Package 'ETRep' reference manual

Title:	Analysis of Elliptical Tubes Under the Relative Curvature Condition
Description:	Analysis of elliptical tubes with applications in biological modeling. The package is based on the references: Taheri, M., Pizer, S. M., & Schulz, J. (2024) "The Mean Shape under the Relative Curvature Condition." arXiv <doi:10.48550/arXiv.2404.01043>. Mohsen Taheri Shalmani (2024) "Shape Statistics via Skeletal Structures", PhD Thesis, University of Stavanger, Norway <doi:10.13140/RG.2.2.34500.23685>. Key features include constructing discrete elliptical tubes, calculating transformations, validating structures under the Relative Curvature Condition (RCC), computing means, and generating simulations. Supports intrinsic and non-intrinsic mean calculations and transformations, size estimation, plotting, and random sample generation based on a reference tube. The intrinsic approach relies on the interior path of the original non-convex space, incorporating the RCC, while the non-intrinsic approach uses a basic robotic arm transformation that disregards the RCC.
Authors:	Mohsen Taheri Shalmani [aut, cre] , Jörn Schulz [aut], Stephen M. Pizer [aut]
Maintainer:	Mohsen Taheri Shalmani <[email protected]>
License:	MIT + file LICENSE
Version:	1.1.0
Built:	2024-12-05 15:03:07 UTC
Source:	CRAN

Check the Legality of an Elliptical Tube (ETRep)

Description

Checks the validity of a given ETRep based on the Relative Curvature Condition (RCC) and principal radii such that forall i a_i>b_i.

Usage

check_Tube_Legality(tube)
check_Tube_Legality(tube)

Arguments

tube

List containing ETRep details.

Value

Logical value: TRUE if valid, FALSE otherwise.

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples

# Load tube
data("colon3D")
check_Tube_Legality(tube = colon3D)
# Load tube
data("colon3D")
check_Tube_Legality(tube = colon3D)

Data

Description

A colon sample as an elliptical tube.

Usage

colon3D
colon3D

Format

A list containing the information of an e-tube

Source

Generated and stored in the package's 'data/' folder.

Create a Discrete Elliptical Tube (ETRep)

Description

Constructs a discrete elliptical tube (ETRep) based on specified parameters.

Usage

create_Elliptical_Tube(
  numberOfFrames,
  method,
  materialFramesBasedOnParents = NA,
  initialFrame = diag(3),
  initialPoint = c(0, 0, 0),
  EulerAngles_Matrix = NA,
  ellipseResolution = 10,
  ellipseRadii_a,
  ellipseRadii_b,
  connectionsLengths,
  plotting = TRUE,
  add = FALSE
)
create_Elliptical_Tube(
  numberOfFrames,
  method,
  materialFramesBasedOnParents = NA,
  initialFrame = diag(3),
  initialPoint = c(0, 0, 0),
  EulerAngles_Matrix = NA,
  ellipseResolution = 10,
  ellipseRadii_a,
  ellipseRadii_b,
  connectionsLengths,
  plotting = TRUE,
  add = FALSE
)

Arguments

`numberOfFrames`	Integer, specifies the number of consecutive material frames.
`method`	String, either "basedOnEulerAngles" or "basedOnMaterialFrames", defines the material frames method.
`materialFramesBasedOnParents`	Array (3 x 3 x numberOfFrames) with pre-defined material frames.
`initialFrame`	Matrix 3 x 3 as the initial frame
`initialPoint`	Real vector with three elemets as the initial point
`EulerAngles_Matrix`	Matrix of dimensions numberOfFrames x 3 with Euler angles to define material frames.
`ellipseResolution`	Integer, resolution of elliptical cross-sections (default is 10).
`ellipseRadii_a`	Numeric vector for the primary radii of cross-sections.
`ellipseRadii_b`	Numeric vector for the secondary radii of cross-sections.
`connectionsLengths`	Numeric vector for lengths of spinal connection vectors.
`plotting`	Logical, enables plotting of the ETRep (default is TRUE).
`add`	Logical, enables overlay plotting

Value

List containing tube details (orientation, radii, connection lengths, boundary points, etc.).

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples

numberOfFrames<-15
EulerAngles_alpha<-c(rep(0,numberOfFrames))
EulerAngles_beta<-c(rep(-pi/20,numberOfFrames))
EulerAngles_gamma<-c(rep(0,numberOfFrames))
EulerAngles_Matrix<-cbind(EulerAngles_alpha,
                          EulerAngles_beta,
                          EulerAngles_gamma)
tube <- create_Elliptical_Tube(numberOfFrames = numberOfFrames,
                               method = "basedOnEulerAngles",
                               EulerAngles_Matrix = EulerAngles_Matrix,
                               ellipseResolution = 10,
                               ellipseRadii_a = rep(3, numberOfFrames),
                               ellipseRadii_b = rep(2, numberOfFrames),
                               connectionsLengths = rep(4, numberOfFrames),
                               plotting = FALSE)
 # Plotting
 plot_Elliptical_Tube(tube = tube,plot_frames = FALSE,
                      plot_skeletal_sheet = TRUE,
                      plot_r_project = FALSE,
                      plot_r_max = FALSE,add = FALSE)
numberOfFrames<-15
EulerAngles_alpha<-c(rep(0,numberOfFrames))
EulerAngles_beta<-c(rep(-pi/20,numberOfFrames))
EulerAngles_gamma<-c(rep(0,numberOfFrames))
EulerAngles_Matrix<-cbind(EulerAngles_alpha,
                          EulerAngles_beta,
                          EulerAngles_gamma)
tube <- create_Elliptical_Tube(numberOfFrames = numberOfFrames,
                               method = "basedOnEulerAngles",
                               EulerAngles_Matrix = EulerAngles_Matrix,
                               ellipseResolution = 10,
                               ellipseRadii_a = rep(3, numberOfFrames),
                               ellipseRadii_b = rep(2, numberOfFrames),
                               connectionsLengths = rep(4, numberOfFrames),
                               plotting = FALSE)
 # Plotting
 plot_Elliptical_Tube(tube = tube,plot_frames = FALSE,
                      plot_skeletal_sheet = TRUE,
                      plot_r_project = FALSE,
                      plot_r_max = FALSE,add = FALSE)

Convert an ETRep to a Matrix in the Convex Transformed Space.

Description

Convert an ETRep to a Matrix in the Convex Transformed Space.

Usage

elliptical_Tube_Euclideanization(tube)
elliptical_Tube_Euclideanization(tube)

Arguments

tube

A list containing the details of the ETRep.

Value

An n*6 matrix, where n is the number of spinal points, representing the ETRep in the transformed Euclidean convex space.

Examples

#Example
# Load tube
data("tube_A")
Euclideanized_Tube<- elliptical_Tube_Euclideanization(tube = tube_A)

#Example
# Load tube
data("tube_A")
Euclideanized_Tube<- elliptical_Tube_Euclideanization(tube = tube_A)

Calculating the intrinsic distance between two ETReps

Description

Calculating the intrinsic distance between two ETReps

Usage

intrinsic_Distance_Between2tubes(tube1, tube2)
intrinsic_Distance_Between2tubes(tube1, tube2)

Arguments

`tube1`	List containing ETRep details.
`tube2`	List containing ETRep details.

Value

Numeric

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples

# Load tubes
data("tube_A")
data("tube_B")
intrinsic_Distance_Between2tubes(tube1 = tube_A,tube2 = tube_B)
# Load tubes
data("tube_A")
data("tube_B")
intrinsic_Distance_Between2tubes(tube1 = tube_A,tube2 = tube_B)

Calculate Intrinsic Mean of ETReps

Description

Computes the intrinsic mean of a set of ETReps. The computation involves transforming the non-convex hypertrumpet space into a convex space, calculating the mean in this transformed space, and mapping the result back to the original hypertrumpet space.

Usage

intrinsic_mean_tube(tubes, type = "sizeAndShapeAnalysis", plotting = TRUE)
intrinsic_mean_tube(tubes, type = "sizeAndShapeAnalysis", plotting = TRUE)

Arguments

`tubes`	List of ETReps.
`type`	String, "ShapeAnalysis" or "sizeAndShapeAnalysis" (default is "sizeAndShapeAnalysis").
`plotting`	Logical, enables visualization of the mean (default is TRUE).

Value

List representing the mean ETRep.

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples

#Example 1
# Load tubes
data("tube_A")
data("tube_B")
intrinsic_mean<-
  intrinsic_mean_tube(tubes = list(tube_A,tube_B),
                      plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = intrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)

#Example 2
data("simulatedColons")
intrinsic_mean<-
  intrinsic_mean_tube(tubes = simulatedColons,
                      plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = intrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)
#Example 1
# Load tubes
data("tube_A")
data("tube_B")
intrinsic_mean<-
  intrinsic_mean_tube(tubes = list(tube_A,tube_B),
                      plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = intrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)

#Example 2
data("simulatedColons")
intrinsic_mean<-
  intrinsic_mean_tube(tubes = simulatedColons,
                      plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = intrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)

Intrinsic Transformation Between Two ETReps

Description

Performs an intrinsic transformation from one ETRep to another, preserving essential e-tube properties such as the Relative Curvature Condition (RCC) while avoiding local self-intersections.

Usage

intrinsic_Transformation_Elliptical_Tubes(
  tube1,
  tube2,
  type = "sizeAndShapeAnalysis",
  numberOfSteps = 5,
  plotting = TRUE,
  colorBoundary = "blue"
)
intrinsic_Transformation_Elliptical_Tubes(
  tube1,
  tube2,
  type = "sizeAndShapeAnalysis",
  numberOfSteps = 5,
  plotting = TRUE,
  colorBoundary = "blue"
)

Arguments

`tube1`	List containing details of the first ETRep.
`tube2`	List containing details of the second ETRep.
`type`	String defining the type of analysis as sizeAndShapeAnalysis or shapeAnalysis
`numberOfSteps`	Integer, number of transformation steps.
`plotting`	Logical, enables visualization during transformation (default is TRUE).
`colorBoundary`	String defining the color of the e-tube

Value

List containing intermediate ETReps.

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples


# Load tubes
data("tube_A")
data("tube_B")
numberOfSteps <- 10
transformation_Tubes<-
  intrinsic_Transformation_Elliptical_Tubes(
    tube1 = tube_A,tube2 = tube_B,
    numberOfSteps = numberOfSteps,
    plotting = FALSE)
# Plotting
for (i in 1:length(transformation_Tubes)) {
  plot_Elliptical_Tube(tube = transformation_Tubes[[i]],
  plot_frames = FALSE,plot_skeletal_sheet = FALSE
  ,plot_r_project = FALSE,
  plot_r_max = FALSE,
  add = FALSE)
}

# Load tubes
data("tube_A")
data("tube_B")
numberOfSteps <- 10
transformation_Tubes<-
  intrinsic_Transformation_Elliptical_Tubes(
    tube1 = tube_A,tube2 = tube_B,
    numberOfSteps = numberOfSteps,
    plotting = FALSE)
# Plotting
for (i in 1:length(transformation_Tubes)) {
  plot_Elliptical_Tube(tube = transformation_Tubes[[i]],
  plot_frames = FALSE,plot_skeletal_sheet = FALSE
  ,plot_r_project = FALSE,
  plot_r_max = FALSE,
  add = FALSE)
}

Calculating the non-intrinsic distance between two ETReps

Description

Calculating the non-intrinsic distance between two ETReps

Usage

nonIntrinsic_Distance_Between2tubes(tube1, tube2)
nonIntrinsic_Distance_Between2tubes(tube1, tube2)

Arguments

`tube1`	List containing ETRep details.
`tube2`	List containing ETRep details.

Value

Numeric

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples

# Load tubes
data("tube_A")
data("tube_B")
intrinsic_Distance_Between2tubes(tube1 = tube_A,tube2 = tube_B)
# Load tubes
data("tube_A")
data("tube_B")
intrinsic_Distance_Between2tubes(tube1 = tube_A,tube2 = tube_B)

Compute Non-Intrinsic Mean of ETReps

Description

Calculates the non-intrinsic mean of a set of ETReps. This method utilizes a non-intrinsic distance metric based on robotic arm non-intrinsic transformations.

Usage

nonIntrinsic_mean_tube(tubes, type = "sizeAndShapeAnalysis", plotting = TRUE)
nonIntrinsic_mean_tube(tubes, type = "sizeAndShapeAnalysis", plotting = TRUE)

Arguments

`tubes`	List of ETReps.
`type`	String, "ShapeAnalysis" or "sizeAndShapeAnalysis" (default is "sizeAndShapeAnalysis").
`plotting`	Logical, enables visualization of the mean (default is TRUE).

Value

List representing the mean ETRep.

Examples

#Example 1
# Load tubes
data("tube_A")
data("tube_B")
nonIntrinsic_mean<-
  nonIntrinsic_mean_tube(tubes = list(tube_A,tube_B),
                         plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = nonIntrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)

#Example 2
data("simulatedColons")
nonIntrinsic_mean<-
  nonIntrinsic_mean_tube(tubes = simulatedColons,
                         plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = nonIntrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)
#Example 1
# Load tubes
data("tube_A")
data("tube_B")
nonIntrinsic_mean<-
  nonIntrinsic_mean_tube(tubes = list(tube_A,tube_B),
                         plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = nonIntrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)

#Example 2
data("simulatedColons")
nonIntrinsic_mean<-
  nonIntrinsic_mean_tube(tubes = simulatedColons,
                         plotting = FALSE)
# Plotting
plot_Elliptical_Tube(tube = nonIntrinsic_mean,
                     plot_frames = FALSE,
                     plot_skeletal_sheet = FALSE,
                     plot_r_project = FALSE,
                     plot_r_max = FALSE,
                     add = FALSE)

Non-Intrinsic Transformation Between Two ETReps

Description

Performs a non-intrinsic transformation from one ETRep to another. This approach is inspired by robotic arm transformations and does not account for the Relative Curvature Condition (RCC).

Usage

nonIntrinsic_Transformation_Elliptical_Tubes(
  tube1,
  tube2,
  type = "sizeAndShapeAnalysis",
  numberOfSteps = 4,
  plotting = TRUE,
  colorBoundary = "blue",
  add = FALSE
)
nonIntrinsic_Transformation_Elliptical_Tubes(
  tube1,
  tube2,
  type = "sizeAndShapeAnalysis",
  numberOfSteps = 4,
  plotting = TRUE,
  colorBoundary = "blue",
  add = FALSE
)

Arguments

`tube1`	List containing details of the first ETRep.
`tube2`	List containing details of the second ETRep.
`type`	String defining the type of analysis as sizeAndShapeAnalysis or shapeAnalysis
`numberOfSteps`	Integer, number of transformation steps.
`plotting`	Logical, enables visualization during transformation (default is TRUE).
`colorBoundary`	String defining the color of the e-tube
`add`	Logical, enables overlay plotting

Value

List containing intermediate ETReps.

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples


# Load tubes
data("tube_A")
data("tube_B")
numberOfSteps <- 10
transformation_Tubes<-
  nonIntrinsic_Transformation_Elliptical_Tubes(
    tube1 = tube_A,tube2 = tube_B,
    numberOfSteps = numberOfSteps,
    plotting = FALSE)
# Plotting
for (i in 1:length(transformation_Tubes)) {
  plot_Elliptical_Tube(tube = transformation_Tubes[[i]],
  plot_frames = FALSE,plot_skeletal_sheet = FALSE
  ,plot_r_project = FALSE,
  plot_r_max = FALSE,
  add = FALSE)
}

# Load tubes
data("tube_A")
data("tube_B")
numberOfSteps <- 10
transformation_Tubes<-
  nonIntrinsic_Transformation_Elliptical_Tubes(
    tube1 = tube_A,tube2 = tube_B,
    numberOfSteps = numberOfSteps,
    plotting = FALSE)
# Plotting
for (i in 1:length(transformation_Tubes)) {
  plot_Elliptical_Tube(tube = transformation_Tubes[[i]],
  plot_frames = FALSE,plot_skeletal_sheet = FALSE
  ,plot_r_project = FALSE,
  plot_r_max = FALSE,
  add = FALSE)
}

Plot an Elliptical Tube (ETRep)

Description

Plots a given ETRep with options for boundary, material frames, and projection visualization.

Usage

plot_Elliptical_Tube(
  tube,
  plot_boundary = TRUE,
  plot_r_max = FALSE,
  plot_r_project = TRUE,
  plot_frames = TRUE,
  frameScaling = NA,
  plot_spine = TRUE,
  plot_normal_vec = FALSE,
  plot_skeletal_sheet = TRUE,
  decorate = TRUE,
  colSkeletalSheet = "blue",
  colorBoundary = "blue",
  add = FALSE
)
plot_Elliptical_Tube(
  tube,
  plot_boundary = TRUE,
  plot_r_max = FALSE,
  plot_r_project = TRUE,
  plot_frames = TRUE,
  frameScaling = NA,
  plot_spine = TRUE,
  plot_normal_vec = FALSE,
  plot_skeletal_sheet = TRUE,
  decorate = TRUE,
  colSkeletalSheet = "blue",
  colorBoundary = "blue",
  add = FALSE
)

Arguments

`tube`	List containing ETRep details.
`plot_boundary`	Logical, enables plotting of the boundary (default is TRUE).
`plot_r_max`	Logical, enables plotting of max projection size (default is FALSE).
`plot_r_project`	Logical, enables plotting of projection along normals (default is TRUE).
`plot_frames`	Logical, enables plotting of the material frames (default is TRUE).
`frameScaling`	Numeric, scale factor for frames.
`plot_spine`	Logical, enables plotting of the spine.
`plot_normal_vec`	Logical, enables plotting of the normals.
`plot_skeletal_sheet`	Logical, enables plotting of the surface skeleton.
`decorate`	Logical, enables decorate the plot
`colSkeletalSheet`	String, defining the color of the surface skeleton
`colorBoundary`	String, defining the color of the e-tube
`add`	Logical, enables overlay plotting

Value

Graphical output.

Examples

# Load tube
data("colon3D")
plot_Elliptical_Tube(tube = colon3D,
                     plot_frames = FALSE,
                     add=FALSE)
# Load tube
data("colon3D")
plot_Elliptical_Tube(tube = colon3D,
                     plot_frames = FALSE,
                     add=FALSE)

Simulate Random Elliptical Tubes (ETReps)

Description

Generates random samples of ETReps based on a reference tube with added variation.

Usage

simulate_etube(
  referenceTube,
  numberOfSimulation,
  sd_v = 10^-10,
  sd_psi = 10^-10,
  sd_x = 10^-10,
  sd_a = 10^-10,
  sd_b = 10^-10,
  rangeSdScale = c(1, 2),
  plotting = TRUE
)
simulate_etube(
  referenceTube,
  numberOfSimulation,
  sd_v = 10^-10,
  sd_psi = 10^-10,
  sd_x = 10^-10,
  sd_a = 10^-10,
  sd_b = 10^-10,
  rangeSdScale = c(1, 2),
  plotting = TRUE
)

Arguments

`referenceTube`	List containing ETRep information as the reference.
`numberOfSimulation`	Integer, number of random samples.
`sd_v`	Standard deviations for various parameters.
`sd_psi`	Standard deviations for various parameters.
`sd_x`	Standard deviations for various parameters.
`sd_a`	Standard deviations for various parameters.
`sd_b`	Standard deviations for various parameters.
`rangeSdScale`	Numeric range for random scaling.
`plotting`	Logical, enables visualization of samples (default is FALSE).

Value

List of random ETReps.

References

Taheri, M., Pizer, S. M., & Schulz, J. (2024). "The Mean Shape under the Relative Curvature Condition." arXiv. doi:10.48550/arXiv.2404.01043

Taheri Shalmani, M. (2024). "Shape Statistics via Skeletal Structures." University of Stavanger. doi:10.13140/RG.2.2.34500.23685

Examples

# Load tube
data("colon3D")
#Set Parameters
sd_v<-sd_psi<-1e-03
sd_x<-sd_a<-sd_b<-1e-04
numberOfSimulation<-3
random_Tubes<-
  simulate_etube(referenceTube = colon3D,
                 numberOfSimulation = numberOfSimulation,
                 sd_v = sd_v,
                 sd_psi = sd_psi,
                 sd_x = sd_x,
                 sd_a = sd_a,
                 sd_b = sd_b,
                 rangeSdScale = c(1, 2),
                 plotting = FALSE)
# Plotting
rgl::open3d()
for (i in 1:numberOfSimulation) {
  plot_Elliptical_Tube(tube = random_Tubes[[i]],
                       plot_frames = FALSE,
                       plot_skeletal_sheet = FALSE,
                       plot_r_project = FALSE,
                       plot_r_max = FALSE,
                       add = TRUE)
}
# Load tube
data("colon3D")
#Set Parameters
sd_v<-sd_psi<-1e-03
sd_x<-sd_a<-sd_b<-1e-04
numberOfSimulation<-3
random_Tubes<-
  simulate_etube(referenceTube = colon3D,
                 numberOfSimulation = numberOfSimulation,
                 sd_v = sd_v,
                 sd_psi = sd_psi,
                 sd_x = sd_x,
                 sd_a = sd_a,
                 sd_b = sd_b,
                 rangeSdScale = c(1, 2),
                 plotting = FALSE)
# Plotting
rgl::open3d()
for (i in 1:numberOfSimulation) {
  plot_Elliptical_Tube(tube = random_Tubes[[i]],
                       plot_frames = FALSE,
                       plot_skeletal_sheet = FALSE,
                       plot_r_project = FALSE,
                       plot_r_max = FALSE,
                       add = TRUE)
}

Data

Description

Simulated samples of e-tubes, modeled after a reference structure resembling a colon.

Usage

simulatedColons
simulatedColons

Format

Five simulated samples of elliptical tubes, modeled after a reference structure resembling a colon.

Source

Generated and stored in the package's 'data/' folder.

Data

Description

A tube with 204 elliptical cross-sections.

Usage

tube_A
tube_A

Format

A list containing the information of an e-tube with 204 elliptical cross-sections

Source

Generated and stored in the package's 'data/' folder.

Data

Description

A tube with 204 elliptical cross-sections.

Usage

tube_B
tube_B

Format

A list containing the information of an e-tube with 204 elliptical cross-sections

Source

Generated and stored in the package's 'data/' folder.

Package 'ETRep'

Help Index

Check the Legality of an Elliptical Tube (ETRep)

Description

Usage

Arguments

Value

References

Examples

Data

Description

Usage

Format

Source

Create a Discrete Elliptical Tube (ETRep)

Description

Usage

Arguments

Value

References

Examples

Convert an ETRep to a Matrix in the Convex Transformed Space.

Description

Usage

Arguments

Value

Examples

Calculating the intrinsic distance between two ETReps

Description

Usage

Arguments

Value

References

Examples

Calculate Intrinsic Mean of ETReps

Description

Usage

Arguments

Value

References

Examples

Intrinsic Transformation Between Two ETReps

Description

Usage

Arguments

Value

References

Examples

Calculating the non-intrinsic distance between two ETReps

Description

Usage

Arguments

Value

References

Examples

Compute Non-Intrinsic Mean of ETReps

Description

Usage

Arguments

Value

Examples

Non-Intrinsic Transformation Between Two ETReps

Description

Usage

Arguments

Value

References

Examples

Plot an Elliptical Tube (ETRep)

Description

Usage

Arguments

Value

Examples

Simulate Random Elliptical Tubes (ETReps)

Description

Usage

Arguments

Value

References