Add helper functions to determine if an intersection is in the half-space of a given plane

csg/src/plane.rs

@@ -72,6 +72,31 @@ impl PlaneIntersection {
         Vec3::from_slice(&vs)
     }
 
+    pub fn in_halfspace_mat(&self, plane: &Plane) -> bool {
+        // "Distance" and side of the point defined by plane against the plane defined
+        // by the 3 points of the intersection planes.
+        //* Note that the sign is dependant on the winding order of the intersection planes
+        let m1 = glam::mat4(
+            self.planes[0].into_vec4(),
+            self.planes[1].into_vec4(),
+            self.planes[2].into_vec4(),
+            plane.into_vec4(),
+        );
+        let d1 = m1.determinant();
+
+        // We can resolve the winding order problem by multiplying by the normal matrix determinant
+        let m2 = self.get_matrix().transpose();
+        let d2 = m2.determinant();
+        let dist = d1 * d2;
+
+        //* Note: dist is only euclidean accurate if all the normals are normalised :)
+        dist < math::EPSILON
+    }
+
+    pub fn in_halfspace(&self, plane: &Plane) -> bool {
+        plane.normal.dot(self.get_intersection_point()) - plane.offset <= math::EPSILON
+    }
+
     fn get_matrix(&self) -> Mat3 {
         glam::mat3(
             self.planes[0].normal,