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Bézier curve fix for arcs longer than 90 degrees #5

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Bézier curve fix for arcs longer than 90 degrees #5

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ce5de83
Update matplotlib-chord.py
cy1110 Jul 29, 2020
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cy1110 Jul 29, 2020
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Update matplotlib-chord.py
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18 changes: 17 additions & 1 deletion README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -22,6 +22,22 @@ def chordDiagram(X, ax, colors=None, width=0.1, pad=2, chordwidth=0.7):
position of the control points for the chords, controlling the shape of the chords
"""
```

## Example
An example can be found at the end of `matplotlib-chord.py`. Here is what the figure looks like:
![](example.png)
![](example_large_new.png)


## Improvements
Fixes inaccurate circle plotting caused by too few vertices on the Bézier curves. This effect becomes visible when arc lengths exceed 90 degrees, but gets much worse when arc lengths exceed 180 degrees.

Vertex count has been quadrupled, using four curves on each arc to ensure plotting remains accurate even with long arcs within the dataset.

## Comparison
The effect is visible even with the default arc lengths.

<img src="example_old.png" width="390" height="375"><img src="example_new.png" width="390" height="375">

The effect is much worse with arcs above 180 degrees in length, like in the example image.

<img src="example_large_old.png" width="393" height="380"><img src="example_large_new.png" width="393" height="380">
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144 changes: 138 additions & 6 deletions matplotlib-chord.py
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Expand Up @@ -22,21 +22,72 @@ def IdeogramArc(start=0, end=60, radius=1.0, width=0.2, ax=None, color=(1,0,0)):
end *= np.pi/180.
# optimal distance to the control points
# https://stackoverflow.com/questions/1734745/how-to-create-circle-with-b%C3%A9zier-curves
opt = 4./3. * np.tan((end-start)/ 4.) * radius
inner = radius*(1-width)
opt = 4./3. * np.tan((end-start)/ 16.) * radius #16-vertex curves (4 quadratic Beziers which accounts for worst case scenario of 360 degrees)
inter1 = start*(3./4.)+end*(1./4.)
inter2 = start*(2./4.)+end*(2./4.)
inter3 = start*(1./4.)+end*(3./4.)
verts = [
polar2xy(radius, start),
polar2xy(radius, start) + polar2xy(opt, start+0.5*np.pi),
polar2xy(radius, inter1) + polar2xy(opt, inter1-0.5*np.pi),
polar2xy(radius, inter1),
polar2xy(radius, inter1),
polar2xy(radius, inter1) + polar2xy(opt, inter1+0.5*np.pi),
polar2xy(radius, inter2) + polar2xy(opt, inter2-0.5*np.pi),
polar2xy(radius, inter2),
polar2xy(radius, inter2),
polar2xy(radius, inter2) + polar2xy(opt, inter2+0.5*np.pi),
polar2xy(radius, inter3) + polar2xy(opt, inter3-0.5*np.pi),
polar2xy(radius, inter3),
polar2xy(radius, inter3),
polar2xy(radius, inter3) + polar2xy(opt, inter3+0.5*np.pi),
polar2xy(radius, end) + polar2xy(opt, end-0.5*np.pi),
polar2xy(radius, end),
polar2xy(inner, end),
polar2xy(inner, end) + polar2xy(opt*(1-width), end-0.5*np.pi),
polar2xy(inner, inter3) + polar2xy(opt*(1-width), inter3+0.5*np.pi),
polar2xy(inner, inter3),
polar2xy(inner, inter3),
polar2xy(inner, inter3) + polar2xy(opt*(1-width), inter3-0.5*np.pi),
polar2xy(inner, inter2) + polar2xy(opt*(1-width), inter2+0.5*np.pi),
polar2xy(inner, inter2),
polar2xy(inner, inter2),
polar2xy(inner, inter2) + polar2xy(opt*(1-width), inter2-0.5*np.pi),
polar2xy(inner, inter1) + polar2xy(opt*(1-width), inter1+0.5*np.pi),
polar2xy(inner, inter1),
polar2xy(inner, inter1),
polar2xy(inner, inter1) + polar2xy(opt*(1-width), inter1-0.5*np.pi),
polar2xy(inner, start) + polar2xy(opt*(1-width), start+0.5*np.pi),
polar2xy(inner, start),
polar2xy(radius, start),
]

codes = [Path.MOVETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Expand Down Expand Up @@ -65,18 +116,48 @@ def ChordArc(start1=0, end1=60, start2=180, end2=240, radius=1.0, chordwidth=0.7
end1 *= np.pi/180.
start2 *= np.pi/180.
end2 *= np.pi/180.
opt1 = 4./3. * np.tan((end1-start1)/ 4.) * radius
opt2 = 4./3. * np.tan((end2-start2)/ 4.) * radius
opt1 = 4./3. * np.tan((end1-start1)/ 16.) * radius #16-vertex curves (4 quadratic Beziers which accounts for worst case scenario of 360 degrees)
opt2 = 4./3. * np.tan((end2-start2)/ 16.) * radius #16-vertex curves (4 quadratic Beziers which accounts for worst case scenario of 360 degrees)
rchord = radius * (1-chordwidth)
inter11 = start1*(3./4.)+end1*(1./4.)
inter12 = start1*(2./4.)+end1*(2./4.)
inter13 = start1*(1./4.)+end1*(3./4.)
inter21 = start2*(3./4.)+end2*(1./4.)
inter22 = start2*(2./4.)+end2*(2./4.)
inter23 = start2*(1./4.)+end2*(3./4.)
verts = [
polar2xy(radius, start1),
polar2xy(radius, start1) + polar2xy(opt1, start1+0.5*np.pi),
polar2xy(radius, inter11) + polar2xy(opt1, inter11-0.5*np.pi),
polar2xy(radius, inter11),
polar2xy(radius, inter11),
polar2xy(radius, inter11) + polar2xy(opt1, inter11+0.5*np.pi),
polar2xy(radius, inter12) + polar2xy(opt1, inter12-0.5*np.pi),
polar2xy(radius, inter12),
polar2xy(radius, inter12),
polar2xy(radius, inter12) + polar2xy(opt1, inter12+0.5*np.pi),
polar2xy(radius, inter13) + polar2xy(opt1, inter13-0.5*np.pi),
polar2xy(radius, inter13),
polar2xy(radius, inter13),
polar2xy(radius, inter13) + polar2xy(opt1, inter13+0.5*np.pi),
polar2xy(radius, end1) + polar2xy(opt1, end1-0.5*np.pi),
polar2xy(radius, end1),
polar2xy(rchord, end1),
polar2xy(rchord, start2),
polar2xy(radius, start2),
polar2xy(radius, start2) + polar2xy(opt2, start2+0.5*np.pi),
polar2xy(radius, inter21) + polar2xy(opt2, inter21-0.5*np.pi),
polar2xy(radius, inter21),
polar2xy(radius, inter21),
polar2xy(radius, inter21) + polar2xy(opt2, inter21+0.5*np.pi),
polar2xy(radius, inter22) + polar2xy(opt2, inter22-0.5*np.pi),
polar2xy(radius, inter22),
polar2xy(radius, inter22),
polar2xy(radius, inter22) + polar2xy(opt2, inter22+0.5*np.pi),
polar2xy(radius, inter23) + polar2xy(opt2, inter23-0.5*np.pi),
polar2xy(radius, inter23),
polar2xy(radius, inter23),
polar2xy(radius, inter23) + polar2xy(opt2, inter23+0.5*np.pi),
polar2xy(radius, end2) + polar2xy(opt2, end2-0.5*np.pi),
polar2xy(radius, end2),
polar2xy(rchord, end2),
Expand All @@ -88,15 +169,39 @@ def ChordArc(start1=0, end1=60, start2=180, end2=240, radius=1.0, chordwidth=0.7
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
]

if ax == None:
Expand All @@ -112,11 +217,26 @@ def selfChordArc(start=0, end=60, radius=1.0, chordwidth=0.7, ax=None, color=(1,
start, end = end, start
start *= np.pi/180.
end *= np.pi/180.
opt = 4./3. * np.tan((end-start)/ 4.) * radius
opt = 4./3. * np.tan((end-start)/ 16.) * radius #16-vertex curves (4 quadratic Beziers which accounts for worst case scenario of 360 degrees)
inter1 = start*(3./4.)+end*(1./4.)
inter2 = start*(2./4.)+end*(2./4.)
inter3 = start*(1./4.)+end*(3./4.)
rchord = radius * (1-chordwidth)
verts = [
polar2xy(radius, start),
polar2xy(radius, start) + polar2xy(opt, start+0.5*np.pi),
polar2xy(radius, inter1) + polar2xy(opt, inter1-0.5*np.pi),
polar2xy(radius, inter1),
polar2xy(radius, inter1),
polar2xy(radius, inter1) + polar2xy(opt, inter1+0.5*np.pi),
polar2xy(radius, inter2) + polar2xy(opt, inter2-0.5*np.pi),
polar2xy(radius, inter2),
polar2xy(radius, inter2),
polar2xy(radius, inter2) + polar2xy(opt, inter2+0.5*np.pi),
polar2xy(radius, inter3) + polar2xy(opt, inter3-0.5*np.pi),
polar2xy(radius, inter3),
polar2xy(radius, inter3),
polar2xy(radius, inter3) + polar2xy(opt, inter3+0.5*np.pi),
polar2xy(radius, end) + polar2xy(opt, end-0.5*np.pi),
polar2xy(radius, end),
polar2xy(rchord, end),
Expand All @@ -125,6 +245,18 @@ def selfChordArc(start=0, end=60, radius=1.0, chordwidth=0.7, ax=None, color=(1,
]

codes = [Path.MOVETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Expand All @@ -139,7 +271,7 @@ def selfChordArc(start=0, end=60, radius=1.0, chordwidth=0.7, ax=None, color=(1,
path = Path(verts, codes)
patch = patches.PathPatch(path, facecolor=color+(0.5,), edgecolor=color+(0.4,), lw=LW)
ax.add_patch(patch)

def chordDiagram(X, ax, colors=None, width=0.1, pad=2, chordwidth=0.7):
"""Plot a chord diagram

Expand Down Expand Up @@ -218,7 +350,7 @@ def chordDiagram(X, ax, colors=None, width=0.1, pad=2, chordwidth=0.7):
fig = plt.figure(figsize=(6,6))
flux = np.array([[11975, 5871, 8916, 2868],
[ 1951, 10048, 2060, 6171],
[ 8010, 16145, 8090, 8045],
[ 8010, 16145, 81090, 8045],
[ 1013, 990, 940, 6907]
])

Expand Down