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PolarisHub

Math-MCP

by PolarisHub

compose_transform_4x4

Compose a 4x4 TRS transform matrix from position, quaternion rotation, and scale for column vectors.

Instructions

Builds a row-major 4x4 TRS transform from position, quaternion rotation, and scale for column vectors

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
scaleNoOptional XYZ scale; defaults to 1,1,1
positionYes
rotationNoOptional normalized or unnormalized quaternion; defaults to identity
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries full burden. It discloses row-major storage, column vector convention, and T*R*S order. However, it omits coordinate system handedness and potential issues with unnormalized quaternions, leaving minor gaps.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

A single 17-word sentence that is front-loaded with key information. Every word is necessary and there is no redundancy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given 3 parameters, nested objects, no output schema, and complexity of 3D transforms, the description adequately covers inputs and combination logic. Missing details like output format (a 4x4 matrix) and coordinate system, but overall sufficient for selection.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema covers 67% with descriptions for scale and rotation. The description adds meaning by explaining how parameters combine into a T*R*S transform, compensating for the missing position description in schema. It clarifies that rotation is a quaternion and scale defaults to 1,1,1.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool builds a row-major 4x4 T*R*S transform from position, quaternion rotation, and scale. This specific verb and resource combination distinguishes it from sibling tools like multiply_matrices_4x4 and transform_point_3d.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage for composing a transform from components but does not explicitly state when to use this over alternatives or when not to use it. Sibling tools include matrix multiplication and other transforms, but no direct comparison or exclusions are provided.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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