラ内部行列 [[fx,0,cx],[0,fy,cy],[0,0,1]]。R,t で外部姿勢。世界モデルの観測写像。

`P_cam = R @ P + t(R (3,3)、t (3,)。None は恒等・零)を u = fx·X/Z + cx`、

`v = fy·Y/Z + cy で投影する。返り値 (uv (N,2), depth (N,)): uv[:,0] = u`(列)、

`uv[:,1] = v(行)、depth` はカメラ座標の Z(clip 前の生値で、負もそのまま)。

`KK[0,0]` 等で添字するので numpy 配列(nested list は不可)。

Z は `1e-6` 以上に clip してから割るので、カメラ後方の点も捨てず巨大な u,v になる

(`depth > 0 で呼び手が除く)。画像外の点も返す(render_point_depth` が範囲で切る)。

`depth_to_points の逆で、depth_to_points(render_point_depth(...))` が往復になる。

Background guides (the physics and conventions behind this op)

blender_interop — Blender との併用 — 形を作って fullseye で測る(軸・単位・正解データの罠)

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

pnp_pose_outlierspy -3.11 examples_3d/pnp_pose_outliers.py

pose_estimationpy -3.11 examples_3d/pose_estimation.py

Ops the type connects to (they accept keypoints as input)

fuse_to_voxel · dlt_pose · pnp_ransac · reprojection_error

Same category (render)

render_point_depth · render_volume_projection · render_shaded · ambient_occlusion · cast_shadow · phong_shade · matcap_shade · supersample_mesh


*Provenance: match3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.