This class is designed for reconstructing beam model from 3d object (or point cloud). The class mainly contains a workflow from loading data, constructing beam skeleton through step slicing, recoordinating and projecting, and finally reconstrut the model in a required coordinate.

Athor: Zeka(Zhekai) Li Time: Jun 2021

Simple example

import trimesh
import numpy as np
import sympy as sy
import scipy as sp

from SkeletonOfBeam import SkeletonOfBeam
from SkeletonOfBeam import GeometryToolBox

# Read mesh infos from object file
mesh = trimesh.load_mesh("beam.stl")

# Initialize beam object
roughVector = [1, 0, 0]
sob = SkeletonOfBeam(mesh, roughVector)

# Main process
## Find out a set of rough skeleton points from the input vector
sob.getScaleAlongSkeletonVec()
sob.getIntersectionsFromStep(step=1) # slice per step length
sob.getSkeletonPoints()

## Project the rough skeleton points onto x-y and x-z planes
sob.getNewCoordinate()
sob.getProjections()

## Fit the curve equations in these two planes separately
sob.getSkeletonEqs()
sob.getDerivativeSkeletonEqs()

## Recalculate the skeleton points, also get the cross-sections
sob.getNewSkeletonPoints()
sob.getNewIntersections()

1. Properties

1.1 Overal properties

mesh

The initial mesh data as input.

• Return type: trimesh.Trimesh

centroid

Beam’s centroid point.

• Return type: (, 3) float

nVec

Rough axial vector as input.

• Return type: (, 3) float

SkeletonPoints

List of skeleton points along the beam axis.

• Return type: (n, 3) float

L

Length of the projection of the skeleton curve on the axial vector.

• Return type: float

1.2 Cross-sections

IntersectionScale

Range between top and bottom sufaces in the axial vector direction.

• Return type: (, 2) float

Intersections

Cross-section cutted on each skeleton point.

• Return type: (, n) trimesh.Path3D

Intersections2D

Cross-sections in 2D.

• Return type: (, n) trimesh.Path2D

1.3 Coordinate

XYZCoordinate

New coordinate system constructed for the target beam.

• Return type: (3, 3) float

coorOrigin

Origin point of the new coordinate.

• Return type: (, 3) float

XYProjections

Positions of skeleton points on x-y plane of new coordinate.

• Return type: (n, 2) float

XZProjections

Positions of skeleton points on x-z plane of new coordinate.

• Return type: (n, 2) float

1.4 Curve Functions

u_xyPlane

Curve function of skeleton’s projection on x-y plane.

• Return type: A sympy symbolic expression with a parameter xi.

This function could be used to get the u value at any parameter xi ($\xi$) in $[0, 1]$:

[float] sob.u_xyPlane.evalf(subs={'xi': 0.5})

u_xzPlane

Curve function of skeleton’s projection on x-z plane.

• Return type: A sympy symbolic expression with a parameter xi

alpha_xyPlane

The parameters fitted for the curve function on x-y plane.

• Return type: (, 4) float

alpha_xzPlane

The parameters fitted for the curve function on x-y plane.

• Return type: (, 4) float

dudx_xyPlane

Derivation of the skeleton curve on x-y plane.

• Return type: A sympy symbolic expression with a parameter xi.

This function could be used to get the du/dx value at any parameter xi ($\xi$) in $[0, 1]$:

[float] sob.dudx_xyPlane.evalf(subs={'xi': 0.5})

dudx_xzPlane

Derivation of the skeleton curve on x-z plane.

• Return type: A sympy symbolic expression with a parameter xi.

2. Methods

2.1 Process

getScaleAlongSkeletonVec()

Get the scale of the target beam along the axial vector.

• Parameters: None
• Returns: None
• Properties refreshed: IntersectionScale((, 2) float)

getIntersectionsFromStep(self, step=1)

Slice one cross-section of the bean per step length along the axial vector.

• Parameters: step (float)
• Returns: None
• Properties refreshed: Intersections((, n) trimesh.Path3D)

getIntersectionsFromSliceNum(sliceNum=5)

Slices a specific number of cross-sections uniformly along the axial vector.

• Parameters: sliceNum (int) - number of slices
• Returns: None
• Properties refreshed: Intersections((, n) trimesh.Path3D)

getSkeletonPoints()

Get the skeleton points, which are the centroids of cross-sections.

• Parameters: None
• Returns: None
• Properties refreshed: SkeletonPoints((n, 3) float)

getNewCoordinate()

Construct a new coordinate, whose x-axis is the property nVec.

• Parameters: None
• Returns: None
• Properties refreshed: XYZCoordinate((3, 3) float)

getProjections()

Project the rough skeleton points onto x-y and x-z planes.

• Parameters: None
• Returns: None
• Properties refreshed:
• • XYProjections((n, 2) float)
• • XZProjections((n, 2) float)

getSkeletonEqs()

Fit the curve equations for projections points in x-y and x-z planes separately

• Parameters: None
• Returns: None
• Properties refreshed:

getDerivativeSkeletonEqs()

Take the derivative of the skeleton curve equations.

• Parameters: None
• Returns: None
• Properties refreshed:

getNewSkeletonPoints()

getNewIntersections()

2.2 Functional methods

returnTangentVectorAtXi(xi_value)

Return the tangent vector at xi=xi_value

returnSkeletonPointsInXiRange(xi_s, xi_e, pNum=10)

showIntersections(ifOverlapped=True)

Visualize the intersections in one graph

_H(xs, L, ifsymbol=False)

H(xs, L, ifsymbol=False)