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PolarisHub

Math-MCP

by PolarisHub

perspective_projection_matrix

Construct a perspective projection matrix for 3D graphics, specifying field of view, aspect ratio, near/far planes, and optional handedness and clip depth range.

Instructions

Creates a perspective view-to-clip matrix with explicit handedness and NDC depth range

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
farPlaneYes
nearPlaneYes
handednessNoDefaults to right-handed
aspectRatioYes
clipDepthRangeNoDefaults to OpenGL-style -1..1; use zero_to_one for DirectX-style depth
verticalFieldOfViewDegreesYes
Behavior2/5

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

With no annotations, the description must disclose behavioral traits. It mentions 'explicit handedness and NDC depth range' but does not describe side effects, error behavior (e.g., invalid near/far plane), or whether the function is pure. Lack of output specification also reduces transparency.

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?

The description is a single, front-loaded sentence with no redundant information. Every word adds value, making it highly efficient for an AI agent to parse.

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

Completeness2/5

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

Given no output schema, the description should clarify the return value (e.g., a 4x4 matrix format). It also lacks details on coordinate system assumptions or matrix ordering, which are critical for a projection matrix. This leaves important gaps for correct usage.

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

Parameters3/5

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

Schema coverage is only 33% (2 of 6 parameters described in schema). The description adds context for 'handedness' and 'clipDepthRange' by stating 'explicit handedness and NDC depth range', but does not explain common parameters like verticalFieldOfViewDegrees, aspectRatio, nearPlane, farPlane. It partially compensates but not sufficiently for a low-coverage schema.

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 creates a perspective view-to-clip matrix, specifying the key aspects of handedness and NDC depth range. This verb+resource construction effectively distinguishes it from sibling tools like 'look_at_view_matrix' or 'view_to_clip'.

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

Usage Guidelines2/5

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

No guidance is provided on when to use this tool vs alternatives. Among siblings are related tools like 'view_to_clip' and 'clip_to_ndc', but the description does not clarify the differences or use cases, leaving an AI agent without decision support.

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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