Concept 1: Beckham Model + Real Kick
Desmos 3D model above; edited Beckham video directly below.
Desmos 3D model
Real kick reference
Explore a Bending Free Kick
The first window pairs a model with a real video. The second window is a test lab: choose a preset, press play, then tweak the launch and spin controls inside Desmos.
Concept 2: Build Your Own Free Kick
Pick a preset, press play, then adjust the vectors to see how the path changes.
Clean bending goal. Use the sliders below to tweak the shot, then press Play.
Purple = initial velocity.
Orange = spin axis. Presets are starting points; the sliders above send values directly into Desmos.
Loading interactive free kick model...
Interactive free-kick challenge
Concept 3: Famous Free Kick Gallery
Placeholder for toggling among Beckham, Roberto Carlos, and another famous free kick.
Later this window can hold the selector for multiple famous kicks, with short descriptions and links to the tuned Desmos/video pairs.
Coming next: famous kick presets.
Famous kick presets
Future buttons: Beckham, Roberto Carlos, knuckleball / third kick.
Concept 4: Views, Forces, and Details
Placeholder for top view, side view, spin-axis visualization, and force diagrams.
This window can later explain the interactive model: top-down curl, side-view height, spin-axis orientation, and the force vectors acting on the ball.
Coming next: model details and supporting views.
Model details placeholder
Future views: top view, side view, spin indicator, force diagram, and parameter summary.
Where It Started
Arjav began with the question of how a soccer ball curves through the air. His prototype framed the project around famous free kicks, video references, and adjustable physical parameters.
Going Further
Next steps include adding more famous kicks, improving the numerical method, refining the net/goal visuals, and comparing the model with real shots and player feedback.