Add blend modes math reference guide

[JOYBOY-0]

Summary

Added a comprehensive reference guide documenting the mathematical formulas behind common layer blend modes used in shader work and graphics programming.

Changes

• New log entry: content/logs/14-blend-modes-math.mdx
  • Quick glossary of blend mode formulas with practical explanations
  • Coverage of 15+ blend modes including multiply, screen, overlay, soft light, color dodge/burn, and more
  • Pattern documentation showing mathematical relationships between related blend modes
  • Opacity blending explanation with common implementation mistakes
  • GLSL shader code examples for practical implementation
  • Emphasis on linear color space requirements and per-channel operation

Notable Details

• Clarifies that blend modes are per-channel functions and names are conventions while formulas are definitive
• Highlights the multiply ↔ screen duality and other mathematical relationships
• Addresses the opacity blending mistake (applying opacity after the blend function, not before)
• Notes that soft light has multiple variants (Photoshop, W3C, Pegtop) and recommends documenting which is used
• Includes practical guidance on clamping for unbounded operations (add, color dodge/burn)

https://claude.ai/code/session_01VvwH3WmqcoMB2AKPvdbt8P

Greptile Summary

Adds a new MDX log entry documenting the mathematical formulas behind 15 common layer blend modes, with GLSL shader examples, an opacity-blending explanation, and notes on linear color space requirements.

• All blend mode formulas are mathematically correct, and the GLSL implementations (including the branchless step-based overlay) are accurate.
• The Overlay section incorrectly states that a = 0.5 is the no-op; the actual neutral color is b = 0.5 (a 50% grey blend layer leaves the base unchanged), and this distinction matters since Hard Light — correctly identified as the swapped variant — uses a = 0.5 as its neutral.

Confidence Score: 3/5

The file is a developer reference guide — the factual error in the Overlay section would mislead readers about which variable carries the neutral color, and the distinction is meaningful when implementing blend modes by hand.

The rest of the formulas, GLSL snippets, and prose are accurate, but the Overlay no-op claim gets the wrong variable (a vs b), which is a concrete factual mistake in a document whose primary purpose is to be a correct reference.

content/logs/14-blend-modes-math.mdx — specifically the Overlay section's neutral-color claim

Important Files Changed

Filename	Overview
content/logs/14-blend-modes-math.mdx	New blend modes reference guide — all formulas correct except the Overlay neutral-color claim, which incorrectly attributes the no-op condition to a = 0.5 instead of b = 0.5.

Prompt To Fix All With AI

Fix the following 1 code review issue. Work through them one at a time, proposing concise fixes.

---

### Issue 1 of 1
content/logs/14-blend-modes-math.mdx:41
The "no-op" claim refers to the wrong variable. When `a = 0.5`, both branches of the Overlay formula reduce to `b`, meaning the base passes through the blend layer unchanged — that's not a no-op, it's a passthrough. The actual neutral/no-op condition for Overlay is when **`b = 0.5`**: plugging in `b = 0.5` gives `2*a*0.5 = a` (dark branch) and `1 - 2*(1-a)*0.5 = a` (bright branch), so the blend layer has zero effect on the base. This matches how Photoshop documents it — a 50% grey layer in Overlay mode leaves the composition unchanged.

```suggestion
Multiply on the dark half of `a`, screen on the bright half. `b = 0.5` is the no-op (a 50% grey blend layer leaves the base unchanged). **Hard Light** is the same formula with `a` and `b` swapped — the blend picks the branch instead of the base, so `a = 0.5` becomes its no-op.
```

_{Reviews (1): Last reviewed commit: "Add log 14: blend modes math glossary" | Re-trigger Greptile}

Greptile also left 1 inline comment on this PR.

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Project	Deployment	Actions	Updated (UTC)
joyco-hub	Ready	Preview, Comment	May 8, 2026 6:35pm

[greptile-apps]

The "no-op" claim refers to the wrong variable. When a = 0.5, both branches of the Overlay formula reduce to b, meaning the base passes through the blend layer unchanged — that's not a no-op, it's a passthrough. The actual neutral/no-op condition for Overlay is when b = 0.5: plugging in b = 0.5 gives 2*a*0.5 = a (dark branch) and 1 - 2*(1-a)*0.5 = a (bright branch), so the blend layer has zero effect on the base. This matches how Photoshop documents it — a 50% grey layer in Overlay mode leaves the composition unchanged.

Suggested change

	Multiply on the dark half of `a`, screen on the bright half. `a = 0.5` is the no-op. **Hard Light** is the same formula with `a` and `b` swapped — the blend picks the branch instead of the base.
	Multiply on the dark half of `a`, screen on the bright half. `b = 0.5` is the no-op (a 50% grey blend layer leaves the base unchanged). **Hard Light** is the same formula with `a` and `b` swapped — the blend picks the branch instead of the base, so `a = 0.5` becomes its no-op.

Prompt To Fix With AI

This is a comment left during a code review.
Path: content/logs/14-blend-modes-math.mdx
Line: 41

Comment:
The "no-op" claim refers to the wrong variable. When `a = 0.5`, both branches of the Overlay formula reduce to `b`, meaning the base passes through the blend layer unchanged — that's not a no-op, it's a passthrough. The actual neutral/no-op condition for Overlay is when **`b = 0.5`**: plugging in `b = 0.5` gives `2*a*0.5 = a` (dark branch) and `1 - 2*(1-a)*0.5 = a` (bright branch), so the blend layer has zero effect on the base. This matches how Photoshop documents it — a 50% grey layer in Overlay mode leaves the composition unchanged.

```suggestion
Multiply on the dark half of `a`, screen on the bright half. `b = 0.5` is the no-op (a 50% grey blend layer leaves the base unchanged). **Hard Light** is the same formula with `a` and `b` swapped — the blend picks the branch instead of the base, so `a = 0.5` becomes its no-op.
```

How can I resolve this? If you propose a fix, please make it concise.