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raylib-src
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								/*******************************************************************************************

								*

								*   raylib [shapes] example - double pendulum

								*

								*   Example complexity rating: [★★☆☆] 2/4

								*

								*   Example originally created with raylib 5.5, last time updated with raylib 5.5

								*

								*   Example contributed by JoeCheong (@Joecheong2006) and reviewed by Ramon Santamaria (@raysan5)

								*

								*   Example licensed under an unmodified zlib/libpng license, which is an OSI-certified,

								*   BSD-like license that allows static linking with closed source software

								*

								*   Copyright (c) 2025 JoeCheong (@Joecheong2006)

								*

								********************************************************************************************/


								#include "raylib.h"


								#include <math.h>       // Required for: sin(), cos(), PI


								//----------------------------------------------------------------------------------

								// Macro Helpers

								//----------------------------------------------------------------------------------

								// Constant for Simulation

								#define SIMULATION_STEPS 30

								#define G 9.81


								//----------------------------------------------------------------------------------

								// Module Functions Declaration

								//----------------------------------------------------------------------------------

								static Vector2 CalculatePendulumEndPoint(float l, float theta);

								static Vector2 CalculateDoublePendulumEndPoint(float l1, float theta1, float l2, float theta2);


								//------------------------------------------------------------------------------------

								// Program main entry point

								//------------------------------------------------------------------------------------

								int main(void)

								{

								    // Initialization

								    //--------------------------------------------------------------------------------------

								    const int screenWidth = 800;

								    const int screenHeight = 450;


								    SetConfigFlags(FLAG_WINDOW_HIGHDPI);

								    InitWindow(screenWidth, screenHeight, "raylib [shapes] example - double pendulum");


								    // Simulation Paramters

								    float l1 = 15, m1 = 0.2, theta1 = DEG2RAD*170, w1 = 0;

								    float l2 = 15, m2 = 0.1, theta2 = DEG2RAD*0, w2 = 0;

								    float lengthScaler = 0.1;

								    float totalM = m1 + m2;


								    Vector2 previousPosition = CalculateDoublePendulumEndPoint(l1, theta1, l2, theta2);

								    previousPosition.x += (screenWidth/2);

								    previousPosition.y += (screenHeight/2 - 100);


								    // Scale length

								    float L1 = l1*lengthScaler;

								    float L2 = l2*lengthScaler;


								    // Draw parameters

								    int lineThick = 20, trailThick = 2;

								    float fateAlpha = 0.01;


								    // Create framebuffer

								    RenderTexture2D target = LoadRenderTexture(screenWidth, screenHeight);

								    SetTextureFilter(target.texture, TEXTURE_FILTER_BILINEAR);


								    SetTargetFPS(60);

								    //--------------------------------------------------------------------------------------


								    // Main game loop

								    while (!WindowShouldClose())    // Detect window close button or ESC key

								    {

								        // Update

								        //----------------------------------------------------------------------------------

								        float dt = GetFrameTime();

								        float step = dt/SIMULATION_STEPS, step2 = step*step;


								        // Update Physics - larger steps = better approximation

								        for (int i = 0; i < SIMULATION_STEPS; ++i)

								        {

								            float delta = theta1 - theta2;

								            float sinD = sinf(delta), cosD = cosf(delta), cos2D = cosf(2*delta);

								            float ww1 = w1*w1, ww2 = w2*w2;


								            // Calculate a1

								            float a1 = (-G*(2*m1 + m2)*sinf(theta1)

								                         - m2*G*sinf(theta1 - 2*theta2)

								                         - 2*sinD*m2*(ww2*L2 + ww1*L1*cosD))

								                        /(L1*(2*m1 + m2 - m2*cos2D));


								            // Calculate a2

								            float a2 = (2*sinD*(ww1*L1*totalM

								                         + G*totalM*cosf(theta1)

								                         + ww2*L2*m2*cosD))

								                        /(L2*(2*m1 + m2 - m2*cos2D));


								            // Update thetas

								            theta1 += w1*step + 0.5f*a1*step2;

								            theta2 += w2*step + 0.5f*a2*step2;


								            // Update omegas

								            w1 += a1*step;

								            w2 += a2*step;

								        }


								        // Calculate position

								        Vector2 currentPosition = CalculateDoublePendulumEndPoint(l1, theta1, l2, theta2);

								        currentPosition.x += screenWidth/2;

								        currentPosition.y += screenHeight/2 - 100;


								        // Draw to render texture

								        BeginTextureMode(target);

								            // Draw a transparent rectangle - smaller alpha = longer trails

								            DrawRectangle(0, 0, screenWidth, screenHeight, Fade(BLACK, fateAlpha));


								            // Draw trail

								            DrawCircleV(previousPosition, trailThick, RED);

								            DrawLineEx(previousPosition, currentPosition, trailThick*2, RED);

								        EndTextureMode();


								        // Update previous position

								        previousPosition = currentPosition;

								        //----------------------------------------------------------------------------------


								        // Draw

								        //----------------------------------------------------------------------------------

								        BeginDrawing();


								            ClearBackground(BLACK);


								            // Draw trails texture

								            DrawTextureRec(target.texture, (Rectangle){ 0, 0, target.texture.width, -target.texture.height }, (Vector2){ 0, 0 }, WHITE);


								            // Draw double pendulum

								            DrawRectanglePro((Rectangle){ screenWidth/2, screenHeight/2 - 100, 10*l1, lineThick },

								                (Vector2){0, lineThick*0.5}, 90 - RAD2DEG*theta1, RAYWHITE);


								            Vector2 endpoint1 = CalculatePendulumEndPoint(l1, theta1);

								            DrawRectanglePro((Rectangle){ screenWidth/2 + endpoint1.x, screenHeight/2 - 100 + endpoint1.y, 10*l2, lineThick },

								                (Vector2){0, lineThick*0.5}, 90 - RAD2DEG*theta2, RAYWHITE);


								        EndDrawing();

								        //----------------------------------------------------------------------------------

								    }


								    // De-Initialization

								    //--------------------------------------------------------------------------------------

								    UnloadRenderTexture(target);


								    CloseWindow();        // Close window and OpenGL context

								    //--------------------------------------------------------------------------------------


								    return 0;

								}


								// Calculate Pendulum End Point

								static Vector2 CalculatePendulumEndPoint(float l, float theta)

								{

								    return (Vector2){ 10*l*sin(theta), 10*l*cos(theta) };

								}


								// Calculate Double Pendulum End Point

								static Vector2 CalculateDoublePendulumEndPoint(float l1, float theta1, float l2, float theta2)

								{

								    Vector2 endpoint1 = CalculatePendulumEndPoint(l1, theta1);

								    Vector2 endpoint2 = CalculatePendulumEndPoint(l2, theta2);

								    return (Vector2){ endpoint1.x + endpoint2.x, endpoint1.y + endpoint2.y };

								}