Adds documentation for Vector4 and incorporates ImGui integration

Adds comprehensive documentation for the `Vector4` class, outlining constructors, operators, and utility functions. Includes detailed notes on `clamp` functionality and potential ImGui integration caveats. Incorporates optional ImGui integration with explanations for correct usage and potential improvements.

docs/linear_algebra/triangle.md

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+# `omath::Triangle` — Simple 3D triangle utility
+
+> Header: your project’s `triangle.hpp`
+> Namespace: `omath`
+> Depends on: `omath::Vector3<float>` (from `vector3.hpp`)
+
+A tiny helper around three `Vector3<float>` vertices with convenience methods for normals, edge vectors/lengths, a right-angle test (at **`v2`**), and the triangle centroid.
+
+> **Note on the template parameter**
+>
+> The class is declared as `template<class Vector> class Triangle`, but the stored vertices are concretely `Vector3<float>`. In practice this type is currently **fixed to `Vector3<float>`**. You can ignore the template parameter or refactor to store `Vector` if you intend true genericity.
+
+---
+
+## Vertex layout & naming
+
+```
+v1
+|\
+| \
+a |  \  hypot = |v1 - v3|
+|   \
+v2 -- v3
+   b
+
+a = |v1 - v2|  (side_a_length)
+b = |v3 - v2|  (side_b_length)
+```
+
+* **`side_a_vector()`**  = `v1 - v2` (points from v2 → v1)
+* **`side_b_vector()`**  = `v3 - v2` (points from v2 → v3)
+* **Right-angle check** uses `a² + b² ≈ hypot²` with an epsilon of `1e-4`.
+
+---
+
+## Quick start
+
+```cpp
+#include "triangle.hpp"
+using omath::Vector3;
+using omath::Triangle;
+
+Triangle<void> tri(                       // template arg unused; any placeholder ok
+  Vector3<float>{0,0,0},                  // v1
+  Vector3<float>{0,0,1},                  // v2  (right angle is tested at v2)
+  Vector3<float>{1,0,1}                   // v3
+);
+
+auto n     = tri.calculate_normal();      // unit normal (right-handed: (v3-v2) × (v1-v2))
+float a    = tri.side_a_length();         // |v1 - v2|
+float b    = tri.side_b_length();         // |v3 - v2|
+float hyp  = tri.hypot();                 // |v1 - v3|
+bool rect  = tri.is_rectangular();        // true if ~right triangle at v2
+auto C     = tri.mid_point();             // centroid (average of v1,v2,v3)
+```
+
+---
+
+## Data members
+
+```cpp
+Vector3<float> m_vertex1;   // v1
+Vector3<float> m_vertex2;   // v2 (the corner tested by is_rectangular)
+Vector3<float> m_vertex3;   // v3
+```
+
+---
+
+## Constructors
+
+```cpp
+constexpr Triangle() = default;
+constexpr Triangle(const Vector3<float>& v1,
+                   const Vector3<float>& v2,
+                   const Vector3<float>& v3);
+```
+
+---
+
+## Methods
+
+```cpp
+// Normal (unit) using right-handed cross product:
+// n = (v3 - v2) × (v1 - v2), then normalized()
+[[nodiscard]] constexpr Vector3<float> calculate_normal() const;
+
+// Edge lengths with the naming from the diagram
+[[nodiscard]] float side_a_length() const;  // |v1 - v2|
+[[nodiscard]] float side_b_length() const;  // |v3 - v2|
+
+// Edge vectors (from v2 to the other vertex)
+[[nodiscard]] constexpr Vector3<float> side_a_vector() const; // v1 - v2
+[[nodiscard]] constexpr Vector3<float> side_b_vector() const; // v3 - v2
+
+// Hypotenuse length between v1 and v3
+[[nodiscard]] constexpr float hypot() const;                  // |v1 - v3|
+
+// Right-triangle check at vertex v2 (Pythagoras with epsilon 1e-4)
+[[nodiscard]] constexpr bool is_rectangular() const;
+
+// Centroid of the triangle (average of the 3 vertices)
+[[nodiscard]] constexpr Vector3<float> mid_point() const;     // actually the centroid
+```
+
+### Notes & edge cases
+
+* **Normal direction** follows the right-hand rule for the ordered vertices `{v2 → v3} × {v2 → v1}`.
+  Swap vertex order to flip the normal.
+* **Degenerate triangles** (collinear or overlapping vertices) yield a **zero vector** normal (since `normalized()` of the zero vector returns the zero vector in your math types).
+* **`mid_point()` is the centroid**, not the midpoint of any single edge. If you need the midpoint of edge `v1–v2`, use `(m_vertex1 + m_vertex2) * 0.5f`.
+
+---
+
+## Examples
+
+### Area and plane from existing API
+
+```cpp
+const auto a = tri.side_a_vector();
+const auto b = tri.side_b_vector();
+const auto n = b.cross(a);             // unnormalized normal
+float area   = 0.5f * n.length();      // triangle area
+
+// Plane equation n̂·(x - v2) = 0
+auto nhat = n.length() > 0 ? n / n.length() : n;
+float d = -nhat.dot(tri.m_vertex2);
+```
+
+### Project a point onto the triangle’s plane
+
+```cpp
+Vector3<float> p{0.3f, 1.0f, 0.7f};
+auto n = tri.calculate_normal();
+float t = n.dot(tri.m_vertex2 - p);     // signed distance along normal
+auto projected = p + n * t;             // on-plane projection
+```
+
+---
+
+## API summary (signatures)
+
+```cpp
+class Triangle final {
+public:
+  constexpr Triangle();
+  constexpr Triangle(const Vector3<float>& v1,
+                     const Vector3<float>& v2,
+                     const Vector3<float>& v3);
+
+  Vector3<float> m_vertex1, m_vertex2, m_vertex3;
+
+  [[nodiscard]] constexpr Vector3<float> calculate_normal() const;
+  [[nodiscard]] float side_a_length() const;
+  [[nodiscard]] float side_b_length() const;
+  [[nodiscard]] constexpr Vector3<float> side_a_vector() const;
+  [[nodiscard]] constexpr Vector3<float> side_b_vector() const;
+  [[nodiscard]] constexpr float hypot() const;
+  [[nodiscard]] constexpr bool is_rectangular() const;
+  [[nodiscard]] constexpr Vector3<float> mid_point() const;
+};
+```
+
+---
+
+## Suggestions (optional improvements)
+
+* If generic vectors are intended, store `Vector m_vertex*;` and constrain `Vector` to the required ops (`-`, `cross`, `normalized`, `distance_to`, `+`, `/`).
+* Consider renaming `mid_point()` → `centroid()` to avoid ambiguity.
+* Expose an `area()` helper and (optionally) a barycentric coordinate routine if you plan to use this in rasterization or intersection tests.
+
+---
+
+*Last updated: 31 Oct 2025*