Ragdoll Physics

A 2D stick-figure ragdoll made of seven point masses, rigid sticks and damped springs, stepped with position Verlet.

About

An interactive ragdoll written from scratch. NumPy does the physics, and Pygame only opens the window, reads input and draws circles and lines. The figure has seven point masses: head, chest, hip, two hands and two feet. Rigid sticks form the trunk and limbs, and six invisible spring-dampers brace the hands and feet so it can stand on its own. Gravity (on every point except the head), air drag and a floor with friction act on the body. You can pick the figure up by the chest, drop or fling it, push it sideways and make it jump.

Quick start

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

Controls

Input	Action
Hold any mouse button	Grab the chest: it snaps to the cursor and follows it, with gravity off
Release the button	Drop the figure; it keeps the motion of the last drag step
A / D (hold)	Push every point left / right at 10 units/s²
Space	Jump: every point gets 2500 units/s² upwards for one step, and the console prints Salto ("jump")
Close the window	Quit

How it works

• World and camera. Positions are in world units with y pointing up. The camera draws 50 px per unit, so the 800 × 600 window shows 16 × 12 units, and the floor $y = 0$ is the bottom edge.

• Position Verlet. Each point stores its current and previous position, and every frame advances a fixed $\Delta t = 0.002$ s. Velocity is never integrated; it is read back from the positions:

  \mathbf r_{n+1} = 2\mathbf r_n - \mathbf r_{n-1} + \frac{\mathbf F}{m}\,\Delta t^2,\qquad \mathbf v = \frac{\mathbf r_{n+1} - \mathbf r_n}{\Delta t}
  

• Forces. Gravity $-mg\hat{\mathbf y}$ with $g = 9.81$ acts on every point except the head, which is created with gravity off. Linear air drag is $-0.7\mathbf v$. A spring-damper between points 1 and 2 acts along $\mathbf d = \mathbf r_2 - \mathbf r_1$, combining Hooke's law with a damper on the relative velocity:

  \mathbf F_1 = \Bigl[k\bigl(\lVert\mathbf d\rVert - L\bigr) + c\,(\mathbf v_2 - \mathbf v_1)\cdot\hat{\mathbf d}\Bigr]\,\hat{\mathbf d},\qquad \mathbf F_2 = -\mathbf F_1
  

• Rigid sticks. A fixed-length joint is a position correction, not a force. Each step, after the forces are summed, every stick moves its two ends along $\hat{\mathbf d}$ until they are $L$ apart again. Each end's share is set by its inverse mass $w_i = 1/m_i$, so the lighter end moves more:

  \delta = L - \lVert\mathbf d\rVert,\qquad \mathbf r_1 \leftarrow \mathbf r_1 - \frac{w_1}{w_1 + w_2}\,\delta\,\hat{\mathbf d},\qquad \mathbf r_2 \leftarrow \mathbf r_2 + \frac{w_2}{w_1 + w_2}\,\delta\,\hat{\mathbf d}
  

  Because Verlet reads velocity from positions, the correction also changes the velocities, so no separate impulse is needed.

• Body plan. There are seven sticks, and five of them are drawn. The six hidden spring-dampers join hand to foot, hand to hand, foot to foot and the chest to each foot, with $k$ from 50 to 10 000 and $c$ from 25 to 150.

• Floor. A point that goes below $y = 0$ is put back on it and its vertical motion is cancelled. On the next step it also gets a sliding-friction force $-10 m v_x$.

• Dragging. While a button is held, the chest's position is overwritten with the cursor's world position every frame. Verlet turns that displacement into velocity, so letting go during a quick drag throws the figure.

Code map

Path	Role
main.py	Builds the figure from points, sticks and spring-dampers, reads input and runs the loop
fisica.py	Physics (fisica): Physics_System with its Point, Spring, Damper, Spring_Damper_Joint and Fixed_Joint classes
draw.py	Drawer: world-to-screen transform, points as circles and joints as lines

Limitations

• Each frame advances the simulation by a fixed 0.002 s and then sleeps 2 ms, with no clock, so the speed depends on the machine.
• The floor is the only obstacle. There are no walls, so a hard throw sends the figure off screen, where it stays unless A / D push it back. Body parts pass through each other.
• Each stick is corrected once per step, with no repeated passes, so the sticks are only approximately rigid. In a headless test they stretched by about 10 % on the first landing, and far more while the chest was dragged quickly.
• On release the code sets the chest's velocity from pygame.mouse.get_rel(), but Verlet recomputes it on the next step, so that value only feeds one step of drag and damping.
• The figure, masses and stiffnesses are hard-coded in main.py, which also keeps two alternative bracing setups as commented-out blocks.

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_{Part of lnivan's projects · Simulations}