Topo-Tracer 0.1.11

Package to extract and trace the topological skeleton of a 2-order stress tensor field

Introduction

This package includes 2 python functions that together are able to extract the topological skeleton of the stress tensor field in the GH/Rhino environment.

Theory

Topo_Tracer_1

This function locates degenerate points and calculates the separating direction for each of them.

import package in GH component: from Topo_Tracer import Topo_Tracer_1

Inputs:

1. neighbors = for partial derivative
2. tol_deg = Tolerance for degeneracy
3. offset_eps = For partial derivative
4. cluster_threshold = distance threshold for clustering
5. seed_amplitude = distance of the new seed points from the degenerate points
6. index_radius = radius of the jordan curve used for index calculation
7. n_sep_merged = the number of separating streamlines for higher order degeneracies (saddles)
8. domain_surface = surface or brep
9. points = points from the structural mesh in karamba (points where stress values are defined)
10. stress_values_1 = stress values from first principal direction
11. stress_values_2 = stress values from secondary principal direction
12. vectors_1 = first principal stress trajectories as vectors
13. vectors_2 = first principal stress trajectories as vectors

Outputs:

1. singularities = degenerate points
2. seed_vectors_field_1 = separating directions for first principal stress field given as 3D vectors
3. seed_vectors_field_2 = separating directions for secondary principal stress field given as 3D vectors
4. new_seeds_1 = new seed for each separating direction slighlty offsetted from the degenerate point for first principal stress field
5. new_seeds_2 = new seed for each separating direction slighlty offsetted from the degenerate point for first principal stress field
6. dege_index = tensor index of the degenerate points measured by eigenvector rotations
7. dege_type = classification/type of degenerate point (wedge, trisector or merged singualrity)

Call function in GH: singularities, seed_vectors_field_1, seed_vectors_field_2, new_seeds_1, new_seeds_2, dege_index, dege_type = Topo_Tracer_1.main(domain_surface, points, stress_values_1, vectors_1, stress_values_2, vectors_2,tol_deg, offset_eps, neighbors, cluster_threshold, seed_amplitude, index_radius, n_sep_merged)

Topo_Tracer_2

This function takes the calculated separating directions and the new seed points and traces the separatrices.

import package in GH component: from Topo_Tracer import Topo_Tracer_2

Inputs:

1. points = points from the structural mesh in karamba (points where stress values are defined)
2. principal_vectors = principal stress trajectories/vectors for chosen field
3. seed_points = the new seed points from Topo_Tracer_1
4. seed_vectors = the new seed vectors / separating direction from Topo_Tracer_1
5. boundary_curves = the curves that form the boundary of the design
6. domain_surface = surface or brep
7. k = k nearest neighbours for interpolation
8. h = step length
9. num_steps = max iterations
10. step_sign = 1
11. boundary_tolerance = from what distance boundaries are detected
12. collision_threshold = threshold for when a PSL merges into anotehr psl
13. n_back = how many traced points to go back when merging
14. seed_dist = distance at what snapping to other seed points occurs.

Outputs:

1. separatrices = traced separatrices
2. connecting_points = lists with start and end point of connecting lines

Call function in GH: separatrices, connecting_points = Topo_Tracer_2.main(points, principal_vectors, seed_points, seed_vectors,boundary_curves, domain_surface, k, h, num_steps, step_sign , boundary_tolerance, collision_threshold, n_back, seed_dist)

Example files

A GH example file can be found on: https://github.com/Brandes21/PyPa/tree/main/Example_files

For any questions or in case of bugs feel free to contact me on: [e-mail]