[examples]: New shapes example - double pendulum

examples/shapes/shapes_double_pendulum.c

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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
+//----------------------------------------------------------------------------------
+#define SCREEN_WIDTH 800
+#define SCREEN_HEIGHT 450
+
+#define CENTER_X SCREEN_WIDTH * 0.5
+#define CENTER_Y SCREEN_HEIGHT * 0.5 - 100
+
+// Constant for Simulation
+#define SIMULATION_STEPS 30
+#define G 9.81
+
+// Helpers for Angles Conversion
+#define RAD(x) x * PI / 180.0
+#define DEG(x) x * 180.0 / PI
+
+#define scalar float
+
+//----------------------------------------------------------------------------------
+// Module Functions Declaration
+//----------------------------------------------------------------------------------
+static Vector2 CalculatePendulumEndPoint(scalar l, scalar theta);
+static Vector2 CalculateDoublePendulumEndPoint(scalar l1, scalar theta1, scalar l2, scalar theta2);
+
+//------------------------------------------------------------------------------------
+// Program main entry point
+//------------------------------------------------------------------------------------
+int main(void)
+{
+    // Initialization
+    //--------------------------------------------------------------------------------------
+	SetConfigFlags(FLAG_WINDOW_HIGHDPI);
+    InitWindow(SCREEN_WIDTH, SCREEN_HEIGHT, "raylib [shapes] example - Double Pendulum");
+
+    // Simulation Paramters
+    //--------------------------------------------------------------------------------------
+    scalar l1 = 15, m1 = 0.2, theta1 = RAD(170), w1 = 0;
+    scalar l2 = 15, m2 = 0.1, theta2 = RAD(0), w2 = 0;
+    scalar lengthScaler = 0.1;
+    scalar totalM = m1 + m2;
+
+    Vector2 previousPosition = CalculateDoublePendulumEndPoint(l1, theta1, l2, theta2);
+    previousPosition.x += CENTER_X;
+    previousPosition.y += CENTER_Y;
+
+    // Scale length
+    scalar L1 = l1 * lengthScaler;
+    scalar L2 = l2 * lengthScaler;
+
+    // Draw Parameters
+    //--------------------------------------------------------------------------------------
+    int lineThick = 20, trailThick = 2;
+    float fateAlpha = 0.01;
+    
+    // Create Framebuffer
+    //--------------------------------------------------------------------------------------
+    RenderTexture2D target = LoadRenderTexture(SCREEN_WIDTH, SCREEN_HEIGHT);
+    SetTextureFilter(target.texture, TEXTURE_FILTER_BILINEAR);
+
+    SetTargetFPS(60);
+    //--------------------------------------------------------------------------------------
+
+    // Main game loop
+    while (!WindowShouldClose())    // Detect window close button or ESC key
+    {
+        // Update
+        scalar dt = GetFrameTime();
+        scalar step = dt / SIMULATION_STEPS, step2 = step * step;
+
+        // Update Physics - larger steps = better approximation
+        //----------------------------------------------------------------------------------
+        for (int i = 0; i < SIMULATION_STEPS; ++i)
+        {
+            scalar delta = theta1 - theta2;
+            scalar sinD = sin(delta), cosD = cos(delta), cos2D = cos(2 * delta);
+            scalar ww1 = w1 * w1, ww2 = w2 * w2;
+
+            // Calculate a1
+            scalar a1 = (-G * (2 * m1 + m2) * sin(theta1) 
+                         - m2 * G * sin(theta1 - 2 * theta2) 
+                         - 2 * sinD * m2 * (ww2 * L2 + ww1 * L1 * cosD))
+                         / (L1 * (2 * m1 + m2 - m2 * cos2D));
+
+            // Calculate a2
+            scalar a2 = (2 * sinD * (ww1 * L1 * totalM
+                         + G * totalM * cos(theta1) 
+                         + ww2 * L2 * m2 * cosD))
+                         / (L2 * (2 * m1 + m2 - m2 * cos2D));
+
+            // Update thetas
+            theta1 += w1 * step + 0.5 * a1 * step2;
+            theta2 += w2 * step + 0.5 * a2 * step2;
+
+            // Update omegas
+            w1 += a1 * step;
+            w2 += a2 * step;
+        }
+        //----------------------------------------------------------------------------------
+
+        // Calculate position
+        Vector2 currentPosition = CalculateDoublePendulumEndPoint(l1, theta1, l2, theta2);
+        currentPosition.x += CENTER_X;
+        currentPosition.y += CENTER_Y;
+
+        // Draw to framebuffer
+        //----------------------------------------------------------------------------------
+        BeginTextureMode(target);
+
+            // Draw a transparent rectangle - smaller alpha = longer trails
+            DrawRectangle(0, 0, SCREEN_WIDTH, SCREEN_HEIGHT, 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){ CENTER_X, CENTER_Y, 10 * l1, lineThick },
+                             (Vector2){0, lineThick * 0.5}, 90 - DEG(theta1), RAYWHITE);
+
+            Vector2 endpoint1 = CalculatePendulumEndPoint(l1, theta1);
+            DrawRectanglePro((Rectangle){ CENTER_X + endpoint1.x, CENTER_Y + endpoint1.y, 10 * l2, lineThick },
+                             (Vector2){0, lineThick * 0.5}, 90 - DEG(theta2), RAYWHITE);
+
+        EndDrawing();
+        //----------------------------------------------------------------------------------
+    }
+
+    // De-Initialization
+    //--------------------------------------------------------------------------------------
+    UnloadRenderTexture(target);
+
+    CloseWindow();        // Close window and OpenGL context
+    //--------------------------------------------------------------------------------------
+
+    return 0;
+}
+
+// Calculate Pendulum End Point
+static Vector2 CalculatePendulumEndPoint(scalar l, scalar theta)
+{
+    return (Vector2){ 10 * l * sin(theta), 10 * l * cos(theta) };
+}
+
+// Calculate Double Pendulum End Point
+static Vector2 CalculateDoublePendulumEndPoint(scalar l1, scalar theta1, scalar l2, scalar theta2)
+{
+    Vector2 endpoint1 = CalculatePendulumEndPoint(l1, theta1);
+    Vector2 endpoint2 = CalculatePendulumEndPoint(l2, theta2);
+    return (Vector2){ endpoint1.x + endpoint2.x, endpoint1.y + endpoint2.y };
+}