typed op• Datenarten: qimage → qimage
• Aufruf: fullseye.apply(img, "tb_quat_color_rotate", a=0.5, b=0.5) (das 2-D-Modell ist ein Bild plus zwei skalare Regler a,b∈[0,1])
*Die Abbildung ist die tatsächliche Ausgabe auf einer synthetischen 128×128-Eingabe. Links Eingabe, rechts Ausgabe. Punktwolken als Draufsicht-Streudiagramm (Helligkeit = z), 1-D-Reihen als Linie, Volumen als Maximum-Projektion entlang z, Videos als mittleres Bild, komplexe Bilder als Betrag; Rückgabewerte, die kein Bild ergeben, werden als Werte gezeigt.*
*Regler a ändert die Ausgabe nicht (gemessen: identisch bei 0,1 / 0,5 / 0,9).*
*Regler b ändert die Ausgabe nicht (gemessen: identisch bei 0,1 / 0,5 / 0,9).*
Stufen (die vorangehenden Ops → dieser Op, von links nach rechts):
▸ tb_quat_color_rotate: Stufen (Doku-Website)
Auf anderen Bildern (synthetische Szene / Foto / Münzen. Obere Reihe: Eingaben, untere Reihe: deren Ausgaben. Regler auf Standard):
▸ tb_quat_color_rotate: andere Eingaben (Doku-Website)
Rotation der Farbe jedes Pixels um eine RGB-Achse: q x conj(q). → (H, W, 4).
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
The operation a complex pixel cannot express. axis_rgb is a direction in RGB space and angle_rad the rotation about it; the rotor q = cos(a/2) + sin(a/2) * axis is built with pose_quat.axis_angle_to_quat and the conjugation is applied to the vector part of every pixel, leaving the scalar part untouched (a conjugation cannot move it).
The conjugation is applied through the 3x3 matrix from pose_quat.quat_to_hom_mat3d rather than by two per-pixel Hamilton products, because for a (512, 512) image that is 500k quaternion multiplications versus one einsum. The two are the *same map*, measured:
against per-pixel pose_quat.quat_rotate_point_3d the agreement is 4.44e-16, the round trip rotate(rotate(q, ax, a), ax, -a) returns q to 2.22e-16, and the colour magnitude is preserved to 2.22e-16.
The matrix identity is also the honest limit of the *capability* claim. SO(3) and the unit quaternions are isomorphic, so a 3x3 orthogonal colour matrix does exactly this and nothing is lost by using one — measured against an explicit Rz(30 deg), the agreement is 2.22e-16. What a quaternion buys is 4 numbers instead of 9, exact closure under composition, and slerp. Measured over 100,000 random small rotations composed in sequence, the quaternion (renormalised each step, 4 divisions) drifts from unit norm by 0.0 while the matrix (composed by multiplication, not re-orthonormalised) drifts to |R^T R - I| = 4.33e-14.
That advantage is real but it is nearly nothing, and an earlier revision of this file oversold it by four orders of magnitude. The same measurement then read 4.4e-10 for the matrix, which looked like a decisive argument for quaternions. It was not an argument about quaternions at all: it was the pose_quat defect described below, feeding a slightly non-orthogonal matrix into every one of the 100,000 steps. With that fixed the honest figure is 4.33e-14, i.e. ordinary rounding over 100k products. The lesson is the repository's own: a number that flatters the thing you are building is the one to re-measure first.
What a *channelwise* pipeline — three independent scalar filters, which is what running the complex ops on R, G and B separately means — cannot do is this operation at all: it never mixes channels, so it cannot turn red towards green. Pure red rotated 90 degrees about the blue axis comes back as (-2.2e-16, 1.0, 0.0); no per-channel gain can put anything in the green channel, because it starts at zero. That is the comparison in tests/test_quatimage.py, and it is the one that is decisive.
pose_quat used to normalise as n / (norm + 1e-12). A zero axis then returned [cos(a/2), 0, 0, 0], which quat_to_hom_mat3d re-normalised to the identity: a rotation request silently became a no-op. Worse, at angle_rad = pi that same path produced [0, 0, 0, 0], whose normalisation was 0/(0+1e-12) = 0 and whose matrix was again the identity — a *180-degree* colour rotation silently becoming a copy. Both were reported and have since been fixed in pose_quat itself (zero length now raises; axis_angle_to_quat(0, 0, 1, pi) now returns exactly [0, 0, 0, 1] with norm 1, where it used to return norm 0.9999999999990).
This operator nevertheless keeps both of its own guards — _require_direction on the axis, and an explicit unit-norm assertion on the finished rotor (tolerance _UNIT_TOL). A check that only holds while a dependency behaves is not a check, and the caller of this module should get this module's error message. A genuine pi rotation still works:
pure red about the blue axis gives (-1.0, 1.2e-16, 0.0).
Raises ValueError: *qimage* is not a valid (H, W, 4) field; *axis_rgb* is not a finite non-zero 3-vector; *angle_rad* is not a finite real scalar; the constructed rotor is not unit norm.
Typed bridge of the quat op quat_color_rotate into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b are unused.
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
Das Programm unten ist nachweislich lauffähig (gleiche Eingabe wie die Abbildung). In der Studio-Hilfe wird dieser Block zu Schaltflächen, die es sofort laden und ausführen.
img_to_rgb 0.50 0.50 tb_rgb_to_quaternion 0.50 0.50 tb_quat_color_rotate 0.50 0.50
▸ Diese Pipeline laden · Laden & ausführen
Die folgenden Beispiele rufen den zugrunde liegenden Ledger-Op quat_color_rotate auf. Dieser Brücken-Op ist dieselbe Implementierung, angepasst an die Konvention fn(v, a, b); das Verhalten gilt unverändert (nur die Aufrufform unterscheidet sich).
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
qimage als Eingabe)identity · tb_quaternion_to_rgb · tb_quat_norm · tb_quat_conjugate_image · tb_quat_normalize_image · tb_monogenic_amplitude · tb_monogenic_phase · tb_monogenic_orientation
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. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.