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PolarisHub

Math-MCP

by PolarisHub

transform_point_3d

Transform a 3D point using a row-major 4x4 matrix and return the result as homogeneous coordinates (x, y, z, w).

Instructions

Transforms a 3D position by a row-major 4x4 matrix using homogeneous w=1 and returns x,y,z,w

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
pointYes
matrixYesRow-major 4x4 matrix used with column vectors: output = matrix * vector
Behavior3/5

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

No annotations are provided, so the description carries the full burden. It discloses the homogeneous coordinate convention (w=1) and the return format (x,y,z,w), but omits edge cases (e.g., w=0 point) or potential issues like matrix singularity.

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?

Single sentence, no wasted words, and front-loaded with the core action. Every part of the description adds value.

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?

For a mathematical tool with two parameters and no output schema, the description sufficiently explains the transformation process and output format. It could mention that w may change after transformation, but overall it is complete enough for an agent to understand usage.

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 description coverage is 50% (only matrix has a description). The description adds significant value by explaining the homogeneous coordinate usage and the return values, going beyond the schema types. This compensates for the limited schema documentation.

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?

Description clearly states the action (transforms), the resource (3D position), and specific details (row-major 4x4 matrix, homogeneous w=1, returns x,y,z,w). It distinguishes from sibling tools like multiply_matrices_4x4 or compose_transform_4x4 which operate on matrices or multiple points.

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?

No explicit guidance on when to use this tool versus alternatives. The description implies its use for transforming a single 3D point, but does not mention when not to use it or suggest alternatives like compose_transform_4x4 for building transformations.

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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