create_Elliptical_Tube function

Create a Discrete Elliptical Tube (ETRep)

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

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

Returns

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

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)

References

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

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