CurviSlicer: Slightly curved slicing for 3-axis printers

Jimmy Etienne, et al.

Introduction

Since we don't do a lot of digital fab...

Additive

Subtractive

  • Fused Deposition Modelling (FDM)
  • Stereolithography (SLA)
  • Selective Laser Sintering (SLS)
  • Etc...
  • CNC Milling
  • CNC Lathe
  • Foam Cutting
  • etc...

Computer Numerically Controlled = CNC

FDM Printing

Generally a simple concept, FDM deposits material via CNC machineary

FDM Printing

Generally a simple concept, FDM deposits material via CNC machineary

3D Printing

Anatomy 

3D Printing

Hotend

3D Printing

Slicing

Slightly Curved Slicing

Addresses a weakness of FDM printers

Slightly Curved Slicing

Addresses a weakness of FDM printers

Slightly Curved Slicing

High level approach

Tetrahedralize

Optimization

Toolpath Generation

Post Processing

Slightly Curved Slicing

Tetrahedralization

Provides a means of representing \(\mathcal{M}\)

\(\Omega\) - Mesh

\(\Gamma\) - Tetrahedral mesh (\(\Gamma_I\) inside \(\Gamma_O\) and out)

\(\mathcal{F}\) - Faces on mesh

\(\forall p \in V, \mathcal{M}(p) = h\) (height)

Fabrication Constraints

Layer thickness

Minimum and maximum layer thicknesses

\(\tau_{min} = 0.1d\), \(\tau_{max} =0.75d\)

For 0.4mm nozzle, this gives [0.04mm, 0.3mm], depending on calibration

Fabrication Constraints

Slope

Key Intuition

Slice at \(\tau_{max}\) in \(\mathcal{M}(\Omega)\), optimize \(\mathcal{M}\) to flatten as many faces as possible

Flatten which faces?

\(\overline{\mathcal{F}}\) - other faces

\(\underline{\mathcal{F}}\) - faces to be flattened

Objective Function

Define an energy function to minimize

\(\lambda\)s are user-chosen trade-off parameters

\(h^0=z\)

Objective Function

Define an energy function to minimize

Attempts to pull vertices of a triangle to the same height

Objective Function

Define an energy function to minimize

\(\mathcal{C}(\underline{\mathcal{F}})\) is the set of connected components of the set to flatten

Objective Function

Define an energy function to minimize

Objective Function

Define an energy function to minimize

Attempts to pull vertices of a triangle to the same height

Objective Function

Constraints on optimization

Thickness constraint

\(\forall t\in \Gamma_I\)

Slope constraint

\(\forall t\in \Gamma_I\)

Objective Function

What if flattened surfaces aren't flat?

Objective Function

What if flattened surfaces aren't flat?

Printing

Extrusion rate must be modified in \(\mathcal{T}\), but is available from the gradient of \(\mathcal{M}\)

Results

Results

Results

Results

Error Comparison

CurviSlice

By Joshua Horacsek

CurviSlice

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