/**** 
* Classes
****/ 
/***********************************************************************************/ 
/********************************** CUBE CLASS ************************************/
/***********************************************************************************/ 
var Cube = Container.expand(function () {
	var self = Container.call(this);
	self.z = 0;
	self.baseSize = 100;
	// Initialize cube faces using SimpleFace class
	self.frontFace = new SimpleFace({
		w: self.baseSize,
		h: self.baseSize,
		d: self.baseSize,
		dx: 0,
		dy: 0,
		dz: 1,
		rx: 0,
		ry: 0,
		rz: 0,
		ti: 0xFFFFFF
	});
	self.backFace = new SimpleFace({
		w: self.baseSize,
		h: self.baseSize,
		d: self.baseSize,
		dx: 0,
		dy: 0,
		dz: -1,
		rx: Math.PI,
		ry: 0,
		rz: 0,
		ti: 0xFFFFFF
	});
	self.leftFace = new SimpleFace({
		w: self.baseSize,
		h: self.baseSize,
		d: self.baseSize,
		dx: -1,
		dy: 0,
		dz: 0,
		rx: 0,
		ry: Math.PI / 2,
		rz: 0,
		ti: 0xFFFFFF
	});
	self.rightFace = new SimpleFace({
		w: self.baseSize,
		h: self.baseSize,
		d: self.baseSize,
		dx: 1,
		dy: 0,
		dz: 0,
		rx: 0,
		ry: -Math.PI * 0.5,
		rz: 0,
		ti: 0xFFFFFF
	});
	self.topFace = new SimpleFace({
		w: self.baseSize,
		h: self.baseSize,
		d: self.baseSize,
		dx: 0,
		dy: -1,
		dz: 0,
		rx: -Math.PI / 2,
		ry: 0,
		rz: 0,
		ti: 0xFFFFFF
	});
	self.bottomFace = new SimpleFace({
		w: self.baseSize,
		h: self.baseSize,
		d: self.baseSize,
		dx: 0,
		dy: 1,
		dz: 0,
		rx: Math.PI / 2,
		ry: 0,
		rz: 0,
		ti: 0xFFFFFF
	});
	self.faces = [self.frontFace, self.backFace, self.leftFace, self.rightFace, self.topFace, self.bottomFace];
	self.faces.forEach(function (face) {
		self.addChild(face);
	});
	self.speedX = 5;
	self.speedY = 5;
	self.speedZ = 5;
	// Rotate cube around its axes
	self.rotate3D = function (angleX, angleY, angleZ) {
		log("cube rotate3D ");
		self.rotation = angleZ;
		var zScaleFactor = 1 + self.z / 500;
		self.faces.forEach(function (face) {
			face.rotate3D(angleX, angleY, angleZ, zScaleFactor);
		});
	};
});
/***********************************************************************************/ 
/******************************* FACE CLASS *********************************/
/***********************************************************************************/ 
var Face = Container.expand(function (options) {
	var self = Container.call(this);
	options = options || {};
	var points = Math.max(2, Math.min(10, options.points || 4)); // Ensure points are between 2 and 10
	self.baseSize = 100;
	self.w = options.w || self.baseSize;
	self.h = options.h || self.baseSize;
	self.d = options.d || self.baseSize;
	self.dx = options.dx || 0;
	self.dy = options.dy || 0;
	self.dz = options.dz || 0;
	self.rx = options.rx || 0;
	self.ry = options.ry || 0;
	self.rz = options.rz || 0;
	self.tint = options.ti || 0xFFFFFF;
	// Generate points for the face based on the number of points specified
	self.baseFaceCoordinates = [];
	for (var i = 0; i < points; i++) {
		var angle = 2 * Math.PI * (i / points);
		self.baseFaceCoordinates.push({
			x: self.w / 2 * Math.cos(angle) + self.dx * self.w,
			y: self.h / 2 * Math.sin(angle) + self.dy * self.h,
			z: self.dz * self.d
		});
	}
	// Create a polygon face using the Shape class
	self.face = new Shape(self.baseFaceCoordinates, self.tint);
	// Attach the face to the Face container
	self.addChild(self.face);
	// Rotate in 3D: X = roasting chicken / Y = whirling dervish / Z = wheel of Fortune
	self.rotate3D = function (angleX, angleY, angleZ, scale) {
		scale = scale || 1;
		self.faceCoordinates = self.baseFaceCoordinates.map(function (coord) {
			return {
				x: coord.x,
				y: coord.y,
				z: coord.z
			};
		});
		// Apply rotation around X-axis
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			var y = coord.y * Math.cos(angleX) - coord.z * Math.sin(angleX);
			var z = coord.y * Math.sin(angleX) + coord.z * Math.cos(angleX);
			return {
				x: coord.x,
				y: y,
				z: z
			};
		});
		// Apply rotation around Y-axis
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			var x = coord.x * Math.cos(angleY) + coord.z * Math.sin(angleY);
			var z = -coord.x * Math.sin(angleY) + coord.z * Math.cos(angleY);
			return {
				x: x,
				y: coord.y,
				z: z
			};
		});
		// Apply rotation around Z-axis
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			var x = coord.x * Math.cos(angleZ) - coord.y * Math.sin(angleZ);
			var y = coord.x * Math.sin(angleZ) + coord.y * Math.cos(angleZ);
			return {
				x: x,
				y: y,
				z: coord.z
			};
		});
		// Apply scaling
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			return {
				x: coord.x * scale,
				y: coord.y * scale,
				z: coord.z * scale
			};
		});
		self.face.updateCoordinates(self.faceCoordinates);
	};
	// Initialize face in 3D space
	self.rotate3D(0, 0, 0, 1);
});
/***********************************************************************************/ 
/********************************** SHAPE CLASS ************************************/
/***********************************************************************************/ 
var Shape = Container.expand(function (coordinates, tint) {
	var self = Container.call(this);
	self.polygon = drawPolygon(coordinates, tint); // Function to create a polygon from a list of coordinates
	self.tint = tint;
	self.attachLines = function () {
		// Iterate through each line in the polygon and attach it to the shape
		self.polygon.forEach(function (line) {
			self.addChild(line);
		});
	};
	self.attachLines();
	self.updateCoordinates = function (newCoordinates) {
		log("Shape updateCoordinates ", newCoordinates);
		// Ensure newCoordinates is an array and has the same length as the current polygon
		if (!Array.isArray(newCoordinates) || newCoordinates.length !== self.polygon.length) {
			error("Invalid newCoordinates length");
			return;
		}
		// Update each line in the polygon with new coordinates
		self.polygon = updatePolygon(self.polygon, newCoordinates);
	};
});
/***********************************************************************************/ 
/******************************* SIMPLE FACE CLASS *********************************/
/***********************************************************************************/ 
var SimpleFace = Container.expand(function (options) {
	var self = Container.call(this);
	log("SimpleFAce init options =", options);
	self.baseSize = 100;
	options = options || {};
	self.w = options.w || self.baseSize;
	self.h = options.h || self.baseSize;
	self.d = options.d || self.baseSize, self.dx = options.dx || 0;
	self.dy = options.dy || 0;
	self.dz = options.dz || 0;
	self.rx = options.rx || 0;
	self.ry = options.ry || 0;
	self.rz = options.rz || 0;
	self.tint = options.ti || 0xFFFFFF;
	// Define faceCoordinates property
	self.baseFaceCoordinates = [{
		x: -self.w + self.dx * self.w,
		y: -self.h + self.dy * self.h,
		z: self.dz * self.d
	},
	// Top-left
	{
		x: self.w + self.dx * self.w,
		y: -self.h + self.dy * self.h,
		z: self.dz * self.d
	},
	// Top-right
	{
		x: self.w + self.dx * self.w,
		y: self.h + self.dy * self.h,
		z: self.dz * self.d
	},
	// Bottom-right
	{
		x: -self.w + self.dx * self.w,
		y: self.h + self.dy * self.h,
		z: self.dz * self.d
	} // Bottom-left
	];
	log("SimpleFAce ready to init ...", self.baseFaceCoordinates, "DX=" + self.dx);
	self.baseFaceCoordinates.forEach(function (point) {
		// Update z of each face point coordinates depending on dz and rx, ry
		point.z += self.dz * Math.cos(self.rx) * Math.cos(self.ry);
	});
	// Create a square face using the Shape class
	self.face = new Shape(self.baseFaceCoordinates, self.tint);
	// Attach the face to the SimpleFace container
	self.addChild(self.face);
	// Rotate in 3d : X = roasting chicken / Y = whirling dervish / Z = wheel of Fortune
	self.rotate3D = function (angleX, angleY, angleZ, scale) {
		scale = scale || 1;
		log("SimpleFace rotate3D old coord=", self.faceCoordinates, Date.now());
		self.faceCoordinates = self.baseFaceCoordinates.map(function (coord) {
			return {
				x: coord.x,
				y: coord.y,
				z: coord.z
			};
		});
		// Apply rotation around X-axis
		// Adjust initial rotation parameters before applying new rotations
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			// Apply initial rotation around Z-axis
			var xZ = coord.x * Math.cos(self.rz) - coord.y * Math.sin(self.rz);
			var yZ = coord.x * Math.sin(self.rz) + coord.y * Math.cos(self.rz);
			// Apply initial rotation around Y-axis
			var xY = xZ * Math.cos(self.ry) + coord.z * Math.sin(self.ry);
			var zY = coord.z * Math.cos(self.ry) - xZ * Math.sin(self.ry);
			// Apply initial rotation around X-axis
			var yX = yZ * Math.cos(self.rx) - zY * Math.sin(self.rx);
			var zX = yZ * Math.sin(self.rx) + zY * Math.cos(self.rx);
			return {
				x: xY,
				y: yX,
				z: zX
			};
		});
		// Apply new rotations
		// Calculate center of the face
		var centerX = self.faceCoordinates.reduce(function (acc, coord) {
			return acc + coord.x;
		}, 0) / self.faceCoordinates.length;
		var centerY = self.faceCoordinates.reduce(function (acc, coord) {
			return acc + coord.y;
		}, 0) / self.faceCoordinates.length;
		var centerZ = self.faceCoordinates.reduce(function (acc, coord) {
			return acc + coord.z;
		}, 0) / self.faceCoordinates.length;
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			// Translate coordinates to rotate around the center including dy and dz adjustment
			var translatedY = (coord.y + self.dy * self.h - centerY) * Math.cos(angleX) - (coord.z + self.dz * self.d - centerZ) * Math.sin(angleX);
			var translatedZ = (coord.y + self.dy * self.h - centerY) * Math.sin(angleX) + (coord.z + self.dz * self.d - centerZ) * Math.cos(angleX);
			return {
				x: coord.x + self.dx * self.w - centerX,
				// Keep X unchanged but translate to rotate around center
				y: translatedY + centerY,
				z: translatedZ + centerZ
			};
		});
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			var translatedX = (coord.z - centerZ) * Math.sin(angleY) + (coord.x - centerX) * Math.cos(angleY);
			var translatedZ = (coord.z - centerZ) * Math.cos(angleY) - (coord.x - centerX) * Math.sin(angleY);
			return {
				x: translatedX + centerX,
				y: coord.y,
				// Keep Y unchanged
				z: translatedZ + centerZ
			};
		});
		self.faceCoordinates = self.faceCoordinates.map(function (coord) {
			return {
				x: coord.x * scale,
				y: coord.y * scale,
				z: coord.z * scale
			};
		});
		log("SimpleFace rotate3D new coord=", self.faceCoordinates, Date.now());
		self.face.updateCoordinates(self.faceCoordinates);
	};
	// initialize face in 3D space
	self.rotate3D(0, 0, 0, 1);
	log("SimpleFace end init coord=", self.baseFaceCoordinates, Date.now());
});
/***********************************************************************************/ 
/********************************** SPHERE CLASS ***********************************/
/***********************************************************************************/ 
var Sphere = Container.expand(function () {
	var self = Container.call(this);
	self.z = 0;
	self.radius = 50; // Sphere radius
	// Initialize sphere as a collection of SimpleFace instances to simulate a 3D sphere
	self.faces = [];
	var segments = 6; // Number of segments to simulate the sphere
	for (var i = 0; i < segments; i++) {
		var angle = 1 * Math.PI * (i / segments);
		var dx = Math.cos(angle);
		var dy = Math.sin(angle);
		// Create a circular segment as a face of the sphere
		var face = new SimpleFace({
			w: self.radius * 2,
			// Width of the face, approximating the sphere's circumference segment
			h: self.radius * 2,
			// Height of the face, arbitrary for visual effect
			d: self.radius * 2,
			// Depth, using width to maintain circular appearance
			dx: 0,
			// X offset based on circle calculation
			dy: 0,
			// Y offset based on circle calculation
			dz: 0,
			// No Z offset for a sphere
			rx: 0,
			// Rotation around X-axis
			ry: angle,
			// Rotation around Y-axis
			rz: 0,
			// Rotation around Z-axis to position the segment correctly
			ti: 0xFFFFFF // Tint color
		});
		self.faces.push(face);
		self.addChild(face);
	}
	self.speedX = 5;
	self.speedY = 5;
	self.speedZ = 5;
	// Rotate sphere around its axes
	self.rotate3D = function (angleX, angleY, angleZ) {
		log("sphere rotate3D ");
		self.rotation = angleZ;
		var zScaleFactor = 1 + self.z / 500;
		self.faces.forEach(function (face) {
			face.rotate3D(angleX, angleY, angleZ, zScaleFactor);
		});
	};
});

/**** 
* Initialize Game
****/ 
// Utility function to draw a polygon using drawLine
var game = new LK.Game({
	backgroundColor: 0x000050 // Initialize game with a black background
});

/**** 
* Game Code
****/ 
var fpsText;
var lastTick;
var frameCount;
var debugText;
/***********************************************************************************/ 
/******************************* UTILITY FUNCTIONS *********************************/
/***********************************************************************************/ 
function drawPolygon(coordinates, tint) {
	log("drawPolygon ", coordinates);
	var lines = [];
	for (var i = 0; i < coordinates.length; i++) {
		var startPoint = coordinates[i];
		var endPoint = coordinates[(i + 1) % coordinates.length]; // Loop back to the first point
		var line = drawLine(startPoint.x, startPoint.y, endPoint.x, endPoint.y, tint);
		lines.push(line);
	}
	return lines;
}
function updatePolygon(lines, newCoordinates, scale) {
	log("updatePolygon ", lines, scale);
	// Ensure lines and newCoordinates have the same length
	if (lines.length !== newCoordinates.length) {
		error("updatePolygon error: lines and newCoordinates length mismatch");
		return lines;
	}
	// Update each line with new coordinates
	for (var i = 0; i < lines.length; i++) {
		var startPoint = newCoordinates[i];
		var endPoint = newCoordinates[(i + 1) % newCoordinates.length]; // Loop back to the first point for the last line
		updateLine(lines[i], startPoint.x, startPoint.y, endPoint.x, endPoint.y, scale);
	}
	return lines;
}
// Utility function to draw lines between two points
function drawLine(x1, y1, x2, y2, tint) {
	log("drawLine ", x1, y1);
	var line = LK.getAsset('line', {
		anchorX: 0.0,
		anchorY: 0.0,
		x: x1,
		y: y1,
		tint: tint
	});
	line.startX = x1;
	line.startY = y1;
	line.endX = x2;
	line.endY = y2;
	// Calculate the distance between the two points
	var distance = Math.sqrt(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2));
	// Set the width of the line to the distance between the points
	line.width = distance;
	// Calculate the angle between the two points
	var angle = Math.atan2(y2 - y1, x2 - x1);
	// Correct angle calculation for all quadrants
	line.rotation = angle;
	return line;
}
// Utility function to draw lines between two points
function updateLine(line, newX1, newY1, newX2, newY2, scale) {
	log("updateLine ", line);
	scale = scale === undefined ? 1 : scale;
	// Calculate midpoint of the original line
	var midX = (newX1 + newX2) / 2;
	var midY = (newY1 + newY2) / 2;
	// Adjust start and end points based on scale
	newX1 = midX + (newX1 - midX) * scale;
	newY1 = midY + (newY1 - midY) * scale;
	newX2 = midX + (newX2 - midX) * scale;
	newY2 = midY + (newY2 - midY) * scale;
	// Update line start and end coordinates after scaling
	line.x = newX1;
	line.y = newY1;
	line.startX = newX1;
	line.startY = newY1;
	line.endX = newX2;
	line.endY = newY2;
	// Recalculate the distance between the new scaled points
	var distance = Math.sqrt(Math.pow(newX2 - newX1, 2) + Math.pow(newY2 - newY1, 2));
	// Update the width of the line to the new distance
	line.width = distance;
	// Recalculate the angle between the new points
	var angle = Math.atan2(newY2 - newY1, newX2 - newX1);
	// Update the rotation of the line to the new angle
	line.rotation = angle;
	return line;
}
function log() {
	if (isDebug) {
		console.log(arguments);
	}
}
/***********************************************************************************/ 
/******************************* GAME VARIABLES*********************************/
/***********************************************************************************/ 
var cube;
var sphere;
var face1;
var face2;
var face3;
var rotationSpeedX = 0;
var rotationSpeedY = 0;
var rotationSpeedZ = 0;
var isDebug = false;
var fullLog = [];
/***********************************************************************************/ 
/***************************** GAME INITIALIZATION *********************************/
/***********************************************************************************/ 
function gameInitialize() {
	cube = new Cube();
	cube.x = 2048 * 0.25; // Center horizontally
	cube.y = 2732 / 2; // Center vertically
	cube.z = 0;
	game.addChild(cube);
	sphere = new Sphere();
	sphere.x = 2048 * 0.75; // Center horizontally
	sphere.y = 2732 / 2; // Center vertically
	sphere.z = 0;
	game.addChild(sphere);
	face1 = new Face({
		points: 10,
		w: 100,
		h: 100,
		d: 100,
		dx: 0,
		dy: 0,
		dz: 0,
		rx: Math.PI * 0.125,
		ry: 0,
		rz: 0,
		ti: 0xFFFFFF
	});
	face1.x = 2048 * 0.5; // Center horizontally
	face1.y = 2732 / 2; // Center vertically
	face1.z = 0;
	game.addChild(face1);
	if (isDebug) {
		var debugMarker = LK.getAsset('debugMarker', {
			anchorX: 0.5,
			anchorY: 0.5,
			x: 2048 * 0.5,
			y: 2732 / 2
		});
		game.addChild(debugMarker);
		fpsText = new Text2('FPS: 0', {
			size: 50,
			fill: "#ffffff"
		});
		// Position FPS text at the bottom-right corner
		fpsText.anchor.set(1, 1); // Anchor to the bottom-right
		LK.gui.bottomRight.addChild(fpsText);
		// Update FPS display every second
		lastTick = Date.now();
		frameCount = 0;
		// Debug text to display cube information
		debugText = new Text2('Debug Info', {
			size: 50,
			fill: "#ffffff"
		});
		debugText.anchor.set(0.5, 0); // Anchor to the bottom-right
		LK.gui.top.addChild(debugText);
	}
}
/***********************************************************************************/ 
/******************************** MAIN GAME LOOP ***********************************/
/***********************************************************************************/ 
game.update = function () {
	// Rotate simpleFace in 3D on each game update
	rotationSpeedX += 1 * Math.PI * 0.125 * 0.02;
	rotationSpeedY += 1 * Math.PI * 0.125 * 0.02;
	rotationSpeedZ += 1 * Math.PI * 0.125 * 0.02;
	// Update cube position with movement speed
	cube.x += cube.speedX;
	cube.y += cube.speedY;
	cube.z += cube.speedZ;
	// Check for cube bouncing on horizontal borders
	if (cube.x <= 100 || cube.x >= 2048 - 100) {
		cube.speedX *= -1; // Reverse horizontal direction
	}
	// Check for cube bouncing on Z dimension boundaries
	if (cube.z <= -250 || cube.z >= 1000) {
		// Assuming -500 and 500 as Z dimension boundaries
		cube.speedZ *= -1; // Reverse Z dimension direction
	}
	// Check for cube bouncing on vertical borders
	if (cube.y <= 100 || cube.y >= 2732 - 100) {
		cube.speedY *= -1; // Reverse vertical direction
	}
	// Rotating the cube
	cube.rotate3D(rotationSpeedX, rotationSpeedY, rotationSpeedZ);
	// Update cube position with movement speed
	sphere.x += sphere.speedX;
	sphere.y += sphere.speedY;
	sphere.z += sphere.speedZ;
	// Check for sphere bouncing on horizontal borders
	if (sphere.x <= 100 || sphere.x >= 2048 - 100) {
		sphere.speedX *= -1; // Reverse horizontal direction
	}
	// Check for cube bouncing on Z dimension boundaries
	if (sphere.z <= -250 || sphere.z >= 1000) {
		// Assuming -500 and 500 as Z dimension boundaries
		sphere.speedZ *= -1; // Reverse Z dimension direction
	}
	// Check for cube bouncing on vertical borders
	if (sphere.y <= 100 || sphere.y >= 2732 - 100) {
		sphere.speedY *= -1; // Reverse vertical direction
	}
	// Rotating the cube
	sphere.rotate3D(rotationSpeedX, rotationSpeedY, rotationSpeedZ);
	if (isDebug) {
		debugText.setText("X: " + Math.round(cube.x) + ", Y: " + Math.round(cube.y) + ", Z: " + Math.round(cube.z) + ", R: " + cube.rotation.toFixed(2));
		// FPS
		var now = Date.now();
		frameCount++;
		if (now - lastTick >= 1000) {
			// Update every second
			fpsText.setText('FPS: ' + frameCount);
			frameCount = 0;
			lastTick = now;
		}
	}
};
gameInitialize(); // Initialize the game

===================================================================
--- original.js
+++ change.js
@@ -523,9 +523,9 @@
 		d: 100,
 		dx: 0,
 		dy: 0,
 		dz: 0,
-		rx: 0,
+		rx: Math.PI * 0.125,
 		ry: 0,
 		rz: 0,
 		ti: 0xFFFFFF
 	});