typed op• Data kinds: points → volume
• Call: fullseye.apply(img, "tb_torus_sdf", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_torus_sdf: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_torus_sdf: other inputs (docs site)
Motion (GIF: frames / views / slices in turn. The still figure is the complete one; the GIF is supplementary):
Exact signed distance field of a torus (doughnut) (negative inside, positive outside).
sdf(p) = ‖(r - major_radius, t)‖ - minor_radius (r is the radius from the axis, t the axial distance). The core line is a circle of radius major_radius with a tube of radius minor_radius around it, so it can be used directly as the analytic form of a fillet (rounded corner).
Arguments and validation (ValueError):
• grid / center / axis: same as cylinder_sdf (the axis is the direction of the doughnut's hole).
• major_radius: radius of the core line (negative is rejected).
• minor_radius: radius of the tube (negative is rejected). With minor_radius >= major_radius the hole collapses (a spindle torus). It is not rejected, but it is exact only when minor_radius < major_radius (corrected 2026-10-07: this used to say "correct as a distance field"). Inside, where the tube overlaps itself on the axis, the value is smaller in magnitude than the true distance to the boundary (at the centre with major 1, minor 2: −1, true value −1.73). The sign, the zero level set and the outside values are correct, and the inside magnitude is a lower bound of the true distance, so it is safe for sphere tracing.
Return value: float64 of grid.shape[:-1].
Usage: carve a fillet into an inner corner with sdf_subtract / form the shape of an O-ring groove with sdf_union. To merely round corners, sdf_smooth_union is easier, but there the rounding radius depends on the shape —— use this one when you want the radius as a design value.
The 3d op torus_sdf bridged into the 2-D evolution registry. The implementation is the same; only the calling convention is adapted to op(v, a, b). This op has no tunable parameters; neither a nor b is used.
• 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.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_points 0.50 0.50 tb_torus_sdf 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op torus_sdf. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• sdf_csg — py -3.11 examples_3d/sdf_csg.py
volume as input)identity · vol_gaussian · vol_median · vol_erode · vol_dilate · vol_threshold · vol_reg_dilate · vol_reg_erode
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D 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.