feat: implement bezier curve support

[DongjaJ]

What

Adds Bezier curve evaluation and sampling support to bracket-geometry::Curve, plus documentation and a runnable example.

Why

Bezier curves are requested in issue #94 and provide a reusable way to evaluate curves from existing Curve control points.

Closes #94

Checklist

Required

• cargo check --all passes
• cargo fmt --all -- --check passes
• cargo clippy --workspace --all-targets -- -D warnings -A clippy::multiple-crate-versions passes
• cargo test --all passes
• I linked the related issue (for example: Closes #123)

Functional Validation

• Behavior related to this change was verified locally (if applicable)
• Rendering/backend behavior was verified when runtime code changed (if applicable)
• Algorithm behavior (pathfinding/FOV/noise/random) was verified when affected (if applicable)
• I added or updated tests for changed behavior (if applicable)

Configuration & Docs

• User-facing docs were updated (README.md, ARCHITECTURE.md, or relevant manual pages, if applicable)
• New dependencies/configuration are documented (if applicable)
• No sensitive values or credentials were introduced

If Applicable

• Security impact considered (run cargo audit locally if needed)
• Breaking behavior changes are clearly described in this PR

Local Validation

• cargo check --all
• cargo fmt --all -- --check
• cargo clippy --workspace --all-targets -- -D warnings -A clippy::multiple-crate-versions
• cargo test --all
• cargo check -p bracket-geometry --example bezier_curve
• cargo run -p bracket-geometry --example bezier_curve

Summary by CodeRabbit

• New Features

  • Bezier curve evaluation and sampling capabilities added, enabling point calculation at any parameter value.
  • New visual example demonstrates Bezier curve rendering with control points marked in terminal output.

• Documentation

  • README expanded with Bezier curve usage examples and execution guidance for the new example.

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 04ee634a-325b-4760-9978-63943c76d3e8

📥 Commits

Reviewing files that changed from the base of the PR and between fe7bf77 and bd3a1f2.

📒 Files selected for processing (3)

• bracket-geometry/README.md
• bracket-geometry/examples/bezier_curve.rs
• bracket-geometry/src/curve.rs

📜 Recent review details

🧰 Additional context used

📓 Path-based instructions (1)

**/*.rs

📄 CodeRabbit inference engine (AGENTS.md)

**/*.rs: Format all Rust code using cargo fmt --all
Fix all cargo clippy warnings — the CI enforces -D warnings
Add tests for new functionality in the relevant module; for split domains, prefer colocated tests.rs

Files:

• bracket-geometry/examples/bezier_curve.rs
• bracket-geometry/src/curve.rs

🔇 Additional comments (3)

bracket-geometry/src/curve.rs (1)

1-1: LGTM!

Also applies to: 52-104, 121-251

bracket-geometry/README.md (1)

71-84: LGTM!

bracket-geometry/examples/bezier_curve.rs (1)

1-42: LGTM!

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📝 Walkthrough

Walkthrough

This PR extends the Curve type with Bezier evaluation and sampling capabilities. New methods compute individual Bezier points and sample curves into fixed-point grids, backed by comprehensive unit tests. Documentation and a visual example demonstrate the API.

Changes

Bezier Curve Evaluation

Layer / File(s)	Summary
Bezier evaluation implementation and tests bracket-geometry/src/curve.rs	Curve gains bezier_point(t) to evaluate points via iterative reduction, returning None for empty curves or non-finite parameters, and bezier_points(steps) to sample into integer Point vectors. A test helper assert_pointf_eq validates PointF with epsilon tolerance. Tests cover empty/single/linear/quadratic/cubic curves, endpoint matching, non-finite rejection, and sampling bounds.
Documentation and example bracket-geometry/README.md, bracket-geometry/examples/bezier_curve.rs	README documents Bezier APIs with code examples and a cargo run command. The example initializes a Curve from six control points, samples 160 Bezier points, and renders them with control points onto a fixed-size character grid using crossterm queued output.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~12 minutes

Possibly related PRs

• utilForever/roguekit#98: Introduced the foundational Curve type that this PR extends with Bezier evaluation methods.

Suggested reviewers

• utilForever

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🐰 A curve springs to life, *
Bezier points dance on the page,
Control flows with grace.

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title 'feat: implement bezier curve support' directly and clearly describes the main change: adding Bezier curve evaluation and sampling functionality to the Curve API, which aligns with the substantial additions to curve.rs, new example, and README documentation.
Docstring Coverage	✅ Passed	Docstring coverage is 100.00% which is sufficient. The required threshold is 80.00%.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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