{"id":14,"date":"2025-06-27T13:12:21","date_gmt":"2025-06-27T13:12:21","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/e252216\/?p=14"},"modified":"2025-06-27T13:18:11","modified_gmt":"2025-06-27T13:18:11","slug":"rope-simulation-with-position-based-dynamics","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/e252216\/2025\/06\/27\/rope-simulation-with-position-based-dynamics\/","title":{"rendered":"Rope Simulation with Position Based Dynamics"},"content":{"rendered":"

This post explains how a simple rope simulator works using OpenGL, Position-Based Dynamics (PBD), and compute shaders. The project is written in C++ and runs completely on the GPU.<\/p>\n

The goal is to simulate a rope that reacts to forces like gravity, stretches under tension, and can break when pulled too far.<\/p>\n

Features<\/h2>\n\n\n\n\n\n\n\n\n\n\n
Feature<\/th>\nIncluded<\/th>\n<\/tr>\n
Position-Based Dynamics<\/td>\nYes<\/td>\n<\/tr>\n
Compute Shader Acceleration<\/td>\nYes<\/td>\n<\/tr>\n
Object Dragging\/Interaction<\/td>\nNo<\/td>\n<\/tr>\n
Rope Breaking<\/td>\nYes<\/td>\n<\/tr>\n
Simple Demo<\/td>\nYes<\/td>\n<\/tr>\n
Tension Visualization<\/td>\nYes<\/td>\n<\/tr>\n
Advanced Demo (Raylib Integration)<\/td>\nNo<\/td>\n<\/tr>\n
Multiple Rope Interaction<\/td>\nNo<\/td>\n<\/tr>\n<\/table>\n

What is Position-Based Dynamics?<\/h2>\n

Position-Based Dynamics (PBD) is a method for simulating soft bodies. Instead of using forces and solving for acceleration, PBD directly updates positions to meet certain constraints.<\/p>\n

In this case, each rope segment is a constraint that tries to keep a fixed distance between two particles.<\/p>\n

struct Particle {\r\n  glm::vec4 pos;   \/\/ xyz = position, w = mass\r\n  glm::vec4 prev;  \/\/ previous position\r\n};\r\n<\/code><\/pre>\n
Compute Shaders<\/h2>\n
This project uses OpenGL compute shaders to run both the simulation and constraint solving on the GPU. There are two main compute shaders:<\/p>\n
Integration Shader<\/h3>\n
vec3 velocity = p.position.xyz - p.prevPosition.xyz;\r\nvec3 newPos = p.position.xyz + velocity + gravity * dt * dt;\r\n<\/code><\/pre>\n
If a particle is selected and dragging is enabled, its position is fixed to the mouse.<\/p>\n
Constraint Solver Shader<\/h3>\n
if (dist > segmentLength * breakThreshold) {\r\n    pairs[id] = ivec2(-1, -1); \/\/ mark as broken\r\n}\r\n<\/code><\/pre>\n
Rope Breaking<\/h2>\n
When the distance between two connected particles becomes too long, the rope segment breaks.<\/p>\n
The break condition is:<\/p>\n
#define BREAK_THRESHOLD 1.5f\r\n<\/code><\/pre>\n
If the distance becomes more than 1.5 times the original length, the connection is removed.<\/p>\n
Rendering with Geometry Shader<\/h2>\n
The rope is drawn using a geometry shader that creates a thick colored line from each segment. The color depends on how much tension the segment is under.<\/p>\n
float tension = abs(dist - segmentLength) \/ segmentLength * tensionScale;\r\nfColor = mix(blue, red, tension);\r\n<\/code><\/pre>\n
    \n
  • Blue = low tension<\/li>\n
  • Red = high tension<\/li>\n<\/ul>\n
    Interaction<\/h2>\n
    The program lets you interact with the rope through the keyboard:<\/p>\n
      \n
    • J<\/code> \/ K<\/code> \u2013 Move selection to next\/previous particle<\/li>\n
    • W<\/code> \/ S<\/code> \u2013 Increase or decrease mass<\/li>\n
    • P<\/code> \u2013 Pin or unpin the selected particle<\/li>\n
    • Space<\/code> \u2013 Toggle dragging (not fully implemented)<\/li>\n<\/ul>\n
      Dragging with the mouse is not finished, but the selected particle is highlighted.<\/p>\n
      Updating Rope Segments<\/h2>\n
      When a segment breaks, the rope structure changes. The program updates the index buffer to reflect these changes and re-renders only the connected parts.<\/p>\n
      How It Works<\/h2>\n
        \n
      1. A number of particles are initialized in a straight line.<\/li>\n
      2. Constraints are added between each pair of particles.<\/li>\n
      3. On each frame:\n
          \n
        • The compute shader updates particle positions.<\/li>\n
        • The constraint shader corrects distances and breaks segments if needed.<\/li>\n
        • The index buffer is rebuilt to reflect which segments are still connected.<\/li>\n<\/ul>\n<\/li>\n
        • The rope is rendered using geometry and fragment shaders.<\/li>\n<\/ol>\n