Foundations of simulating physical phenomena

Imagine a virtual solar system in 3D.

This is how my simulation operates:

[Calculate new positions] -> [Render] -> [Calculate new positions] -> [Render] etc....

The loop maintains a steady pace of 25 frames per second.

One of the planets in my simulation is hurtling towards the sun at high speed, almost on a collision course. Let's dive into the details of the simulation loop:

  1. Positions are calculated for the planet and the sun (they have not collided yet, but are dangerously close).
  2. The scene is rendered.
  3. Due to finite FPS, there is a slight pause before the next calculation.
  4. New positions are calculated for the planet and sun - and here lies the issue - they did not collide because during the 'pause,' the planet passed through the sun and now their positions are significantly far apart. The collision detection algorithm fails to register any collision.

Here are some possible solutions that I'm considering:

  • Increase the FPS
  • Decrease the speeds of the planets (reduce gravitational constant maybe?)
  • Implement a separate simulation loop that runs concurrently with the rendering loop, but at a faster rate

For those curious, I am utilizing three.js.

javascriptthree.jssimulationphysicsgame-physics

Answer №1

In shooter games, dealing with projectiles can be tricky. One workaround is to have the movement stage project a line segment ahead to detect potential collisions before the next frame update. This approach assumes only one object is moving quickly. Alternatively, you could trace a segment between the previous and current positions, although I personally haven't tried this method. Another effective strategy is extending the collider definition forward into an elliptical shape to cover any uncovered areas.

Answer №2

To determine the potential collision of two objects, analyze the change in angle between them. If this change is close to 180 degrees or pi radians, a collision is likely. Utilize linear algebra concepts, specifically the dot product method, to calculate this change:

dx0 = object[i].x - object[j].x;
dy0 = object[i].y - object[j].y;
dz0 = object[i].z - object[j].z;
dx1 = object[i].x + timeStep * object[i].u - object[j].x - timeStep * object[j].u;
dy1 = object[i].y + timeStep * object[i].v - object[j].y - timeStep * object[j].v;
dz1 = object[i].z + timeStep * object[i].w - object[j].z - timeStep * object[j].w;
dangle = acos((dx0 * dx1 + dy0 * dy1 + dz0 * dz1) / (sqrt(dx0 * dx0 + dy0 * dy0 + dz0 * dz0) * sqrt(dx1 * dx1 + dy1 * dy1 + dz1 * dz1)));

Avoid calculating the arc cosine as cos(dangle) approaching -1 indicates a near-180 degree change.

It's vital to experiment with different values to accurately detect collisions. This method should not be the only one used; consider accounting for the objects' constant speed and linear movement during the timestep. Solving a quadratic equation will reveal potential collision times, although it might return more than one solution. To simplify, use the discriminant to confirm a possible collision without pinpointing the exact timing.

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