Add triangle SAT intersection

include/J3ML/Geometry/Common.h

@@ -27,5 +27,13 @@ namespace J3ML::Geometry
 // Methods required by Geometry types
 namespace J3ML::Geometry
 {
+    // Represents a segment along an axis, with the axis as a unit
+    struct Interval {
+        float min;
+        float max;
 
+        bool Intersects(const Interval& rhs) const;
+
+        bool operator==(const Interval& rhs) const = default;
+    };
 }

include/J3ML/Geometry/Triangle.h

@@ -1,5 +1,6 @@
 #pragma once
 
+#include "J3ML/LinearAlgebra/Vector3.h"
 #include <J3ML/Geometry/Common.h>
 #include <J3ML/LinearAlgebra.h>
 #include <cfloat>
@@ -13,11 +14,18 @@ namespace J3ML::Geometry
         Vector3 V1;
         Vector3 V2;
     public:
-
         float DistanceSq(const Vector3 &point) const;
 
+        /// Returns a new triangle, translated with a direction vector
+        Triangle Translated(const Vector3& translation) const;
+        /// Returns a new triangle, scaled from 3D factors
+        Triangle Scaled(const Vector3& scaled) const;
+
         bool Intersects(const AABB& aabb) const;
         bool Intersects(const Capsule& capsule) const;
+        bool Intersects(const Triangle& rhs) const;
+        friend bool Intersects(const Triangle& lhs, const Triangle &rhs);
+
         AABB BoundingAABB() const;
 
         /// Tests if the given object is fully contained inside this triangle.
@@ -29,6 +37,8 @@ namespace J3ML::Geometry
         bool Contains(const LineSegment& lineSeg, float triangleThickness = 1e-3f) const;
         bool Contains(const Triangle& triangle, float triangleThickness = 1e-3f) const;
 
+        /// Project the triangle onto an axis, and returns the min and max value with the axis as a unit
+        Interval ProjectionInterval(const Vector3& axis) const;
         void ProjectToAxis(const Vector3 &axis, float &dMin, float &dMax) const;
 
         /// Quickly returns an arbitrary point inside this Triangle. Used in GJK intersection test.
@@ -108,6 +118,8 @@ namespace J3ML::Geometry
 
         Plane PlaneCW() const;
 
+        Vector3 FaceNormal() const;
+
         Vector3 Vertex(int i) const;
 
         LineSegment Edge(int i) const;