Gordon Surface Library for CadQuery's OCP

This library provides a Python implementation for creating Gordon surfaces, a method for interpolating a network of curves to generate a smooth surface. It is designed to be compatible with CadQuery's OCP and leverages B-spline mathematics.

The implementation is written entirely in Python and is adapted from the original C++ code in occ_gordon

It is currently used by build123d, but can also be used independently.

Features

• Gordon surface interpolation from profile and guide curves.
• Compatibility with B-spline representations.
• Integration with CadQuery's OCP (OpenCASCADE Python) for geometric primitives.

Installation

This package can be installed using pip.

pip install ocp_gordon

Dependencies

• CadQuery OCP 8.x (cadquery-ocp-novtk)
• NumPy
• SciPy

The OCP 8 bindings expose typed arrays through OCP.collections (for example, Array1_gp_Pnt, Array2_gp_Pnt, Array1_double, and Array1_int). Array elements are read with .Value(...) and written with SetValue(...).

Usage

Here's a basic example of how to use the library:

# Assume you have profile_curves and guide_curves defined as lists of B-spline objects
# profile_curves = [...] # List of Geom_BSplineCurve objects
# guide_curves = [...]   # List of Geom_BSplineCurve objects

from ocp_gordon import interpolate_curve_network

gordon_surface = interpolate_curve_network(profile_curves, guide_curves, tolerance=3e-4)

For more detailed examples, please refer to the examples/ directory in the source code.

Test

To run tests, first install pytest, then:

python -m pytest

Notable Difference from C++ Code

• In intersect_bsplines.py, the math_BFGS method is polyfilled and used in place of math_FRPR, as neither math_BFGS nor math_FRPR is usable in OCP due to the lack of math_Vector exposure. The intersect detection algorithm has been improved for both speed and reliability.
• In the _solve() function of bspline_approx_interp.py, regularization has been added to prevent singular matrix issues, which can occur in cases such as when the input curve is a B-spline derived from a circle.
• A new file, misc.py, has been introduced to implement missing OCP utilities. The primary additions include clone_bspline and math_BFGS.
• Modified curve_network_sorter.py, bspline_algorithms.py, and interpolate_curve_network.py to allow a single point to be used as either a profile or a guide.
• The reparameterization process is now skipped if the input profiles and guides are already iso-parametric, improving accuracy and performance for such cases.
• In bspline_algorithms.py, the GeomConvert_ApproxCurve() function is utilized for improved representation of conic curves.

Caveats

Potential misalignments can occur between the generated Gordon surface and its input curves, especially at boundaries. This is primarily due to the approximation involved in the reparameterization process for non-iso-parametric inputs. For a detailed explanation and mitigation strategies, please refer to the Gordon Surface Misalignment wiki page.

License

This project is licensed under the Apache 2.0 License - see the LICENSE file for details.

Citing

The algorithm was originally described in:

Siggel M. et. al. (2019), TiGL: An Open Source Computational Geometry Library for Parametric Aircraft Design

@article{siggel2019tigl,
	title={TiGL: an open source computational geometry library for parametric aircraft design},
	author={Siggel, Martin and Kleinert, Jan and Stollenwerk, Tobias and Maierl, Reinhold},
	journal={Mathematics in Computer Science},
	volume={13},
	number={3},
	pages={367--389},
	year={2019},
	publisher={Springer},
    doi={10.1007/s11786-019-00401-y}
}