RH Petal Hue Sat Den MT

🌸 Asymmetric Hue, Saturation & Density Engine
Fix Hues the Way You Actually See Them.

Standard hue selectors push greens and yellows in the same direction with the same strength but in real footage, they don’t behave that way. RH Petal Hue Sat Den MT gives each of the six hue vectors its own independently shaped influence zone, so you can tighten a green without touching the foliage, or push reds without contaminating skin tones on either side.

The key innovation of this tool is how the six vectors' influence zones are defined. Rather than a simple cosine exponent function (which forces all vectors to have a symmetric shape), each vector uses a proprietary Mock Theta basis weight.

---

Key Features

• Mock Theta Basis Weights

• Asymmetry Per Vector (Deviation)

• Independent Width Per Vector

• Per-Vector Density Controls

• Mathematically Exact Null

---

Overview

RH Petal Hue Sat Den MT is a precision six-vector hue, saturation, and density tool built on the Petal Color Model (IQ Projection) using Mock Theta Basis Weights, a mathematically superior alternative to the cosine-power basis functions used in conventional HSL-style hue controls.

Standard hue selectors treat each primary's influence zone as a symmetric bell curve. In reality, each hue primary interacts differently with its neighbours, yellows bleed into greens differently than they bleed into reds. The Mock Theta Basis gives each vector its own independently tunable sharpness (Width) and asymmetry (Deviation), allowing you to shape how each primary's influence falls off on either side without affecting any other vector.

This is not a replacement for the hue curve. It is a more surgical, mathematically principled tool for colorists who need to correct or manipulate individual hue families with confidence that adjacent colours are unaffected, complete with dedicated density controls.

---

1. Core Concept 💡

For each pixel, the tool:

1. Separates intensity from chromaticity, placing the normalised pixel on the proprietary IQ surface.
2. Converts to polar coordinates — giving a pure angular hue and a pure radial saturation that are independent of scene brightness.
3. Evaluates the Mock Theta basis weight for each of the six primaries at the pixel's hue angle, using each primary's individual sharpness and asymmetry parameters.
4. Accumulates the weighted hue rotations, saturation scales, and density adjustments from all six vectors.
5. Reconstructs the final RGB output from the new polar coordinates and rescales it by the modified density.

The critical guarantee: all six vectors at their default settings (Hue = 0°, Sat = 1.0, Den = 0.0) is a mathematically exact null operation — the output is identical to the input regardless of the alpha and beta values. This means you can adjust the Width and Deviation sliders freely before committing to any colour adjustment without introducing any artefacts.

---

2. Color Model — IQ Projection 🔬

The Petal Model operates in the max-normalized IQ space:

• Intensity (M): Extracted by taking the maximum of the RGB components and preserved separately throughout the processing chain.
• Normalised Chromaticity: The RGB values are normalised against the intensity, ensuring the maximum component is always 1.
• Opponent Axes (U, V): The normalised values are projected onto two orthogonal opponent colour axes.
• Hue & Saturation: Converted into continuous polar coordinates (angle and magnitude) from the opponent axes, providing a pure angular hue without sextant boundaries and a radial saturation metric.

Primary hue angles in this space (exact values):

Because M is preserved separately, hue rotation is a pure angular arc (saturation untouched) and saturation scaling is a pure radial scale (hue untouched). These two operations are exactly decoupled — hue and saturation controls do not cross-contaminate, and density controls manipulate M independently.

---

3. Mock Theta Basis Weights 🧮

The key innovation of this tool is how the six vectors' influence zones are defined. Rather than a simple cosine exponent function (which forces all vectors to have a symmetric shape), each vector uses a proprietary Mock Theta basis weight.

Effect of Asymmetry (Beta):

• Zero Beta: Produces a symmetric zone.
• Positive Beta: The zone decays faster toward the next primary (right shoulder suppressed).
• Negative Beta: The zone decays faster toward the previous primary (left shoulder suppressed).

This allows, for example, the Green vector to have a tighter shoulder toward Yellow but a gentler one toward Cyan matching the perceptual reality that greens appear closer to yellows than to cyans for many footage types.

---

4. Per-Vector Controls 🎛️

Six identical control groups — Red, Yellow, Green, Cyan, Blue, Magenta — each with five parameters:

[Color] Hue

• Default: 0.0° (no rotation)
• Range: −90° – +90°
• The rotation is applied as a pure angular arc — saturation and density are not affected.
• The weighted sum of all active rotations is accumulated; pixels near multiple overlapping zones receive contributions from each.

[Color] Sat

• Default: 1.0 (no change — exact null)
• Range: 0.0 – 2.0
• 1.0 = mathematically exact null (deviation-from-unity formulation guarantees this).
• 0.0 = fully desaturated for that hue zone.
• 2.0 = doubled chroma amplitude for that hue zone.
• A soft-toe near zero prevents hard-clamp artefacts when desaturating close to neutral.

[Color] Den

• Default: 0.0 (no change)
• Range: −1.0 – +1.0
• Manipulates the luminance of the specified hue without altering its chromaticity. This allows for rich, deep subtractive colours or bright, glowing pastels.

[Color] Width (Alpha)

• Default: 3.0
• Range: 0.5 – 10.0
• Lower values = wider, more diffuse influence zone (similar to cosine^1 at low alpha).
• Higher values = narrower, more concentrated zone (approaching a delta function at the primary's centre).
• At alpha = 3.0, the half-width is approximately ±50°, similar to cosine^2 with n ≈ 2.

[Color] Deviation (Beta)

• Default: 0.0 (symmetric)
• Range: −3.0 – +3.0
• Positive values bias the zone to respond more to hues behind the primary (toward the previous primary).
• Negative values bias the zone to respond more to hues ahead of the primary (toward the next primary).
• Only meaningful when the primary's Width is narrow enough that the asymmetry is visible.

---

5. Master Saturation 🎚️

Master Saturation

A global multiplicative saturation scale applied uniformly to all pixels, after the per-vector engine.

• Default: 1.0 (no change)
• Range: 0.0 – 2.0
• This is applied as a final overall scale on top of any per-vector saturation changes.
• 1.0 = exact null; 0.0 = full global desaturation.

---

6. Node Placement 🗂️

Expected pipeline:

• Scene-linear input (linear sRGB or any linear RGB triplet)

Important: This tool operates entirely in linear scene-referred space. It does not contain a log encode/decode or any colorimetric transform.

Recommended placement:

• Directly on linear scene data.
• If working in DWG/DI, place a CST (Color Space Transform) before this node (DWG/DI → Linear sRGB) and a CST after it (Linear sRGB → DWG/DI).
• After primary exposure/balance corrections, before any creative colour work.

Note: This tool has zero effect on achromatic pixels (where M ≤ 1e-7 or sat ≤ 1e-7). Perfectly neutral grey values pass through unchanged by design.

---

7. Usage Tips 💬

• Default settings are a true null: Width and Deviation sliders can be adjusted freely without changing the image — only Hue, Sat, and Den sliders create visible changes.
• Use Width to isolate a hue family: Increasing Width (Alpha) to 6–8 narrows the zone to only the most saturated, on-primary hues. Useful for surgical skin-tone or sky correction.
• Use Deviation to protect neighbours: If adjusting Green Sat is bleeding into Yellow foliage, set Green Deviation to a negative value to reduce the zone's influence on the Yellow side.
• Combine Width + Hue Rotation for look development: A wide zone (low Alpha) with a subtle hue rotation creates broad, naturalistic hue shifts similar to a cross-process effect.
• Saturation at 0.0 on adjacent vectors: Simultaneously desaturating Yellow and Green at moderate Width values is effective for creating the muted, desaturated foliage look common in cinematic grades.
• Use Density for subtractive shaping: With the addition of the Den controls, you can now deepen hues as they become more saturated, emulating the subtractive behaviour of film print stocks natively within the tool.