4.9 KiB
Wave Overhangs + Heat-2D Integration
Why this belongs here
PrusaSlicer-WaveOverhangs introduces wave-generated toolpaths for unsupported FDM overhangs. The slicer fills unsupported bottom-surface regions with recursively generated wave paths instead of ordinary support material. The algorithm is described as wave-propagation inspired: waves continue until they fill available space and can diffract around corners and holes.
This makes it a natural companion to heat-2D:
wavefront toolpath geometry
-> deposited polymer strand
-> cooling / reheating / contraction
-> warping or stable overhang
heat-2D should not try to reproduce the slicer. Its role is narrower:
Given a wave-overhang toolpath source pattern, estimate the thermal residue field and failure-risk envelope.
Core PDE
The native heat-2D equation is:
\partial_t u = \nabla\cdot(\alpha\nabla u)+f
For wave overhangs:
| Term | Interpretation |
|---|---|
u(x,y,t) |
local thermal state / cooling residue of the overhang layer |
alpha(x,y) |
effective thermal diffusivity of polymer, air gap, perimeter anchor, or fiber-filled material |
f(x,y,t) |
moving deposition source from nozzle path |
| boundary conditions | cooling from air/fan, anchor conduction into perimeter, or imposed bed/chamber temperature |
Toolpath-as-source model
Represent the wave path as a moving heat source:
f(x,y,t)=Q_n\exp\left(-\frac{\|\mathbf{x}-\mathbf{x}_{nozzle}(t)\|^2}{2\sigma_n^2}\right)
where:
| Symbol | Meaning |
|---|---|
Q_n |
deposited thermal source strength |
x_nozzle(t) |
time-parametrized wave toolpath |
sigma_n |
effective bead/nozzle heat radius |
Cooling sink:
f_{cool}(x,y,t)=-h_f(u-u_{air})
Combined:
\partial_t u=\nabla\cdot(\alpha\nabla u)+f_{nozzle}+f_{reheat}+f_{cool}
Warping risk proxies
WaveOverhangs documentation identifies warping as a coupled thermal, mechanical, and process-control problem. This adapter only models the thermal part directly, but it can output risk proxies.
1. Temperature-gradient stress proxy
G_T=\|\nabla u\|
Higher local thermal gradients imply higher differential contraction risk.
2. Reheat activation proxy
R_{reheat}(x,y)=\max_t \mathbf{1}_{u(x,y,t)>T_g}
This estimates where previous strands may re-enter a mobile polymer state.
3. Curl-risk proxy
C_{curl}=w_1\|\nabla u\|+w_2R_{reheat}+w_3t_{hot}-w_4A_{anchor}
where A_anchor measures proximity/connection to perimeter or previously stabilized strand.
4. Span-size risk
C_{span}\propto L_{unsupported}^2
Large unsupported spans amplify nozzle-pressure and contraction risks.
Parameter bridge to slicer settings
| WaveOverhangs setting | Heat-2D proxy |
|---|---|
| line spacing | source-path spacing / wavelength |
| line width | source radius and deposited amount |
| flow ratio | source amplitude Q_n |
| print speed | source dwell time |
| fan speed | cooling coefficient h_f |
| perimeter overlap | anchor conduction / boundary coupling |
| minimum wave width | geometry mask pruning threshold |
| monotonic / zig-zag / smart | source ordering and local reheat history |
Test cases
Test A: single wave stripe
Goal: validate moving-source thermal trail.
Expected:
- smooth trail behind nozzle,
- peak temperature decays after source passes,
- stronger fan coefficient reduces hot lifetime.
Test B: adjacent wave lines
Goal: test line spacing / line width / flow ratio coupling.
Expected:
- tighter spacing increases overlap,
- higher flow ratio increases heat accumulation,
- slower print speed increases local dwell and bonding but may reheat earlier lines.
Test C: monotonic vs zig-zag ordering
Goal: quantify local heat buildup from path ordering.
Expected:
- monotonic gives neighboring lines more cooling time,
- zig-zag lowers travel but can increase local heat accumulation,
- smart ordering should reduce unsupported-start risk, though geometry support is outside pure heat diffusion.
Test D: large unsupported span
Goal: identify when thermal gradients and hot lifetime become too large.
Expected:
- larger spans increase curl-risk proxy,
- uniform two-sided cooling reduces vertical-gradient proxy if modeled with layered extension,
- fiber-filled material proxy should use higher conductivity, lower expansion risk, and higher stiffness in downstream mechanical model.
Scope warning
This is not a full FDM mechanics model. Pure heat-2D does not solve:
- bead sag,
- viscoelastic shape memory,
- nozzle pressure deformation,
- polymer crystallization,
- 3D strand geometry,
- mechanical stress equilibrium.
Correct use:
thermal afterimage and risk proxy generator for wave-overhang toolpaths
Downstream mechanical models should consume the heat-field output rather than be hidden inside this solver.