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			@ -22,12 +22,6 @@ | 
			
		
		
	
		
			
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			//---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			// Macro Helpers | 
			
		
		
	
		
			
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			//---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			#define SCREEN_WIDTH 800 | 
			
		
		
	
		
			
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			#define SCREEN_HEIGHT 450 | 
			
		
		
	
		
			
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			#define CENTER_X SCREEN_WIDTH * 0.5 | 
			
		
		
	
		
			
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			#define CENTER_Y SCREEN_HEIGHT * 0.5 - 100 | 
			
		
		
	
		
			
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			// Constant for Simulation | 
			
		
		
	
		
			
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			#define SIMULATION_STEPS 30 | 
			
		
		
	
		
			
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			#define G 9.81 | 
			
		
		
	
	
		
			
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			@ -45,32 +39,32 @@ int main(void) | 
			
		
		
	
		
			
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			{ | 
			
		
		
	
		
			
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			    // Initialization | 
			
		
		
	
		
			
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			    //-------------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			    const int screenWidth = 800; | 
			
		
		
	
		
			
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			    const int screenHeight = 450; | 
			
		
		
	
		
			
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			    SetConfigFlags(FLAG_WINDOW_HIGHDPI); | 
			
		
		
	
		
			
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			    InitWindow(SCREEN_WIDTH, SCREEN_HEIGHT, "raylib [shapes] example - Double Pendulum"); | 
			
		
		
	
		
			
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			    InitWindow(screenWidth, screenHeight, "raylib [shapes] example - double pendulum"); | 
			
		
		
	
		
			
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			    // Simulation Paramters | 
			
		
		
	
		
			
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			    //-------------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			    float l1 = 15, m1 = 0.2, theta1 = DEG2RAD * 170, w1 = 0; | 
			
		
		
	
		
			
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			    float l2 = 15, m2 = 0.1, theta2 = DEG2RAD * 0, w2 = 0; | 
			
		
		
	
		
			
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			    float lengthScaler = 0.1; | 
			
		
		
	
		
			
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			    float totalM = m1 + m2; | 
			
		
		
	
		
			
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			    Vector2 previousPosition = CalculateDoublePendulumEndPoint(l1, theta1, l2, theta2); | 
			
		
		
	
		
			
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			    previousPosition.x += n">CENTER_X; | 
			
		
		
	
		
			
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			    previousPosition.y += n">CENTER_Y; | 
			
		
		
	
		
			
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			    previousPosition.x += p">(screenWidth/2); | 
			
		
		
	
		
			
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			    previousPosition.y += p">(screenHeight/2 - 100); | 
			
		
		
	
		
			
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			    // Scale length | 
			
		
		
	
		
			
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			    float L1 = l1 * lengthScaler; | 
			
		
		
	
		
			
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			    float L2 = l2 * lengthScaler; | 
			
		
		
	
		
			
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			    // Draw Parameters | 
			
		
		
	
		
			
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			    //-------------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			    // Draw parameters | 
			
		
		
	
		
			
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			    int lineThick = 20, trailThick = 2; | 
			
		
		
	
		
			
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			    float fateAlpha = 0.01; | 
			
		
		
	
		
			
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			     | 
			
		
		
	
		
			
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			    // Create Framebuffer | 
			
		
		
	
		
			
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			    //-------------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			    RenderTexture2D target = LoadRenderTexture(SCREEN_WIDTH, SCREEN_HEIGHT); | 
			
		
		
	
		
			
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			    // Create framebuffer | 
			
		
		
	
		
			
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			    RenderTexture2D target = LoadRenderTexture(screenWidth, screenHeight); | 
			
		
		
	
		
			
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			    SetTextureFilter(target.texture, TEXTURE_FILTER_BILINEAR); | 
			
		
		
	
		
			
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			    SetTargetFPS(60); | 
			
		
		
	
	
		
			
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			@ -80,60 +74,56 @@ int main(void) | 
			
		
		
	
		
			
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			    while (!WindowShouldClose())    // Detect window close button or ESC key | 
			
		
		
	
		
			
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			    { | 
			
		
		
	
		
			
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			        // Update | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			        float dt = GetFrameTime(); | 
			
		
		
	
		
			
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			        float step = dt / SIMULATION_STEPS, step2 = step * step; | 
			
		
		
	
		
			
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			        // Update Physics - larger steps = better approximation | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			        for (int i = 0; i < SIMULATION_STEPS; ++i) | 
			
		
		
	
		
			
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			        { | 
			
		
		
	
		
			
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			            float delta = theta1 - theta2; | 
			
		
		
	
		
			
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			            float sinD = sin(delta), cosD = cos(delta), cos2D = cos(2 * delta); | 
			
		
		
	
		
			
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			            float sinD = sinf(delta), cosD = cosf(delta), cos2D = cosf(2*delta); | 
			
		
		
	
		
			
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			            float ww1 = w1 * w1, ww2 = w2 * w2; | 
			
		
		
	
		
			
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			            // Calculate a1 | 
			
		
		
	
		
			
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			            float a1 = (-G * (2 * m1 + m2) * sin(theta1)  | 
			
		
		
	
		
			
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			                         - m2 * G * sin(theta1 - 2 * theta2)  | 
			
		
		
	
		
			
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			                         - 2 * sinD * m2 * (ww2 * L2 + ww1 * L1 * cosD)) | 
			
		
		
	
		
			
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			                         / (L1 * (2 * m1 + m2 - m2 * cos2D)); | 
			
		
		
	
		
			
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			            float a1 = (-G*(2*m1 + m2)*sinf(theta1) | 
			
		
		
	
		
			
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			                         - m2*G*sinf(theta1 - 2*theta2) | 
			
		
		
	
		
			
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			                         - 2*sinD*m2*(ww2*L2 + ww1*L1*cosD)) | 
			
		
		
	
		
			
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			                         / (L1*(2*m1 + m2 - m2*cos2D)); | 
			
		
		
	
		
			
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			            // Calculate a2 | 
			
		
		
	
		
			
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			            float a2 = (2 * sinD * (ww1 * L1 * totalM | 
			
		
		
	
		
			
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			                         + G * totalM * cos(theta1)  | 
			
		
		
	
		
			
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			                         + ww2 * L2 * m2 * cosD)) | 
			
		
		
	
		
			
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			                         / (L2 * (2 * m1 + m2 - m2 * cos2D)); | 
			
		
		
	
		
			
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			            float a2 = (2*sinD*(ww1*L1*totalM | 
			
		
		
	
		
			
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			                         + G*totalM*cosf(theta1) | 
			
		
		
	
		
			
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			                         + ww2*L2*m2*cosD)) | 
			
		
		
	
		
			
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			                         / (L2*(2*m1 + m2 - m2*cos2D)); | 
			
		
		
	
		
			
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			            // Update thetas | 
			
		
		
	
		
			
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			            theta1 += w1 * step + 0.5 * a1 * step2; | 
			
		
		
	
		
			
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			            theta2 += w2 * step + 0.5 * a2 * step2; | 
			
		
		
	
		
			
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			            theta1 += w1*step + 0.5f*a1*step2; | 
			
		
		
	
		
			
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			            theta2 += w2*step + 0.5f*a2*step2; | 
			
		
		
	
		
			
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			            // Update omegas | 
			
		
		
	
		
			
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			            w1 += a1 * step; | 
			
		
		
	
		
			
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			            w2 += a2 * step; | 
			
		
		
	
		
			
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			            w1 += a1*step; | 
			
		
		
	
		
			
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			            w2 += a2*step; | 
			
		
		
	
		
			
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			        } | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			        // Calculate position | 
			
		
		
	
		
			
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			        Vector2 currentPosition = CalculateDoublePendulumEndPoint(l1, theta1, l2, theta2); | 
			
		
		
	
		
			
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			        currentPosition.x += CENTER_X; | 
			
		
		
	
		
			
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			        currentPosition.y += CENTER_Y; | 
			
		
		
	
		
			
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			        currentPosition.x += screenWidth/2; | 
			
		
		
	
		
			
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			        currentPosition.y += screenHeight/2 - 100; | 
			
		
		
	
		
			
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			        // Draw to framebuffer | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			        // Draw to render texture | 
			
		
		
	
		
			
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			        BeginTextureMode(target); | 
			
		
		
	
		
			
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			            // Draw a transparent rectangle - smaller alpha = longer trails | 
			
		
		
	
		
			
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			            DrawRectangle(0, 0, SCREEN_WIDTH, SCREEN_HEIGHT, Fade(BLACK, fateAlpha)); | 
			
		
		
	
		
			
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			            DrawRectangle(0, 0, screenWidth, screenHeight, Fade(BLACK, fateAlpha)); | 
			
		
		
	
		
			
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			            // Draw trail | 
			
		
		
	
		
			
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			            DrawCircleV(previousPosition, trailThick, RED); | 
			
		
		
	
		
			
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			            DrawLineEx(previousPosition, currentPosition, trailThick * 2, RED); | 
			
		
		
	
		
			
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			        EndTextureMode(); | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			        // Update previous position | 
			
		
		
	
		
			
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			        previousPosition = currentPosition; | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
		
			
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			        // Draw | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
	
		
			
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			@ -141,17 +131,16 @@ int main(void) | 
			
		
		
	
		
			
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			            ClearBackground(BLACK); | 
			
		
		
	
		
			
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			            // Draw Trails Texture | 
			
		
		
	
		
			
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			            DrawTextureRec(target.texture, (Rectangle){ 0, 0, target.texture.width, -target.texture.height }, | 
			
		
		
	
		
			
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			                             (Vector2){ 0, 0 }, WHITE); | 
			
		
		
	
		
			
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			            // Draw trails texture | 
			
		
		
	
		
			
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			            DrawTextureRec(target.texture, (Rectangle){ 0, 0, target.texture.width, -target.texture.height }, (Vector2){ 0, 0 }, WHITE); | 
			
		
		
	
		
			
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			            // Draw n">Double Pendulum | 
			
		
		
	
		
			
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			            DrawRectanglePro((Rectangle){ CENTER_X, CENTER_Y, 10 * l1, lineThick }, | 
			
		
		
	
		
			
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			                             (Vector2){0, lineThick * 0.5}, 90 - RAD2DEG * theta1, RAYWHITE); | 
			
		
		
	
		
			
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			            // Draw kt">double pendulum | 
			
		
		
	
		
			
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			            DrawRectanglePro((Rectangle){ screenWidth/2, screenHeight/2 - 100, 10 * l1, lineThick }, | 
			
		
		
	
		
			
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			                (Vector2){0, lineThick * 0.5}, 90 - RAD2DEG * theta1, RAYWHITE); | 
			
		
		
	
		
			
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			            Vector2 endpoint1 = CalculatePendulumEndPoint(l1, theta1); | 
			
		
		
	
		
			
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			            DrawRectanglePro((Rectangle){ CENTER_X + endpoint1.x, CENTER_Y + endpoint1.y, 10 * l2, lineThick }, | 
			
		
		
	
		
			
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			                             (Vector2){0, lineThick * 0.5}, 90 - RAD2DEG * theta2, RAYWHITE); | 
			
		
		
	
		
			
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			            DrawRectanglePro((Rectangle){ screenWidth/2 + endpoint1.x, screenHeight/2 - 100 + endpoint1.y, 10 * l2, lineThick }, | 
			
		
		
	
		
			
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			                (Vector2){0, lineThick * 0.5}, 90 - RAD2DEG * theta2, RAYWHITE); | 
			
		
		
	
		
			
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			        EndDrawing(); | 
			
		
		
	
		
			
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			        //---------------------------------------------------------------------------------- | 
			
		
		
	
	
		
			
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