Set Classification

Point Cloud Discontinuity Set Classification

The Set Classification module in DSEpy partitions the 3D point cloud into individual Discontinuity Sets (DS) based on the angular proximity between each point's surface normal vector n_i and the mean normal vectors of the identified principal poles (p₁, p₂, ..., p_K).

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1. Theoretical Background

1.1 Angular Proximity Distance

For every point i in the point cloud with unit normal vector n_i = (N_x, N_y, N_z), DSEpy evaluates the acute 3D angle θ_i,k ∈ [0°, 90°] against each principal set pole p_k (k = 1, 2, ..., K):

$$\theta_{i,k} = \arccos\left( |\mathbf{n}_i \cdot \mathbf{p}_k| \right) \cdot \frac{180^\circ}{\pi}$$

Where:

• n_i · p_k represents the dot product between the point normal vector n_i and the k-th set mean pole vector p_k.
• Absolute value |·| accounts for normal vector orientation invariance in planar geometry.

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1.2 Point Assignment Rule & Unclassified Thresholding

A point i is assigned to the principal pole set k^* that minimizes the angular distance, provided the minimum angle does not exceed the user-defined maximum angular tolerance threshold (θ_threshold):

$$k^* = \arg\min_{k \in {1, \dots, K}} \theta_{i,k} \quad \text{subject to} \quad \theta_{i,k^*} \le \theta_{\text{threshold}}$$

Classification Outcomes:

• Assigned Point (k ∈ {1, 2, ..., K}): The point belongs to Discontinuity Set J_k.
• Unclassified Point (k = 0): If θ_i,k > θ_threshold for all principal poles, the point exceeds the maximum allowable orientation dispersion. It is flagged as unclassified background noise and assigned the scalar value 0.

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1.3 CloudCompare Scalar Field Integration

DSEpy attaches the classification results directly to the active point cloud in CloudCompare (CC) as a new integer Scalar Field (SF) named DS_family (or Discontinuity_Set):

$$\text{SF}_i = \begin{cases} 0 & \text{if unclassified / random orientation} \\ 1 & \text{if assigned to Set } J_1 \\ 2 & \text{if assigned to Set } J_2 \\ \vdots & \vdots \\ K & \text{if assigned to Set } J_K \end{cases}$$

This integration allows real-time visual assessment of family boundaries both in stereographic space and on the 3D outcrop surface.

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2. Interactive GUI Workflow in DSEpy

Classification is executed within the 2. DS classification tab.

*DSEpy Stage 2 Interface: Set classification parameters and point cloud family distribution summary.*

Step-by-Step Procedure

1. Set Angular Threshold (θ_threshold):
   • Adjust the maximum allowed angle (θ_threshold, typically between 15° and 30°).
   • A smaller angle produces tighter, highly specific set clusters but leaves more points as unclassified (0). A larger angle includes more points but risks assigning noisy or transitional surfaces.
2. Execute Classification:
   • Click Classify Point Cloud. DSEpy computes the angular distances for all points and transfers the resulting scalar field directly to CloudCompare.
3. Inspect Set Distribution Summary:
   • Review the classification summary table in DSEpy showing the percentage and total count of points assigned to each discontinuity set (J₁, J₂, ..., J_K) as well as unclassified points (0).

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3. Visual Validation & Diagnostic Stereonets

3.1 Poles by Family Stereonet

In addition to 3D cloud rendering, DSEpy provides a dedicated Poles by Family stereogram plot. This visual diagnostic tool renders all point cloud poles color-coded according to their assigned discontinuity set family:

*Stereogram plot showing point cloud poles color-coded by assigned discontinuity family (J1, J2, J3) with unclassified points in grey and mean principal poles marked in yellow.*

Diagnostic Advantages:

• Cluster Dispersion Verification: Allows immediate evaluation of orientation spread for each joint set (e.g., J₁ in blue, J₂ in orange, J₃ in green).
• Unclassified Point Inspection: Unclassified points (k^* = 0, grey points) are clearly visible outside the set boundaries or scattered randomly across the grid.
• Overlapping Boundary Identification: Helps detect if the angular threshold (θ_threshold) is too large, causing adjacent joint family clusters to touch or overlap.
• Principal Pole Alignment: Mean principal poles are highlighted as yellow labelled markers (J₁, J₂, J₃) at the centroid of each assigned cluster.

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3.2 3D Point Cloud Validation in CloudCompare

Switch to CloudCompare's 3D window and select the active scalar field DS_family to verify family assignments directly on the rock mass geometry.

*3D Point Cloud in CloudCompare color-coded by the newly generated Discontinuity Set scalar field.*

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4. Filtering Unclassified Points in CloudCompare

Unclassified points (value 0) represent non-systematic jointing, blast damage, or curved rock surfaces. To isolate classified joint families for downstream analysis or visual presentation:

1. In CloudCompare, select the active point cloud in the DBTree.
2. Go to Edit $\rightarrow$ Scalar Fields $\rightarrow$ Filter by Value.
3. Set parameter ranges:
   • Min: 1 (excludes unclassified points with value 0).
   • Max: Set to the highest family index (K).
4. Click OK. CloudCompare creates a new child point cloud containing only classified discontinuity sets.

Filtering unclassified points (value 0) in CloudCompare using the Filter by Value tool.

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5. Iterative Classification Refinement

If visual inspection in the Poles by Family stereonet or CloudCompare reveals misassigned joint planes or poorly defined set boundaries:

1. Return to DSEpy: Adjust the angular threshold (θ_threshold) or switch back to tab 1. Principal poles to refine, add, or delete principal pole orientations.
2. Re-run Classification: Click Classify Point Cloud again.
3. Automatic Overwriting: DSEpy automatically updates and overwrites the scalar field on the active CloudCompare point cloud without requiring manual deletion of previous results.

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6. Interface Parameter Reference

Parameter	Recommended Value	Description
Angular Threshold (θthreshold)	15.0° – 30.0°	Maximum angular tolerance between a point normal vector ni and the mean set pole vector pk.
Scalar Field Name	DS_family	Name assigned to the newly created scalar field attached to the CloudCompare point cloud entity.
Poles Visualisation	Poles by Family	Stereogram rendering mode where individual poles are color-coded according to assigned discontinuity set ID (J1 ... JK).
Color Ramp	Banded / Custom	Discrete color scheme used to visually differentiate joint sets J1 ... JK.

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🔗 Next Steps

• Learn about spatial cluster segmentation and 3D facet extraction in Clustering-&-Facets.
• Return to principal pole extraction in Stereonet-&-Poles.