Beta Release of ezdxf v1.4.0b0

[mozman]

Two new construction related modules:

• ezdxf.edgeminer: seaching for connected edges and closed loops
• ezdxf.edgesmith: creating edges from DXF entities and creating polylines and hatches from connected edges

The API may change until the final release.

Documentation

• EdgeMiner
• EdgeSmith
• Tutorial for Finding Chains and Loops
• Examples

[subsurfaceiodev]

This feature is awesome, it would be great to be able to have a function like spline_from_chain where lines, arcs, etc would be combined as a single spline, which is what autocad does when using JOIN command with said shapes. This would make max_sagitta parameter irrelevant since no linearization would be needed.

[mozman]

No, I don't think so (I can't remember):

High level Python stuff:

• https://github.com/mozman/ezdxf/blob/master/src/ezdxf/math/bspline.py

Low level Python/Cython code:

• https://github.com/mozman/ezdxf/blob/master/src/ezdxf/math/_bspline.py
• https://github.com/mozman/ezdxf/blob/master/src/ezdxf/acc/bspline.pyx

[mozman]

FYI: The NURBS Book (Piegl & Tiller) - Chapter 5.5 Degree Elevation (Algorithm A5.9)

[subsurfaceiodev]

Thanks a lot Manfred

[mozman]

I translated the algorithm A5.9 (Page 206) from the Piegl & Tiller Book from C to Python .
(You can find a PDF of the book online if you search for "Nurbs Piegl Tiller" at a university in eastern Europe, text is in English)

The code doesn't work, there are two index errors. Maybe you can fix this. I will not invest more time in that.

The Python code keeps the original code structure and variable names for debugging. The numpy package is used to calculate the x-, y- and z-axis at once.

Good luck!

EDIT: added the script to the exploration folder of the ezdxf repo: bb9ca49

[subsurfaceiodev]

Hi Manfred, as it turns out, AutoCAD performs degree elevation in a much more simple way: it first subdivides, if needed, the spline in Bézier curves and then applies below algorithm(written by me based on some reading) to perform degree elevation on each curve.

import ezdxf.entities
import math
from ezdxf.math import BSpline
from ezdxf import zoom


def degree_elevation(spline: BSpline) -> BSpline:
    # Rational and non-rational Bézier curves degree elevation
    # https://en.wikipedia.org/wiki/B%C3%A9zier_curve

    n = spline.degree
    control_points = spline.control_points
    weights = spline.weights()

    pns = []
    wns = []

    for i_ in range(spline.degree):
        i = i_ + 1
        c0 = i / (n + 1)
        c1 = (n + 1 - i) / (n + 1)
        p0, p1 = control_points[i_], control_points[i_ + 1]
        w0, w1 = weights[i_], weights[i_ + 1]
        pn = c0 * p0 * w0 + c1 * p1 * w1
        wn = c0 * w0 + c1 * w1
        pn /= wn
        pns.append(pn)
        wns.append(wn)

    return BSpline(
        [control_points[0], *pns, control_points[-1]],
        weights=[weights[0], *wns, weights[-1]],
        order=spline.order + 1
    )


def test():
    spline = BSpline(
        [(0, 0), (0, 1), (1, 1)],
        weights=[1, 1 / math.sqrt(2), 1],
        order=3,
    )
    doc = ezdxf.new()
    msp = doc.modelspace()
    msp.add_spline().apply_construction_tool(spline)
    for i in range(3):
        spline = degree_elevation(
            spline
        )
        msp.add_spline().apply_construction_tool(spline)
    zoom.extents(msp)
    doc.saveas('test.dxf')