# Geomorph 3D Visualization

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Dear geomorph users,

version 2.0 of geomorph brings new developments in how shape deformations from 3D coordinate shape data can be viewed. We have implemented **warping of 3D surface files **(e.g., .ply files), which allows the user to visualize the shape deformations along Principal Component axes, Multivariate Regression slopes, Partial Least Squares axes and group differences, to name a few.

The new function warpRefMesh() reads in a .ply ﬁle and landmark coordinates associated with this specimen, and uses the thin-plate spline method (Bookstein 1989) to warp the mesh into the shape deﬁned by a second set of landmark coordinates, usually

those of the mean shape for a set of aligned specimens.

When using this function for warping, it is highly recommended that the mean shape (derived from the users sample using mshape()) is used as the reference for warping (see Rohlf 1998).

The workﬂow is as follows:

1. Calculate the mean shape using mshape()

2. Choose an actual specimen to use for the warping – the specimen used as the template for this warping is recommended to be one most similar in shape to the average of the sample, but can be any reasonable specimen – do this by eye, or use findMeanSpec()

3. Warp this specimen into the mean shape using warpRefMesh()

4. Use this average mesh where it asks for a mesh= in the analysis functions and visualization functions (plotTangentSpace(), plotAllometry(), bilat.symmetry(), and plotRefToTarget()).

> ref <- mshape(data)

> refmesh <- warpRefMesh("plyfile.ply", data[,,1], ref, color=NULL, centered=T) # here the digitized coordinates for specimen plyfile are the first in the array

warpRefMesh plots the imported mesh (below left) and the new warped mesh that represents the ref shape (mean shape, below right):

The function also returns to object *refmesh* a mesh3d object of this new warped mesh, which can be used in any function in geomorph where mesh= is an option. For example,

> plotTangentSpace(data, axis1 = 1, axis2 = 2, warpgrids=T, mesh= refmesh)

Here, we see that function plotTangentSpace returns the shape deformation matching the most negative and most positive shape along the axis specified in axis1=.

The warping capabilities in *geomorph* are similar to those done using IDAV Landmark (e.g., Drake and Klingenberg 2010), but of course the benefit is that now all your analyses and visualizations can be done in *R*.

Emma

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