Count the number of missing landmarks in an array

Description

Count the number of missing landmarks in an array

Usage

countMissing(A)

Arguments

Value

A length n vector giving the number of missing landmarks for each specimen.

Examples

 A <- array(1:(3*6*7), dim = c(7, 3, 6))
 A[2, , 1] <- NA
 countMissing(A)

Calculate covariance matrix between individual landmark coordinates

Description

Calculate covariance matrix between individual landmark coordinates. Skips any missing values in computation of covariance matrix.

Usage

covar(A)

Arguments

Details

This function does not guarantee that the returned matrix is positive definite. If the covariance matrix is not positive definite a warning is given and the matrix can be bent to create the closest positive definite matrix with as.matrix(Matrix::nearPD(mat)$mat).

Value

3N x 3N covariance matrix

Examples

A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) 
A.cov <- covar(A)

Calculate 3D vector correlation matrix using the congruence coefficient. Skips any missing values in computation of correlation matrix

Description

Calculate 3D vector correlation matrix using the congruence coefficient. Skips any missing values in computation of correlation matrix. Gives an N x N correlation matrix.

Usage

dotcorr(A)

Arguments

Value

Correlation matrix

Examples

A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) 
A.corr <- dotcorr(A)

Calculate 2d or 3D covariance matrix using unscaled congruence coefficient. Skips any missing values in computation of covariance matrix

Description

Calculate 2D or 3D covariance matrix using unscaled congruence coefficient. Skips any missing values in computation of covariance matrix

Usage

dotcvm(A)

Arguments

Details

This function does not guarantee that the returned matrix is positive definite. If the covariance matrix is not positive definite a warning is given and the matrix can be bent to create the closest positive definite matrix with as.matrix(Matrix::nearPD(mat)$mat).

Value

N x N covariance matrix

Examples

A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) 
A.cvm <- dotcvm(A)

Fill missing symmetrical landmarks for all specimens in an array using mirrored values from other side of a bilaterally symmetrical object where present

Description

Given an N x 3 x M matrix, where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens, fill in missing landmarks using their mirrored counterpart.

Usage

mirrorfill(A, l1, l2)

Arguments

Details

l2 should be either

• An even length vector containing pairs of landmarks on either side of the specimen. i.e. l2[1] and l2[2] are paired, l2[3] and l2[4] are paired etc.

• A two column matrix with each row giving a pair of symmetrical landmarks.

l2 should be an even number length containing pairs of landmarks on either side of the specimen.

Examples

 # Create array
 A <- array(rep(1:36, by = 4), dim = c(12, 3, 4))

 # Make it symmetrical
 A[7:12, 1:2, ] <- A[1:6, 1:2, ]
 A[7:12, 3, ] <- -A[1:6, 3, ]

 # Remove some data points
 missinga <- A
 missinga[1:2, , 1:3] <- NA

 mirrorA <- mirrorfill(missinga, l1 = c(3:6, 9:12), l2 = c(1, 7, 2, 8))

Fill missing landmarks for a single specimen using mirrored values from other side of object

Description

Given an n x 3 matrix, replace a set of landmarks using their mirrored counterpart.

Usage

mirrorfill1(s, l1, l2)

Arguments

Details

l2 should be either

• An even length vector containing pairs of landmarks on either side of the specimen. i.e. l2[1] and l2[2] are paired, l2[3] and l2[4] are paired etc.

• A two column matrix with each row giving a pair of symmetrical landmarks.

Examples

 # Make data that is reflected in x plane
 s <- matrix(rep(1:21, 2), byrow = TRUE, ncol = 3)
 s[1:7, 1] <- -s[1:7, 1]

 # Now remove some data
 s[1, ] <- NA
 
 # Mirror point 1 using it's complimentary landmark, point 8.
 mirrorS <- mirrorfill1(s, l1 = c(2:7, 9:14), l2 = c(1, 8))

Plot an array of specimen landmark data in an interactive 3D frame

Description

This function requires the rgl package. Given a N x 3 x M array (where M is the number of specimens and N is the number of landmarks), as used elsewhere in this package, plot each specimen in a different colour in an intereactive 3D frame.

Usage

plotSpecimens(A, l1 = NULL, midlineSpecimens = NULL, cols = NULL,
  bySpecimen = TRUE, planeOptions = NULL, ...)

Arguments

See Also

plot3d mirrorfill planes3d rgl.material

Examples

A <- array(rep(rnorm(3 * 20, sd = 30), by = 6) + rnorm(6 * 20 * 3), 
       dim = c(20, 3, 6))
plotSpecimens(A)

plotSpecimens(A, bySpecimen = FALSE)

plotSpecimens(A, cols = grey(seq(0, 1, length.out = 6)))

plotSpecimens(A, l1 = c(1:4), planeOptions = list(alpha = 0.4, color = 'red'))

Conducts Procrustes superimposition to align 3D shapes with or without scaling to centroid size.

Description

Conducts Procrustes superimposition to align 3D shapes with or without scaling to centroid size. Skips any missing values in computation of Procrustes coordinates.

Usage

procrustes(A, scale = TRUE, scaleDelta = FALSE, maxiter = 1000,
  tolerance = 1e-05)

Arguments

Details

A number of computations are run until the difference between two iterations is less than tolerance. The more specimens and landmarks you have, the less each landmark is allowed to move before this tolerance is reached. Setting scaleDelta = TRUE will make the alignment run faster but have potentially less well aligned results. But the alignment between a large and small array of shapes should be more comparable with scaleDelta = TRUE. However, preliminary tests imply that run time scales linearly with scaleDelta set to TRUE or FALSE.

Value

A new (N x 3 x M) array, where each 3d vector has been rotated and translated to minimize distances among specimens, and scaled to unit centroid size if requested.

Examples

# Make an array with 6 specimens and 20 landmarks
A <- array(rep(rnorm(6 * 20, sd = 20), each = 6) + rnorm(20 * 3 * 6 ), 
      dim = c(20, 3, 6))

# Align the data (although it is already largely aligned)
aligned <- procrustes(A)

plotSpecimens(aligned)