Bend path close to Bezier curve

lib/rmg/Functions.cpp

@@ -24,9 +24,25 @@
 
 VCMI_LIB_NAMESPACE_BEGIN
 
-void replaceWithCurvedPath(rmg::Path & path, const Zone & zone, const int3 & src, bool onlyStraight /* = true */)
+void replaceWithCurvedPath(rmg::Path & path, Zone & zone, const int3 & src, bool onlyStraight /* = true */)
 {
-	auto costFunction = rmg::Path::createCurvedCostFunction(zone.area()->getBorder());
+	// Get random control points from within the zone
+	auto & rng = zone.getRand();
+	const auto & tiles = zone.area()->getTilesVector();
+
+	if(tiles.size() < 2)
+	{
+		logGlobal->warn("Zone too small for curved path");
+		return;
+	}
+
+	// Pick two random control points (Q1, Q2) from zone tiles
+	int3 control1 = tiles[rng.nextInt(0, static_cast<int>(tiles.size()) - 1)];
+	int3 control2 = tiles[rng.nextInt(0, static_cast<int>(tiles.size()) - 1)];
+
+	// Create Bezier cost function: Q0=start, Q1=control1, Q2=control2, Q3=src
+	auto costFunction = rmg::Path::createBezierCostFunction(src, control1, control2, zone.getPos());
+
 	auto pathArea = zone.areaForRoads();
 	rmg::Path curvedPath(pathArea);
 	curvedPath.connect(zone.freePaths().get());

lib/rmg/Functions.h

@@ -34,7 +34,7 @@ public:
 	}
 };
 
-void replaceWithCurvedPath(rmg::Path & path, const Zone & zone, const int3 & src, bool onlyStraight = true);
+void replaceWithCurvedPath(rmg::Path & path, Zone & zone, const int3 & src, bool onlyStraight = true);
 
 rmg::Tileset collectDistantTiles(const Zone & zone, int distance);
 

lib/rmg/RmgPath.cpp

@@ -229,4 +229,55 @@ Path::MoveCostFunction Path::createCurvedCostFunction(const Area & border)
 	};
 }
 
+float Path::distanceToCubicBezier(const int3 & point, const int3 & p0, const int3 & p1, const int3 & p2, const int3 & p3)
+{
+	// Approximate distance to cubic Bezier curve by sampling
+	// B(t) = (1-t)³P0 + 3(1-t)²tP1 + 3(1-t)t²P2 + t³P3
+	constexpr int SAMPLES = 20;
+	float minDistSq = std::numeric_limits<float>::max();
+
+	for(int i = 0; i <= SAMPLES; ++i)
+	{
+		float t = static_cast<float>(i) / SAMPLES;
+		float oneMinusT = 1.0f - t;
+		float oneMinusT2 = oneMinusT * oneMinusT;
+		float oneMinusT3 = oneMinusT2 * oneMinusT;
+		float t2 = t * t;
+		float t3 = t2 * t;
+
+		// Cubic Bezier formula
+		float bx = oneMinusT3 * p0.x + 3.0f * oneMinusT2 * t * p1.x + 3.0f * oneMinusT * t2 * p2.x + t3 * p3.x;
+		float by = oneMinusT3 * p0.y + 3.0f * oneMinusT2 * t * p1.y + 3.0f * oneMinusT * t2 * p2.y + t3 * p3.y;
+
+		float dx = point.x - bx;
+		float dy = point.y - by;
+		float distSq = dx * dx + dy * dy;
+
+		if(distSq < minDistSq)
+			minDistSq = distSq;
+	}
+
+	//return std::sqrt(minDistSq);
+	return minDistSq;
+}
+
+Path::MoveCostFunction Path::createBezierCostFunction(const int3 & p0, const int3 & p1, const int3 & p2, const int3 & p3)
+{
+	// p0: start point (Q0)
+	// p1: first control point (Q1) - any tile in zone
+	// p2: second control point (Q2) - any tile in zone
+	// p3: end point (Q3)
+	return [p0, p1, p2, p3](const int3 & src, const int3 & dst) -> float
+	{
+
+		// Distance from destination tile to the Bezier curve
+		float distToCurve = distanceToCubicBezier(dst, p0, p1, p2, p3);
+
+		// Penalize tiles far from the curve
+		// Square for stronger effect
+		return distToCurve * distToCurve;
+
+	};
+}
+
 VCMI_LIB_NAMESPACE_END

lib/rmg/RmgPath.h

@@ -45,7 +45,9 @@ public:
 	
 	static Path invalid();
 	static MoveCostFunction createCurvedCostFunction(const Area & border);
+	static MoveCostFunction createBezierCostFunction(const int3 & p0, const int3 & p1, const int3 & p2, const int3 & p3);
 	static float nonEuclideanCostFunction(const int3& src, const int3& dst, const int3& center);
+	static float distanceToCubicBezier(const int3 & point, const int3 & p0, const int3 & p1, const int3 & p2, const int3 & p3);
 	
 private: