intrinsic_Transformation_Elliptical_Tubes function

Intrinsic Transformation Between Two ETReps

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.

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

Returns

List containing intermediate ETReps.

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)
}

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")