FreePublished on GitHub

3d-rotation-theory

Abstract math for 3D rotation representations and conversions. USE FOR: understanding axis-angle representation; Euler angles (yaw/pitch/roll, convention choices); rotation matrices (SO(3)); quaternion-based rotation; converting between representations; identifying and avoiding gimbal lock; composing rotations; half-angle formula; right-hand rule. DO NOT USE FOR: quaternion arithmetic details (use quaternion-algebra); slerp/lerp interpolation (use interpolation-on-manifolds); coordinate system definitions (use coordinate-system-conversions).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36 stars(GitHub 36 + cccskills 0)

Run score Not tested

See how to install

Files included (3)

SKILL.md2.9 KB
references/formulas.md2.5 KB
references/numerical-stability.md2.1 KB

SKILL.md (original)

Review the instructions the agent will receive before you install.

3D Rotation Theory

SO(3) = group of 3×3 orthogonal matrices with det = +1. Every rotation has an inverse (transpose).

Representations

Representation	Parameters	Strengths	Weaknesses
Axis-angle	axis n̂ + angle θ	Intuitive, minimal	Not closed under composition
Rotation matrix	3×3, 9 numbers	Fast multi-vector transform	9 params, orthogonality drift
Euler angles	3 angles (many conventions)	Human-readable	Gimbal lock, convention ambiguity
Quaternion	4 numbers, unit	Stable interpolation, fast compose	Double-cover ambiguity

Axis-Angle (Rodrigues Formula)

Rotation by θ around unit n̂ = (nₓ, nᵧ, n_z):

v' = v cos θ + (n̂ × v) sin θ + n̂(n̂·v)(1 − cos θ)

Right-hand rule: thumb along n̂, fingers curl in positive rotation direction.

Euler Angles (ZYX Intrinsic = Yaw-Pitch-Roll)

Yaw ψ (Z), Pitch φ (Y), Roll ρ (X) — most common aerospace/robotics convention:

R = Rz(ψ) · Ry(φ) · Rx(ρ)        applied right-to-left: roll first, yaw last

Gimbal Lock

When pitch = ±90° (second rotation hits a pole), yaw and roll become degenerate — one degree of freedom is lost. Avoid for systems requiring full orientation control.

Quaternions and rotation matrices do NOT suffer gimbal lock.

Quaternion ↔ Axis-Angle

Axis-angle → quaternion (load quaternion-algebra):

q = (sin(θ/2)·nₓ, sin(θ/2)·nᵧ, sin(θ/2)·n_z, cos(θ/2))

Quaternion → axis-angle:

θ = 2 arccos(w)
n̂ = (x, y, z) / sin(θ/2)        (undefined when θ = 0; use n̂ = (0,0,1) by convention)

Composition Order (Right-to-Left)

R_total = R_second · R_first applies R_first first, then R_second. For quaternions: q_total = q_second · q_first (same convention).

Reference Files

File	Load When
references/formulas.md	Full rotation matrix for each Euler sequence, Rodrigues formula expansion, quaternion↔matrix conversion
references/numerical-stability.md	Orthogonality drift, gimbal lock detection, near-zero axis extraction

Reviews

No reviews yet. Tell others what you thought.

Comments

No login needed. Share how it worked for you, ask a question, or note where it did not run.

No comments yet. Be the first to write one.

More skills from this repository

agent-graph-orchestration

Free

Design and scaffold multi-agent squads/swarms using the graph orchestration pattern (nodes = agents, edges = dependencies/data flow). USE FOR: designing a coordination topology for a multi-agent squad (sequential pipeline, parallel fan-out/aggregation, branching, feedback loop, cyclic); building an orchestrator agent that delegates to specialist agents; setting up an adversarial/tribunal code or document review with independent reviewers; scaffolding a squad's agent files for a target coding-agent harness (e.g. Copilot CLI or Claude Code custom agents). DO NOT USE FOR: authoring a single agent's frontmatter/prompt body (use copilot-cli-custom-agents, claude-code-custom-agents, or the target harness's own skill); SKILL.md authoring (use create-skill); ad-hoc multi-agent chat with no explicit topology.

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

agent-harness-logs

Free

Find, inspect, query, redact, and troubleshoot logs, transcripts, sessions, and OpenTelemetry data from coding-agent harnesses on Windows, macOS, Linux, and WSL. USE FOR: GitHub Copilot in VS Code; Copilot CLI; Claude Code; OpenAI Codex; Gemini CLI; OpenCode; Cursor, Windsurf, Kiro, or other VS Code-family editors; locating log files; diagnosing tool or model failures; correlating turns, subagents, and tool calls; querying JSONL, plaintext, or SQLite without spending model tokens; preparing sanitized diagnostics. DO NOT USE FOR: application logs unrelated to coding agents; uploading raw logs; treating unstable transcript schemas as public APIs.

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

agents-md

Free

Author and maintain AGENTS.md files — the open, tool-agnostic format for giving coding agents project context. Use when: creating AGENTS.md; writing an agent instructions file; root or nested AGENTS.md for monorepos; migrating CLAUDE.md, AGENT.md, .cursor/rules, or copilot-instructions.md to AGENTS.md; greenfield project setup before code exists; brownfield onboarding for an existing codebase; documenting build/test/lint commands, code style, PR/commit conventions, and security considerations for agents; AGENTS.md discovery and precedence rules. Works for any language, framework, or project size. DO NOT USE FOR: authoring SKILL.md skill files (use create-skill); APM package/plugin authoring (use apm-producer); language-specific style rules (use language skills e.g. csharp-best-practices).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

angles-and-circular-arithmetic

Free

Abstract math for angle measurement, unit systems, and circular arithmetic. USE FOR: implementing angle types; converting between degrees/radians/gradians/revolutions; reducing angles to canonical range [0, Full); computing reference angles and quadrants; implementing safe modular arithmetic with negative inputs; angle addition and subtraction; classifying angles by sign and size. DO NOT USE FOR: trigonometric functions (use trigonometric-functions); coordinate conversions (use coordinate-system-conversions); interpolation (use interpolation-on-manifolds).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

claude-code-custom-agents

Free

Create and maintain Claude Code custom subagents (.claude/agents/*.md files). USE FOR: authoring project (.claude/agents/) or user (~/.claude/agents/) subagent files; frontmatter fields (name, description, tools, disallowedTools, model, permissionMode, maxTurns, skills, mcpServers, hooks, memory, background, effort, isolation, color, initialPrompt); writing descriptions that drive automatic delegation and 'use proactively' phrasing; invoking subagents via natural language, @-mention, session-wide --agent, or the Agent tool; restricting which subagent types a coordinator can spawn with Agent(name1, name2); nested subagents and depth limits; built-in subagents (Explore, Plan, general-purpose, claude); troubleshooting a subagent that won't load or isn't invoked. DO NOT USE FOR: GitHub Copilot CLI custom agents (use copilot-cli-custom-agents); agent teams/teammates (a different, session-spanning feature); MCP server authoring; SKILL.md authoring (use create-skill).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

codebase-memory

Free

Install, verify, and integrate codebase-memory-mcp (CBM) — a local C binary indexing a codebase into a persistent knowledge graph (functions, classes, call chains, routes) queryable via 15 tools. USE FOR: creating or editing any agent/skill/prompt/subagent that reads, searches, or reasons about a codebase — CBM's CLI must replace grep/ripgrep/glob-and-read exploration for structural questions (who calls X, dead code, architecture overview, diff impact, Cypher queries); checking whether `codebase-memory-mcp` is installed; installing/updating it; checking whether a project's index is fresh/in sync (`index_status`); choosing CLI vs MCP (always prefer the CLI, far fewer tokens per call than MCP); picking the right CBM tool per workflow stage (discovery, verification, implementation, review). DO NOT USE FOR: semantic/business-logic code review; non-code repos with nothing to index.

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

See all skills by NetFabric

Report a problem with this skill

Install

Install with a command

npx skills add https://github.com/NetFabric/NetFabric.Numerics --skill 3d-rotation-theory

Paste it into your terminal and run it (requires Node.js). You can choose which agents to install it for, such as Claude Code or Codex.

Ask your agent

Please install the following Agent Skill.
https://github.com/NetFabric/NetFabric.Numerics/tree/main/.agents/skills/3d-rotation-theory

First review SKILL.md and the bundled files and confirm there is nothing suspicious (such as sending data externally or reading credentials). Then place it in ~/.claude/skills/3d-rotation-theory/ for Claude Code, or ~/.agents/skills/3d-rotation-theory/ for Codex.

Send this text to Claude Code or Codex as is. It checks the contents before installing.

View source on GitHub

Repository: NetFabric/NetFabric.Numerics
Stars: 36
Forks: 1
Category: Documents
License: MIT
Original language: English
Last updated: Aug 10, 2026

A skill is a set of instructions and scripts for an agent. cccskills does not guarantee that skills are safe. Review the contents before you install.