Soft Body Sim

A ring of point masses, every pair joined by a damped spring, that falls and slumps onto the floor in Pygame.

About

A 2D soft-body experiment written from scratch, vector class included. The body is a ring of 30 point masses placed in polar coordinates, and every pair of points, not only neighbours, is joined by a damped spring: 435 springs in all. The ring drops under gravity, lands on a floor and slumps into a dome under its own weight. Only the outline is drawn. As a first step towards collisions between bodies, the outline edges crossed by a horizontal ray from the mouse cursor turn red, which is the crossing test behind point-in-polygon checks.

Quick start

python -m pip install -r requirements.txt
python SoftBody.py

Controls

Input	Action
Move the mouse	Edges crossed by the ray to the right of the cursor turn red
Close the window	Quit

How it works

• Building the body. softBodyPolar takes (angle, radius) pairs and places each point at $(r\cos\theta,\ r\sin\theta)$ around the centre $(700, 400)$, here 30 points at radius 100. softBody then joins every pair with a springJoint whose rest length $L_0$ is the starting distance, so the $\binom{30}{2} = 435$ springs act as an internal scaffold that resists both stretching and shearing.

• Spring force. With $\mathbf d = \mathbf x_1 - \mathbf x_2$, Hooke's law along the spring plus damping on the relative velocity along it:

  \mathbf F_1 = k\,\bigl(L_0 - \lVert \mathbf d \rVert\bigr)\,\hat{\mathbf d} \;-\; c\,\bigl(\mathbf d \cdot (\mathbf v_1 - \mathbf v_2)\bigr)\,\hat{\mathbf d},
  \qquad \mathbf F_2 = -\mathbf F_1
  

  with $k = 1$ and $c = 0.01$. The damping term uses $\mathbf d$ rather than $\hat{\mathbf d}$, so it also grows with the spring's length.

• Integration. Each point adds its weight $(0,,-9.8,m)$ to the spring forces and uses the sum directly as its acceleration. It then steps with semi-implicit Euler, where $\Delta t$ is the real time since the previous frame:

  \mathbf v \leftarrow \mathbf v + \mathbf F\,\Delta t,\qquad \mathbf x \leftarrow \mathbf x + \mathbf v\,\Delta t
  

  The springs compute their forces after the points have moved, so those forces act on the next frame.

• Floor. The physics uses $y$ pointing up and the drawing flips it. A point that goes below $y = 10$ is put back at 10 and loses its vertical velocity, so nothing bounces. In a test run with a fixed 1/60 s step the 200 px ring touched the floor after about 2.4 seconds and settled about 167 px tall and 208 px wide.

• Ray-cast edge test. segmentCollideSemirrect ("segment meets half-line") intersects the line through an edge with the horizontal half-line running right from a point, and accepts the crossing only if the point's height lies strictly between the edge's endpoints. Counting the crossings gives the even-odd rule: an odd count means the point is inside the outline. draw applies it to the mouse position; update already counts crossings for the points of other soft bodies but does nothing with the count yet.

Code map

Path	Role
SoftBody.py	Main version: the 30-point ring, outline drawing, the mouse ray test and the unfinished body-to-body crossing count
SoftBodyCollisions.py	Earlier, simpler variant despite its name: no collision code, an 8-point ring with $k = 10$ and all 28 springs drawn as a mesh

Limitations

• There is only one body and no collisions apart from the floor: bodies cannot touch each other yet, and nothing stops points at the sides of the window.
• Mass only scales the weight. Forces are not divided by mass, so a heavier point is pulled down harder but is no harder to accelerate.
• $\Delta t$ is the wall-clock frame time in an uncapped loop. The first step also includes the window start-up time, and a stiffer $k$ or a stall can make the integration unstable.
• The ray test divides by zero if an outline edge ever becomes exactly vertical.
• The body is drawn twice every frame, which is harmless but wasted work.

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_{Part of lnivan's projects · Simulations}