The bridge between deterministic math and physical ink on paper.
Our engine simulates three distinct mechanical systems known for their continuous-path aestheticāessential for avoiding pen-up/pen-down mechanical wear.
Simulates multiple pendulums acting on a single pen. Features frequency-coupled harmonic ratios (1:1, 2:3, etc.) and exponential decay curves.
x = Ī£ A*exp(-d*t)*sin(t*f+p)
Mathematical simulation of Hypotrochoids and Epitrochoids. We use GCD logic to ensure loops close perfectly without point overlap.
x = (R-r)cos(t) + d*cos((R-r)/r * t)
A 4-bar linkage system simulation. Uses inverse kinematics to calculate the intersection of two oscillating physical arms.
Inverse Kinematics / Mechanical Linkage
Built for users of AxiDraw, iDraw, and DIY pen plotters who require production-ready SVG files.
| Feature | Technical Implementation | Benefit for Artist |
|---|---|---|
| RDP Path Simplification | RamerāDouglasāPeucker algorithm with variable Īµ (epsilon) sampling. | Reduces vertex count by 40-70%. Prevents plotter "jitter" and reduces file size. |
| Physical Scale Precision | SVG 1.1 metric headers (mm units) mapped to internal pixel coordinates. | Outputs files at exact A4, A3, or Letter scale. Open and plotāno resizing needed. |
| Multi-Pen Layering | Temporal path splitting into SVG <g id="Pen_1"> groups. |
Assign different segments of the path to different ink colors. |
| Hidden Line Removal | 3D Z-Depth occlusion clipping and discontinuous path generation. | Creates a 3D effect. The pen lifts when a line goes "under" another ornament. |
| Pen Weight Simulation | Resolution-aware stroke rendering (mm to Pixel conversion). | Visualize ink bleed. See exactly how a 0.5mm pen will look on an A4 page. |
The engine generates a highly optimized .svg file compatible with all major plotting
software (Inkscape, LightBurn, AxiDraw Control):