Create theoretical intersection curve along feature

How to create theoretical intersection curves (and feature curves approximations) that can later be used for surface development.

An input curve (as an approximation of the feature curve) and radius of influence must be provided to calculate the theoretical intersection curve. If you do not have such a curve, you can input a series of points along the feature to create an approximation to the feature curve.

The output consists of a theoretical curve, and, if using the point method, a feature curve approximation. The feature curve attempts to lie on the mesh as much as possible. The theoretical curve is drawn where both sides of the mesh (across the feature curve) would intersect if they were extended. The theoretical curve generally lies off the mesh.

Preliminary steps

Turn on the Curvature Evaluation shader from the Diagnostic Shading panel.
This will show you areas of high curvature where you may want to define theoretical intersection (or feature) curves.
Optionally, create a curve along the mesh in the area where you want the feature line to lie. Using blend curves is recommended since you can constrain the blend points to the mesh.

To extract a theoretical curve from a mesh (curve method)

Choose Mesh > Mesh Curves > Mesh Extract Theoretical Intersection ❒
Select the mesh
If the Show Curvature Evaluation option is on, the mesh is shaded with a curvature map.
Select an existing curve drawn along the feature
A blue radius manipulator appears at the start of the curve.
Adjust the radius through the option window or by dragging the mouse on the blue circle. (This value corresponds to the Tangent line distance in the option window).

TipMake sure the tube defined by the curve and radius is large enough to encompass the entire area of transition. That is, the outer edges of the tube should lie in the flatter mesh regions (green on curvature map).
If necessary, you can click along the curve to create extra radius manipulators and adjust them with the mouse (click and drag the small circle at the center to move a manipulator).
This creates a variable-radius cylinder and controls the shape of the resulting curve.
Press the Recalc button.
A degree 1 curve is produced: the theoretical intersection curve.

Tangent lines, drawn in yellow, show you where the tube intersects the mesh. They help you ensure that the radius is large enough to cover the entire transition region.

You can still add more radius manipulators or change others options in the option window then press Recalc to recompute.

To extract a theoretical curve and feature curve approximation from a mesh (point method)

Choose Mesh > Mesh Curves > Mesh Extract Theoretical Intersection ❒.
Select the mesh.
If the Show Curvature Evaluation option was on, the mesh is shaded with a curvature map.
Click down along the feature to position a series of points.
Each point appears with a blue radius manipulator and a cross in the middle. The cross can be selected to reposition the manipulator inside the feature.
Adjust the radii by dragging the mouse on the blue circles. Changing the Tangent line distance value in the option window will set all the radii to the same value.
Press the Recalc button.
An approximation feature curve is produced in addition to a theoretical intersection curve. Both curves have degree 1.

Tangent lines, drawn in yellow, show you where the tube intersects the mesh. They help you ensure that the radius is large enough to cover the entire transition region.

You can add more radius manipulators (by clicking on the feature curve) or change other options in the option window then press Recalc to recompute.