Tools for Working with 3D Surface Measurements

The x3p file format is specified in ISO standard 5436:2000 to describe 3d surface measurements. 'x3ptools' allows reading, writing and basic modifications to the 3D surface measurements.

Heike Hofmann, Ganesh Krishnan, Eric Hare March 30, 2018

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x3ptools

Installation

x3ptools is available from CRAN:

install.packages("x3ptools")

The development version is available from Github:

devtools::install_github("heike/x3ptools", build_vignettes = TRUE)

The file format

The x3p file format is an xml based file format created to describe digital surface measurements. x3p has been developed by OpenFMC (Open Forensic Metrology Consortium, see http://www.openfmc.org/) and has been adopted as ISO ISO5436 – 2000. x3p files are a zip archive of a directory consisting of an xml file of meta information and a matrix of numeric surface measurements.

x3p objects

Internally, x3p objects are stored as a list consisting of the surface matrix (the measurements) and meta information in four records: header info, feature info, general info, and matrix info:

library(x3ptools)
logo <- read_x3p(system.file("csafe-logo.x3p", package="x3ptools"))
names(logo)

## [1] "header.info"    "surface.matrix" "feature.info"   "general.info"  
## [5] "matrix.info"

The four info objects specify the information for Record1 through Record4 in the xml file. An example for an xml file is provided with the package and can be accessed as system.file("templateXML.xml", package="x3ptools").

header.info contains the information relevant to interpret locations for the surface matrix:

logo$header.info

## $sizeY
## [1] 419
## 
## $sizeX
## [1] 741
## 
## $incrementY
## [1] 6.45e-07
## 
## $incrementX
## [1] 6.45e-07

matrix.info expands on header.info and provides the link to the surface measurements in binary format.

general.info consists of information on how the data was captured, i.e. both author and capturing device are specified here.

feature.info is informed by the header info and provides the structure for storing the information.

While these pieces can be changed and adapted manually, it is more convenient to save information on the capturing device and the creator in a separate template and bind measurements and meta information together in the command addtemplate_x3p.

Reading and writing x3p files

read_x3p and write_x3p are the two functions allows us to read x3p files and write to x3p files.

logo <- read_x3p(system.file("csafe-logo.x3p", package="x3ptools"))
names(logo)

## [1] "header.info"    "surface.matrix" "feature.info"   "general.info"  
## [5] "matrix.info"

Usage

Visualizing x3p objects

The function image_x3p uses rgl to render a 3d object in a separate window. The user can then interact with the 3d surface (zoom and rotate). In case a file name is specified in the function call the resulting surface is saved in a file (the extension determines the actual file format of the image).

image_x3p(logo, file=NULL)

Casting between data types

The functions x3p_to_df and df_to_x3p allow casting between an x3p format and an x-y-z data set:

logo_df <- x3p_to_df(logo)
head(logo_df)

##           x          y value
## 1 0.000e+00 0.00026961 4e-07
## 2 6.450e-07 0.00026961 4e-07
## 3 1.290e-06 0.00026961 4e-07
## 4 1.935e-06 0.00026961 4e-07
## 5 2.580e-06 0.00026961 4e-07
## 6 3.225e-06 0.00026961 4e-07

When converting from the x3p format to a data frame, the values from the surface matrix are interpreted as heights (saved as value) on an x-y grid. The dimension of the matrix sets the number of different x and y levels, the information in header.info allows us to scale the levels to the measured quantities. Similarly, when moving from a data frame to a surface matrix, the assumption is that measurements are taken on an equi-spaced and complete grid of x-y values. The information on the resolution (i.e. the spacing between consecutive x and y locations) is saved in form of the header info, which is added to the list. General info and feature info can not be extracted from the measurements, but have to be recorded with other means.

Once data is in a regular data frame, we can use our regular means to visualize these raster images, e.g. using ggplot2:

library(ggplot2)
logo_df %>% ggplot(aes( x= x, y=y, fill= value)) +
  geom_tile() +
  scale_fill_gradient2(midpoint=4e-7)

Elementary operations

Rotation and Transposition

rotate_x3p rotates an x3p image in steps of 90 degrees, transpose_x3p transposes the surface matrix of an image and updates the corresponding meta information. The function y_flip_x3p is a combination of transpose and rotation, that allows to flip the direction of the y axis to move easily from legacy ISO x3p scans to ones conforming to the most recent ISO standard.

Sampling

sample_x3p allows to sub-sample an x3p object to get a lower resolution image. In sample_x3p we need to set a sampling factor. A sample factor m of 2 means that we only use every 2nd value of the surface matrix, m of 5 means, we only use every fifth value:

dim(logo$surface.matrix)

## [1] 741 419

logo_sample <- sample_x3p(logo, m=5)
dim(logo_sample$surface.matrix)

## [1] 149  84

Interpolation

interpolate_x3p allows, like sample_x3p, to create a new x3p file at a new resolution, as specified in the parameters resx and resy. The new resolution should be lower (i.e. larger values for resx and resy) than the resolution specified as IncrementX and IncrementY in the header info of the x3p file. interpolate_x3p can also be used to interpolate missing values (set parameter maxgap according to specifications in zoo::na.approx).