feat(Core/CreatureAI): improve npc position during the combat (#3369)

+ tangent equation to find correct angle and distance when moving

+ implemented proper backward

* Improved performance + random angle margin

* chore: add tollerance calculation in instance

* improved LOS checks with movements

* implemented collisions using raycast (imported by TC)

+ improved collision detection for CanReachPositionAndGetCoords

+ improved collision check

+ set correct flags for the backward movement

+ first implementation of slope angle (to improve)

Co-authored-by: Yehonal <yehonal.azeroth@gmail.com>

src/common/Collision/Management/VMapManager2.cpp

@@ -29,6 +29,7 @@
 #include "DBCStores.h"
 #include "Log.h"
 #include "VMapDefinitions.h"
+#include "GridDefines.h"
 
 using G3D::Vector3;
 
@@ -54,7 +55,7 @@ namespace VMAP
     Vector3 VMapManager2::convertPositionToInternalRep(float x, float y, float z) const
     {
         Vector3 pos;
-        const float mid = 0.5f * 64.0f * 533.33333333f;
+        const float mid = 0.5f * MAX_NUMBER_OF_GRIDS * SIZE_OF_GRIDS;
         pos.x = mid - x;
         pos.y = mid - y;
         pos.z = z;
@@ -308,4 +309,4 @@ namespace VMAP
         return StaticMapTree::CanLoadMap(std::string(basePath), mapId, x, y);
     }
 
-} // namespace VMAP
+} // namespace VMAP

src/common/Utilities/Geometry.h

@@ -0,0 +1,45 @@
+/*
+ * Copyright (C) 2016+     AzerothCore <www.azerothcore.org>, released under GNU AGPL v3 license: https://github.com/azerothcore/azerothcore-wotlk/blob/master/LICENSE-AGPL3
+ */
+
+#ifndef _GEOMETRY_H
+#define _GEOMETRY_H
+
+#include <cmath>
+#include <iostream>
+#include <cstdlib>
+
+using namespace std;
+
+inline float getAngle(float startX, float startY, float destX, float destY)
+{
+    auto dx = destX - startX;
+    auto dy = destY - startY;
+
+    auto ang = atan2(dy, dx);
+    ang = (ang >= 0) ? ang : 2 * M_PI + ang;
+    return ang;
+}
+
+inline float getSlopeAngle(float startX, float startY, float startZ, float destX, float destY, float destZ)
+{
+    auto a = (startX * destX + startY * destY + startZ * destZ);
+    auto b = sqrt(pow(startX,2.0f) + pow(startY,2.0f) + pow(startZ, 2.0f));
+    auto c = sqrt(pow(destX,2.0f) + pow(destY,2.0f) + pow(destZ, 2.0f));
+
+    auto ang = acos(a / (b * c));
+
+    if (isnan(ang))
+    {
+        return 0.0f;
+    }
+
+    return ang;
+}
+
+inline float getSlopeAngleAbs(float startX, float startY, float startZ, float destX, float destY, float destZ)
+{
+    return abs(getSlopeAngle(startX, startY, startZ, destX, destY, destZ));
+}
+
+#endif