Squish

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Squish Double-Curved Surface

The Squish command flattens a non-developable (curved in two directions) 3-D mesh or NURBS surface into a flat 2‑D pattern.

The Squish command marks areas of compression with a red point cloud and areas of stretching with a green point cloud and displays statistics about the amount of compression or stretch. Up to ten text dots mark the locations with the most dramatic deformation. The number in the text dot is the percentage of change in length.

Report

Area

Change in area from original.

Compression

The material will be compressed when the 2-D pattern is deformed into the 3-D shape. The percentages are an estimate of how much of the pattern will be compressed.

Expansion

The material will be stretched when the 2-D pattern is deformed into the 3-D shape. The percentages are an estimate of how much of the pattern will be stretched.

Command-line options

SplitSeams

Allows a mesh to be split at a seam so it can be flattened. This is good for closed surfaces like cylindrical shapes.

PreserveBoundary

Avoids distorting boundary lengths.

Deformation

Choose an option depending on your bias for stretching or compressing, and the ability to specify custom deformation settings.

Free

No preference for compression or stretching.

StretchMostly

Strong bias for expansion when the pattern is deformed into the 3-D shape.

StretchOnly

Absolutely no compression when the pattern is deformed into the 3-D shape.

CompressMostly

Strong bias for compression when the pattern is deformed into the 3-D shape.

CompressOnly

Absolutely no expansion when the pattern is deformed into the 3-D shape.

CustomA/CustomB/CustomC

Custom deformations.

Lets you set the parameters used by the custom deformations. There are four parameters you can set.

BndStretch

BndCompress

InteriorStretch

InteriorCompress

The default value for these parameters is 1 and they can be set to any positive number. A larger value reduces the amount of the specified deformation compared to what happens when all four parameters are equal. For example, if you want to severely limit interior expansion, you could do something like:

BndStretch=1

BndCompress=1

InteriorStretch=1

InteriorCompress=100

If you want to preserve boundary lengths you could use the settings:

BndStretch=10

BndCompress=10

InteriorStretch=1

InteriorCompress=1

CustomSetup

Specifies settings used by the CustomA/CustomB/CustomC options.

Material

Describes the type of material that will be used for manufacture.

Rigid

Minimizes stresses when forming the 3-D surface from the 2-D pattern when a rigid material will be used for manufacture.

Floppy

Limits geometric distortion as much as possible when a pliable material will be used for manufacture.

Outside

Up

The outside of the 3-D surface is up in the 2-D pattern.

Down

The outside of the 3-D surface is down in the 2-D pattern.

DecorateEdgeLengths

Shows feedback on the diagonals of the squished mesh faces that were added as length constraints in the squish algorithm.

DecorateAreas

Shows how the triangular mesh faces that received an area constraint were deformed in the squish.

Limitations

Does NOT unroll, unfold, or peel.
Does not work great on developable surfaces. Use the UnRollSrf command.

Technical details and caveats

Squish is an algorithm that works on meshes. Squish flattens the mesh by "minimizing the changes in facet area and changes in facet edge lengths" between the 3‑D mesh and the 2‑D mesh, subject to some constraints.

For example, if A,B,C are the corners of a 3‑D triangle and a,b,c are the corresponding corners of the 2‑D triangle, the changes in edge length are

d1 = |Distance(A,B) - Distance(a,b)|

d2 = |Distance(B,C) - Distance(b,c)|

d3 = |DIstance(C,A) - Distance(c,a)|

da = |Area(A,B,C) - area(a,b,c)|

DL = d1+d2+d3

DL2 = d1² + d2² + d3²

DA = da

DA2 = da²

D = some combination of DL, DL2, DA and DA2

The "minimizing the changes in area and or edge lengths" above means create the 2‑D mesh so that "D" is as small as possible.

In practice, there are thousands of facets and many ways to minimize D, most of which don't make practical sense. So Squish constrains the answer to prevent the 2‑D mesh from folding back onto itself and forcing certain 3‑D points end up in specified 2‑D locations.

A trimmed NURBS surface is squished by squishing a dense mesh of the surface.

The squish options determine how DA, DA2, D1 and D2 are combined and allow for more complicated ways to calculate of DA, DA2, D1, and D2 and to allow for a bias towards stretching or compression.

However, the Squish algorithm is much too simple to even begin to model the true physical properties of most materials that come in sheets, particularly those that where material thickness plays a role and those that can compress or stretch any appreciable amount,

In short, if a sheet of material is expensive, cutting it is expensive, or bending it is expensive, or related issues in the manufacturing process are time critical or money critical, then consider using Squish to give you an initial hint about the shape of a pattern, but real material and manufacturing expertise will have to be used to create a pattern that will work on the shop floor.