Blender Bridge Edge Loops

In Blender, when you want to bridge edge loops with an unequal number of vertices on the edges (i.e., the number of vertices on each edge is different), you can use the Bridge Edge Loops tool, but Blender by default tries to match the vertices based on their order, which might not always give you the best result if you want to connect them based on minimizing displacement along the non-Z axis (such as the X or Y axes).

To achieve the goal of connecting the vertices based on the smallest displacement in the non-Z axis (essentially minimizing the stretching or shrinking of the geometry), you will need to use a custom approach since the default Bridge Edge Loops doesn't have an option for this. Below is a workaround that can help you align the vertices with minimal displacement in the X/Y axis:

Approach:

1. Manually Align Vertices:
   • First, make sure the edge loops you want to bridge are aligned or have a similar shape in the X/Y plane (depending on your mesh orientation).
   • If the edge loops are at different positions, you can manually move the vertices in the X/Y plane to better align them before bridging. To do this, go to Edit Mode, select the vertices along one edge loop, and then use the Proportional Editing Tool (O to toggle) to move the vertices smoothly along the X/Y axes.
2. Use the "Bridge Edge Loops" Tool:
   • With both edge loops selected, press Ctrl+E to open the Edge menu and choose Bridge Edge Loops. This will connect the loops, but the geometry might get stretched or skewed depending on the number of vertices.
   • In the Bridge Edge Loops options (in the bottom left of the 3D Viewport, or in the F9 panel), try tweaking the settings like Segment Count, Smoothness, or Profile to adjust the final shape. However, these don't specifically minimize displacement in the non-Z axis.
3. Use the "Surface Snapping" (Alternative Method):
   • A more manual approach would be to use Surface Snapping to help connect the vertices by maintaining minimal displacement in the non-Z axis.
   • You can achieve this by turning on Snap to Surface (in the snapping options menu, set to Face) and then manually snapping vertices to align with each other based on the smallest displacement.
4. Use a Script (Advanced Solution):
   • If you're familiar with scripting in Python, you can write a small Python script to calculate the minimal displacement for each vertex pair and then connect them based on that calculation. This would allow you to programmatically select the best pairing of vertices with the smallest displacement in the X/Y axes. Here's a basic conceptual outline of a script that would do this:

import bpy
import mathutils

# Assuming you are in Edit Mode with two edge loops selected

def bridge_with_min_displacement():
    # Get the selected edges and vertices
    selected_edges = [edge for edge in bpy.context.active_object.data.edges if edge.select]
    loop_1_verts = [v for v in selected_edges[0].vertices]  # First edge loop
    loop_2_verts = [v for v in selected_edges[1].vertices]  # Second edge loop

    # Pair vertices based on minimal displacement (X, Y axes)
    pairs = []
    for v1 in loop_1_verts:
        best_match = None
        best_distance = float('inf')

        for v2 in loop_2_verts:
            displacement = (v1.co.xy - v2.co.xy).length  # Calculate X/Y displacement
            if displacement < best_distance:
                best_distance = displacement
                best_match = v2

        pairs.append((v1, best_match))

    # Bridge or connect the pairs based on the optimal match
    for v1, v2 in pairs:
        bpy.ops.mesh.connect_vert_pairs(v1, v2)  # Connect vertices with minimal displacement

bridge_with_min_displacement()