<filename>examples/spline_interpolation_of_sine_wave.py
# Copyright (c) 2020-2021, <NAME>
# License: MIT License

from typing import Iterable
from pathlib import Path
import math
import ezdxf
from ezdxf import zoom
from ezdxf.math import (
    Vec3,
    estimate_tangents,
    linspace,
    estimate_end_tangent_magnitude,
)
from ezdxf.math import (
    local_cubic_bspline_interpolation,
    global_bspline_interpolation,
)

DIR = Path("~/Desktop/Outbox").expanduser()


def sine_wave(count: int, scale: float = 1.0) -> Iterable[Vec3]:
    for t in linspace(0, math.tau, count):
        yield Vec3(t * scale, math.sin(t) * scale)


doc = ezdxf.new()
msp = doc.modelspace()

# Calculate 8 points on sine wave as interpolation data
data = list(sine_wave(count=8, scale=2.0))

# Reference curve as fine approximation
msp.add_lwpolyline(
    sine_wave(count=800, scale=2.0),
    dxfattribs={"color": 1, "layer": "Reference curve (LWPolyline)"},
)

# AutoCAD/BricsCAD interpolation
msp.add_spline(data, dxfattribs={"layer": "BricsCAD B-spline", "color": 2})

# tangent estimation method
METHOD = "5-p"

# create not normalized tangents (default is normalized)
tangents = estimate_tangents(data, METHOD, normalize=False)

# show tangents
for p, t in zip(data, tangents):
    msp.add_line(
        p,
        p + t,
        dxfattribs={"color": 5, "layer": f"Estimated tangents ({METHOD})"},
    )

# local interpolation: a normalized tangent vector for each data point is required,
s = local_cubic_bspline_interpolation(
    data, tangents=[t.normalize() for t in tangents]
)
# or set argument 'method' for automatic tangent estimation, default method is
# '5-points' interpolation
# s = local_cubic_bspline_interpolation(data, method=METHOD)
msp.add_spline(
    dxfattribs={"color": 3, "layer": f"Local interpolation ({METHOD})"}
).apply_construction_tool(s)

# global interpolation: take first and last vector from 'tangents' as start-
# and end tangent
m1, m2 = estimate_end_tangent_magnitude(data, method="chord")
s = global_bspline_interpolation(
    data, tangents=(tangents[0].normalize(m1), tangents[-1].normalize(m2))
)
msp.add_spline(
    dxfattribs={"color": 4, "layer": f"Global interpolation ({METHOD})"}
).apply_construction_tool(s)

zoom.extents(msp, factor=1.1)
doc.saveas(DIR / f"sine-wave-{METHOD}.dxf")

<filename>examples/spline_interpolation_of_sine_wave.py
# Copyright (c) 2020-2021, <NAME>
# License: MIT License

from typing import Iterable
from pathlib import Path
import math
import ezdxf
from ezdxf import zoom
from ezdxf.math import (
    Vec3,
    estimate_tangents,
    linspace,
    estimate_end_tangent_magnitude,
)
from ezdxf.math import (
    local_cubic_bspline_interpolation,
    global_bspline_interpolation,
)

DIR = Path("~/Desktop/Outbox").expanduser()


def sine_wave(count: int, scale: float = 1.0) -> Iterable[Vec3]:
    for t in linspace(0, math.tau, count):
        yield Vec3(t * scale, math.sin(t) * scale)


doc = ezdxf.new()
msp = doc.modelspace()

# Calculate 8 points on sine wave as interpolation data
data = list(sine_wave(count=8, scale=2.0))

# Reference curve as fine approximation
msp.add_lwpolyline(
    sine_wave(count=800, scale=2.0),
    dxfattribs={"color": 1, "layer": "Reference curve (LWPolyline)"},
)

# AutoCAD/BricsCAD interpolation
msp.add_spline(data, dxfattribs={"layer": "BricsCAD B-spline", "color": 2})

# tangent estimation method
METHOD = "5-p"

# create not normalized tangents (default is normalized)
tangents = estimate_tangents(data, METHOD, normalize=False)

# show tangents
for p, t in zip(data, tangents):
    msp.add_line(
        p,
        p + t,
        dxfattribs={"color": 5, "layer": f"Estimated tangents ({METHOD})"},
    )

# local interpolation: a normalized tangent vector for each data point is required,
s = local_cubic_bspline_interpolation(
    data, tangents=[t.normalize() for t in tangents]
)
# or set argument 'method' for automatic tangent estimation, default method is
# '5-points' interpolation
# s = local_cubic_bspline_interpolation(data, method=METHOD)
msp.add_spline(
    dxfattribs={"color": 3, "layer": f"Local interpolation ({METHOD})"}
).apply_construction_tool(s)

# global interpolation: take first and last vector from 'tangents' as start-
# and end tangent
m1, m2 = estimate_end_tangent_magnitude(data, method="chord")
s = global_bspline_interpolation(
    data, tangents=(tangents[0].normalize(m1), tangents[-1].normalize(m2))
)
msp.add_spline(
    dxfattribs={"color": 4, "layer": f"Global interpolation ({METHOD})"}
).apply_construction_tool(s)

zoom.extents(msp, factor=1.1)
doc.saveas(DIR / f"sine-wave-{METHOD}.dxf")

# Copyright (c) 2020-2021, <NAME> # License: MIT License # Calculate 8 points on sine wave as interpolation data # Reference curve as fine approximation # AutoCAD/BricsCAD interpolation # tangent estimation method # create not normalized tangents (default is normalized) # show tangents # local interpolation: a normalized tangent vector for each data point is required, # or set argument 'method' for automatic tangent estimation, default method is # '5-points' interpolation # s = local_cubic_bspline_interpolation(data, method=METHOD) # global interpolation: take first and last vector from 'tangents' as start- # and end tangent