Documents pattern scanning API

Adds comprehensive documentation for the pattern scanning API.

Details parsing behavior, complexity, and usage examples.
Includes troubleshooting tips and minimal test sketches.
Clarifies edge-case handling and implementation notes.

docs/3d_primitives/plane.md

@@ -0,0 +1,98 @@
+# `omath::primitives::create_plane` — Build an oriented quad (2 triangles)
+
+> Header: your project’s `primitives/plane.hpp`
+> Namespace: `omath::primitives`
+> Depends on: `omath::Triangle<omath::Vector3<float>>`, `omath::Vector3<float>`
+
+```cpp
+[[nodiscard]]
+std::array<Triangle<Vector3<float>>, 2>
+create_plane(const Vector3<float>& vertex_a,
+             const Vector3<float>& vertex_b,
+             const Vector3<float>& direction,
+             float size) noexcept;
+```
+
+---
+
+## What it does
+
+Creates a **rectangle (quad)** in 3D oriented by the edge **A→B** and a second in-plane **direction**. The quad is returned as **two triangles** suitable for rendering or collision.
+
+* Edge axis: `e = vertex_b - vertex_a`
+* Width axis: “direction”, **projected to be perpendicular to `e`** so the quad is planar and well-formed.
+* Normal (by right-hand rule): `n ∝ e × width`.
+
+> **Sizing convention**
+> Typical construction uses **half-width = `size`** along the (normalized, orthogonalized) *direction*, i.e. the total width is `2*size`.
+> If your implementation interprets `size` as full width, adjust your expectations accordingly.
+
+---
+
+## Parameters
+
+* `vertex_a`, `vertex_b` — two adjacent quad vertices defining the **long edge** of the plane.
+* `direction` — a vector indicating the **cross-edge direction** within the plane (does not need to be orthogonal or normalized).
+* `size` — **half-width** of the quad along the (processed) `direction`.
+
+---
+
+## Return
+
+`std::array<Triangle<Vector3<float>>, 2>` — the quad triangulated (consistent CCW winding, outward normal per `e × width`).
+
+---
+
+## Robust construction (expected math)
+
+1. `e = vertex_b - vertex_a`
+2. Make `d` perpendicular to `e`:
+
+   ```
+   d = direction - e * (e.dot(direction) / e.length_sqr());
+   if (d.length_sqr() == 0) pick an arbitrary perpendicular to e
+   d = d.normalized();
+   ```
+3. Offsets: `w = d * size`
+4. Four corners:
+
+   ```
+   A0 = vertex_a - w;  A1 = vertex_a + w;
+   B0 = vertex_b - w;  B1 = vertex_b + w;
+   ```
+5. Triangles (CCW when viewed from +normal):
+
+   ```
+   T0 = Triangle{ A0, A1, B1 }
+   T1 = Triangle{ A0, B1, B0 }
+   ```
+
+---
+
+## Example
+
+```cpp
+using omath::Vector3;
+using omath::Triangle;
+using omath::primitives::create_plane;
+
+Vector3<float> a{ -1, 0, -1 };    // edge start
+Vector3<float> b{  1, 0, -1 };    // edge end
+Vector3<float> dir{ 0, 0, 1 };    // cross-edge direction within the plane (roughly +Z)
+float half_width = 2.0f;
+
+auto quad = create_plane(a, b, dir, half_width);
+
+// e.g., compute normals
+for (const auto& tri : quad) {
+  auto n = tri.calculate_normal(); (void)n;
+}
+```
+
+---
+
+## Notes & edge cases
+
+* **Degenerate edge**: if `vertex_a == vertex_b`, the plane is undefined.
+* **Collinearity**: if `direction` is parallel to `vertex_b - vertex_a`, the function must choose an alternate perpendicular; expect a fallback.
+* **Winding**: If your renderer expects a specific face order, verify and swap the two vertices in each triangle as needed.