I have trouble with matplotlib / pyplot / basemap. I plot contour lines (air pressure) on a map. I use clabel to show the value of the contour lines.
But the problem is: the padding between the value and the contour line is too much. I have found the parameter "inline_spacing", which i have set to zero. But there is still to much free space. Any ideas?
Python Code:
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
import pygrib
filename = "file.grib2"
grbs = pygrib.open('/data/' + filename)
grb = grbs[2]
data = grb.values
datac = data*0.01
lats, lons = grb.latlons()
fig = plt.figure()
m = Basemap(projection='stere',lon_0=5,lat_0=90.0,\
llcrnrlon=-25.0,urcrnrlon=60.0,llcrnrlat=30.0,urcrnrlat=60.0,resolution='l')
x, y = m(lons, lats)
levs = range(940,1065,5)
S1=plt.contour(x,y,datac,levs,linewidths=0.5,colors='b')
plt.clabel(S1,inline=1,inline_spacing=0,fontsize=8,fmt='%1.0f',colors='b')
m.drawmapboundary(fill_color='w')
m.drawcoastlines(linewidth=0.2)
plt.savefig('test.png', bbox_inches='tight',pad_inches=0.05, dpi=100)
Thanks.
The "inline_spacing" parameter can be set to negative values. It gave me a warning, but trying -2 or -3 should probably fix your problem.
cb = plt.clabel(S1,inline=1,inline_spacing=0,fontsize=8,fmt='%1.0f',colors='b')
[txt.set_bbox(dict(boxstyle='square,pad=0',fc='red')) for txt in cb]
Matplotlib Text class create a bbox. You need to set the pad = 0.Then inline_spacing works.
Refer to the Question!
Related
This question is adapted from this answer, however the solution provided does not work and following is my result. I am interested in adding individual title on the right side for individual subgraphs.
(p.s no matter how much offset for y-axis i provide the title seems to stay at the same y-value)
from matplotlib import pyplot as plt
import numpy as np
fig, axes = plt.subplots(nrows=2)
ax0label = axes[0].set_ylabel('Axes 0')
ax1label = axes[1].set_ylabel('Axes 1')
title = axes[0].set_title('Title')
offset = np.array([-0.15, 0.0])
title.set_position(ax0label.get_position() + offset)
title.set_rotation(90)
fig.tight_layout()
plt.show()
Something like this? This is the only other way i can think of.
from matplotlib import pyplot as plt
import numpy as np
fig, axes = plt.subplots(nrows=2)
ax0label = axes[0].set_ylabel('Axes 0')
ax1label = axes[1].set_ylabel('Axes 1')
ax01 = axes[0].twinx()
ax02 = axes[1].twinx()
ax01.set_ylabel('title')
ax02.set_ylabel('title')
fig.tight_layout()
plt.show()
Below is the plot I generated using axes.text option,
ax[0].text(row.TIMESTAMP, row.HIGH+(0.1*width),row['candlestick_pattern'], fontsize=5, rotation='vertical')
I'm trying to achieve the same output using TextPath and PathPatch, in order to increase/decrease the font size when I zoom in/out of the plot, and below is the code I have (taken from here and here )
textPath = TextPath((data_coord[1], -data_coord[0]), row['candlestick_pattern'], size=2)
pathPatch = PathPatch(textPath, color="black")
transform = mpl.transforms.Affine2D().rotate_deg(90) + ax[0].transData
pathPatch.set_transform(transform)
ax[0].add_patch(pathPatch)
Output with this is
You could see that the text is cramped into a very small region and its not what I want. I would want to set the font size to a smaller value and increase the width (in vertical mode - height) of the TextPath. Is that possible?
Below is the complete code with which we can reproduce the problem for the dataset here
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.textpath import TextPath
from matplotlib.patches import PathPatch
from mplfinance.original_flavor import candlestick_ohlc
from matplotlib import transforms as tf
import pandas as pd
plotDf = pd.read_csv("data.csv")
plotDf.reset_index(inplace=True)
del plotDf['TIMESTAMP']
del plotDf['TOTTRDQTY']
fig, ax = plt.subplots(1)
candlestick_ohlc(ax,plotDf.values,width=0.6, \
colorup='green', colordown='red', alpha=0.8)
maxHigh = plotDf['HIGH'].max()
minLow = plotDf['LOW'].min()
width = maxHigh - minLow
threshold = (width)*0.6
for idx, row in plotDf.iterrows():
if (row['candlestick_pattern'] != 'NO_PATTERN'):
if (row.HIGH < (threshold+minLow)):
data_coord = (idx, row.HIGH+(0.1*width))
#ax.text(idx, row.HIGH+(0.1*width), row['candlestick_pattern'], fontsize=5, rotation='vertical')
else:
data_coord = (idx, row.LOW-(0.4*width))
#ax.text(idx, row.LOW-(0.4*width), row['candlestick_pattern'], fontsize=5, rotation='vertical')
textPath = TextPath((data_coord[1], -data_coord[0]), row['candlestick_pattern'], size=2)
pathPatch = PathPatch(textPath, color="black")
transform = mpl.transforms.Affine2D().rotate_deg(90) + ax.transData
pathPatch.set_transform(transform)
ax.add_patch(pathPatch)
fig.autofmt_xdate()
fig.tight_layout()
fig.suptitle("test", fontsize=16)
fig.set_size_inches(10.5, 10.5)
plt.subplots_adjust(top=0.95)
plt.show()
Apparently, your problem is a scaling problem. Messing around with .scale(x,y), ax.set_xlim and ax.set_ylim might allow you to "unsqueeze" the text. You can also try to set an anchor for your plot like done here:
ts = ax.transData
coords = ts.transform([0,0]) #<-anchor
tr = mpl.transforms.Affine2D().rotate_deg_around(coords[0],coords[1],90).scale(1,3) #<- scale
t = ts + tr
#<extra code>
pathPatch = PathPatch(textPath, color="black", transform = t)
EDIT
I tried many things, but I couldn't find a good way of doing it. I'll leave below what I tried and some resources that might help.
The way to properly use .rotate_deg_around would be like such:
ts = ax.transData
# ts = fig.dpi_scale_trans #this guy uses the fig scale, if you're interested
coords = ts.transform([data_coord[0],data_coord[1]])
converter = (coords[0]/data_coord[0], coords[1]/data_coord[1])
#plot the anchor points for visualization:
plt.plot(coords[0]/converter[0], coords[1]/converter[1],'xk')
tr = mpl.transforms.Affine2D().rotate_deg_around(coords[0]/converter[0],coords[1]/converter[1],90).scale(converter[0],converter[1])
pathPatch = PathPatch(textPath, color="black", transform = tr)
ax.add_patch(pathPatch)
Nonetheless, the results are still similar to what you had at the beginning:
It appears that TextPath does not behave like it should when using transform. Here .get_offset_transform is used, and it apparently fixes this sort of issue, but I was unable to use it since the plt has a Line type.
Also, you will see that if you increase the y axis in .scale, you can start to see the text, but it spreads the coordinates as well. One idea you can try is setting a good readable y scale (use ax.set_ylim to see your text) and then use that value as a divisor when setting the coordinates for your plot.
There are also some ideas here that might serve you.
I am trying to plot some latitude and longitudes on the map of delhi which I am able to do by using a shape file in python3.8 using geopandas
Here is the link for the shape file:
https://drive.google.com/file/d/1CEScjlcsKFCgdlME21buexHxjCbkb3WE/view?usp=sharing
Following is my code to plot points on the map:
lo=[list of longitudes]
la=[list of latitudes]
delhi_map = gpd.read_file(r'C:\Users\Desktop\Delhi_Wards.shp')
fig,ax = plt.subplots(figsize = (15,15))
delhi_map.plot(ax = ax)
geometry = [Point(xy) for xy in zip(lo,la)]
geo_df = gpd.GeoDataFrame(geometry = geometry)
print(geo_df)
g = geo_df.plot(ax = ax, markersize = 20, color = 'red',marker = '*',label = 'Delhi')
plt.show()
Following is the result:
Now this map is not very clear and anyone will not be able to recognise the places marked so i tried to use basemap for a more detailed map through the following code:
df = gpd.read_file(r'C:\Users\Jojo\Desktop\Delhi_Wards.shp')
new_df = df.to_crs(epsg=3857)
print(df.crs)
print(new_df.crs)
ax = new_df.plot()
ctx.add_basemap(ax)
plt.show()
And following is the result:
I am getting the basemap but my shapefile is overlapping it. Can i get a map to plot my latitudes and longitudes where the map is much more detailed with names of places or roads or anything similar to it like in google maps or even something like the map which is being overlapped by the blue shapefile map?
Is it possible to plot on a map like this??
https://www.researchgate.net/profile/P_Jops/publication/324715366/figure/fig3/AS:618748771835906#1524532611545/Map-of-Delhi-reproduced-from-Google-Maps-12.png
use zorder parameter to adjust the layers' orders (lower zorder means lower layer), and alpha to the polygon. anyway, I guess, you're plotting df twice, that's why it's overlapping.
here's my script and the result
import geopandas as gpd
import matplotlib.pyplot as plt
import contextily as ctx
from shapely.geometry import Point
long =[77.2885437011719, 77.231931, 77.198767, 77.2750396728516]
lat = [28.6877899169922, 28.663863, 28.648287, 28.5429172515869]
geometry = [Point(xy) for xy in zip(long,lat)]
wardlink = "New Folder/wards delimited.shp"
ward = gpd.read_file(wardlink, bbox=None, mask=None, rows=None)
geo_df = gpd.GeoDataFrame(geometry = geometry)
ward.crs = {'init':"epsg:4326"}
geo_df.crs = {'init':"epsg:4326"}
# plot the polygon
ax = ward.plot(alpha=0.35, color='#d66058', zorder=1)
# plot the boundary only (without fill), just uncomment
#ax = gpd.GeoSeries(ward.to_crs(epsg=3857)['geometry'].unary_union).boundary.plot(ax=ax, alpha=0.5, color="#ed2518",zorder=2)
ax = gpd.GeoSeries(ward['geometry'].unary_union).boundary.plot(ax=ax, alpha=0.5, color="#ed2518",zorder=2)
# plot the marker
ax = geo_df.plot(ax = ax, markersize = 20, color = 'red',marker = '*',label = 'Delhi', zorder=3)
ctx.add_basemap(ax, crs=geo_df.crs.to_string(), source=ctx.providers.OpenStreetMap.Mapnik)
plt.show()
I don't know about google maps being in the contextily, I don't think it's available. alternatively, you can use OpenStreetMap base map which shows quite the same toponym, or any other basemap you can explore. use `source` keyword in the argument, for example, `ctx.add_basemap(ax, source=ctx.providers.OpenStreetMap.Mapnik)` . here's how to check the available providers and the map each providers provides:
>>> ctx.providers.keys()
dict_keys(['OpenStreetMap', 'OpenSeaMap', 'OpenPtMap', 'OpenTopoMap', 'OpenRailwayMap', 'OpenFireMap', 'SafeCast', 'Thunderforest', 'OpenMapSurfer', 'Hydda', 'MapBox', 'Stamen', 'Esri', 'OpenWeatherMap', 'HERE', 'FreeMapSK', 'MtbMap', 'CartoDB', 'HikeBike', 'BasemapAT', 'nlmaps', 'NASAGIBS', 'NLS', 'JusticeMap', 'Wikimedia', 'GeoportailFrance', 'OneMapSG'])
>>> ctx.providers.OpenStreetMap.keys()
dict_keys(['Mapnik', 'DE', 'CH', 'France', 'HOT', 'BZH'])
I don't know geopandas. The idea I'm suggesting uses only basic python and matplotlib. I hope you can adapt it to your needs.
The background is the following map. I figured out the GPS coordinates of its corners using google-maps.
The code follows the three points of my remark. Note that the use of imread and imshow reverses the y coordinate. This is why the function coordinatesOnFigur looks non-symmetrical in x and y.
Running the code yields the map with a red bullet near Montijo (there is a small test at the end).
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib import patches
from matplotlib.widgets import Button
NE = (-8.9551, 38.8799)
SE = (-8.9551, 38.6149)
SW = (-9.4068, 38.6149)
NW = (-9.4068, 38.8799)
fig = plt.figure(figsize=(8, 6))
axes = fig.add_subplot(1,1,1, aspect='equal')
img_array = plt.imread("lisbon_2.jpg")
axes.imshow(img_array)
xmax = axes.get_xlim()[1]
ymin = axes.get_ylim()[0] # the y coordinates are reversed, ymax=0
# print(axes.get_xlim(), xmax)
# print(axes.get_ylim(), ymin)
def coordinatesOnFigure(long, lat, SW=SW, NE=NE, xmax=xmax, ymin=ymin):
px = xmax/(NE[0]-SW[0])
qx = -SW[0]*xmax/(NE[0]-SW[0])
py = -ymin/(NE[1]-SW[1])
qy = NE[1]*ymin/(NE[1]-SW[1])
return px*long + qx, py*lat + qy
# plotting a red bullet that corresponds to a GPS location on the map
x, y = coordinatesOnFigure(-9, 38.7)
print("test: on -9, 38.7 we get", x, y)
axes.scatter(x, y, s=40, c='red', alpha=0.9)
plt.show()
I'm trying to plot data around the Antarctica while masking the continent. While I'm using basemap and it has an option to easily mask continents using map.fillcontinents(), the continent considered by basemap includes the ice shelves, which I do not want to mask.
I tried using geopandas from a code I found on the Internet. This works, except the coastline produces an undesired line in what I assume is the beginning/end of the polygon for the Antarctica:
import numpy as np
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
from matplotlib.collections import PatchCollection
import geopandas as gpd
import shapely
from descartes import PolygonPatch
lats = np.arange(-90,-59,1)
lons = np.arange(0,361,1)
X, Y = np.meshgrid(lons, lats)
data = np.random.rand(len(lats),len(lons))
world = gpd.read_file(gpd.datasets.get_path('naturalearth_lowres'))
fig=plt.figure(dpi=150)
ax = fig.add_subplot(111)
m = Basemap(projection='spstere',boundinglat=-60,lon_0=180,resolution='i',round=True)
xi, yi = m(X,Y)
cf = m.contourf(xi,yi,data)
patches = []
selection = world[world.name == 'Antarctica']
for poly in selection.geometry:
if poly.geom_type == 'Polygon':
mpoly = shapely.ops.transform(m, poly)
patches.append(PolygonPatch(mpoly))
elif poly.geom_type == 'MultiPolygon':
for subpoly in poly:
mpoly = shapely.ops.transform(m, poly)
patches.append(PolygonPatch(mpoly))
else:
print(poly, 'blah')
ax.add_collection(PatchCollection(patches, match_original=True,color='w',edgecolor='k'))
The same line appears when I try to use other shapefiles, such as the land one that is available to download for free from Natural Earth Data. So I edited this shapefile in QGIS to remove the borders of the Antarctica. The problem now is that I don't know how to mask everything that's inside the shapefile (and couldn't find how to do it either). I also tried combining the previous code with geopandas by setting the linewidth=0, and adding on top the shapefile I created. The problem is that they are not exactly the same:
Any suggestion on how to mask using a shapefile, or with geopandas but without the line?
Edit: Using Thomas Khün's previous answer with my edited shapefile produces a well masked Antarctica/continents, but the coastline goes outside the round edges of the map:
I uploaded here the edited shapefile I used, but it's the Natural Earth Data 50m land shapefile without the line.
Here an example of how to achieve what you want. I basically followed the Basemap example how to deal with shapefiles and added a bit of shapely magic to restrict the outlines to the map boundaries. Note that I first tried to extract the map outline from ax.patches, but that somehow didn't work, so I defined a circle which has a radius of boundinglat and transformed it using the Basemap coordinate transformation functionality.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
from matplotlib.collections import PatchCollection
from matplotlib.patches import Polygon
import shapely
from shapely.geometry import Polygon as sPolygon
boundinglat = -40
lats = np.arange(-90,boundinglat+1,1)
lons = np.arange(0,361,1)
X, Y = np.meshgrid(lons, lats)
data = np.random.rand(len(lats),len(lons))
fig, ax = plt.subplots(nrows=1, ncols=1, dpi=150)
m = Basemap(
ax = ax,
projection='spstere',boundinglat=boundinglat,lon_0=180,
resolution='i',round=True
)
xi, yi = m(X,Y)
cf = m.contourf(xi,yi,data)
#adjust the path to the shapefile here:
result = m.readshapefile(
'shapefiles/AntarcticaWGS84_contorno', 'antarctica',
zorder = 10, color = 'k', drawbounds = False)
#defining the outline of the map as shapely Polygon:
rim = [np.linspace(0,360,100),np.ones(100)*boundinglat,]
outline = sPolygon(np.asarray(m(rim[0],rim[1])).T)
#following Basemap tutorial for shapefiles
patches = []
for info, shape in zip(m.antarctica_info, m.antarctica):
#instead of a matplotlib Polygon, create first a shapely Polygon
poly = sPolygon(shape)
#check if the Polygon, or parts of it are inside the map:
if poly.intersects(outline):
#if yes, cut and insert
intersect = poly.intersection(outline)
verts = np.array(intersect.exterior.coords.xy)
patches.append(Polygon(verts.T, True))
ax.add_collection(PatchCollection(
patches, facecolor= 'w', edgecolor='k', linewidths=1., zorder=2
))
plt.show()
The result looks like this:
Hope this helps.
For anyone still trying to figure out a simple way to mask a grid from a shapefile, here is a gallery example from the python package Antarctic-Plots which makes this simple.
from antarctic_plots import maps, fetch, utils
import pyogrio
# fetch a grid and shapefile
grid = fetch.bedmachine(layer='surface')
shape = fetch.groundingline()
# subset the grounding line from the coastline
gdf = pyogrio.read_dataframe(shape)
groundingline = gdf[gdf.Id_text == "Grounded ice or land"]
# plot the grid
fig = maps.plot_grd(grid)
# plot the shapefile
fig.plot(groundingline, pen='1p,red')
fig.show()
# mask the inside region
masked_inside = utils.mask_from_shp(
shapefile=groundingline, xr_grid=grid, masked=True)
masked_inside.plot()
# mask the outside region
masked_outside = utils.mask_from_shp(
shapefile=groundingline, xr_grid=grid, masked=True, invert=False)
masked_outside.plot()
How does one set the color of a line in matplotlib with scalar values provided at run time using a colormap (say jet)? I tried a couple of different approaches here and I think I'm stumped. values[] is a storted array of scalars. curves are a set of 1-d arrays, and labels are an array of text strings. Each of the arrays have the same length.
fig = plt.figure()
ax = fig.add_subplot(111)
jet = colors.Colormap('jet')
cNorm = colors.Normalize(vmin=0, vmax=values[-1])
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=jet)
lines = []
for idx in range(len(curves)):
line = curves[idx]
colorVal = scalarMap.to_rgba(values[idx])
retLine, = ax.plot(line, color=colorVal)
#retLine.set_color()
lines.append(retLine)
ax.legend(lines, labels, loc='upper right')
ax.grid()
plt.show()
The error you are receiving is due to how you define jet. You are creating the base class Colormap with the name 'jet', but this is very different from getting the default definition of the 'jet' colormap. This base class should never be created directly, and only the subclasses should be instantiated.
What you've found with your example is a buggy behavior in Matplotlib. There should be a clearer error message generated when this code is run.
This is an updated version of your example:
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import matplotlib.cm as cmx
import numpy as np
# define some random data that emulates your indeded code:
NCURVES = 10
np.random.seed(101)
curves = [np.random.random(20) for i in range(NCURVES)]
values = range(NCURVES)
fig = plt.figure()
ax = fig.add_subplot(111)
# replace the next line
#jet = colors.Colormap('jet')
# with
jet = cm = plt.get_cmap('jet')
cNorm = colors.Normalize(vmin=0, vmax=values[-1])
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=jet)
print scalarMap.get_clim()
lines = []
for idx in range(len(curves)):
line = curves[idx]
colorVal = scalarMap.to_rgba(values[idx])
colorText = (
'color: (%4.2f,%4.2f,%4.2f)'%(colorVal[0],colorVal[1],colorVal[2])
)
retLine, = ax.plot(line,
color=colorVal,
label=colorText)
lines.append(retLine)
#added this to get the legend to work
handles,labels = ax.get_legend_handles_labels()
ax.legend(handles, labels, loc='upper right')
ax.grid()
plt.show()
Resulting in:
Using a ScalarMappable is an improvement over the approach presented in my related answer:
creating over 20 unique legend colors using matplotlib
I thought it would be beneficial to include what I consider to be a more simple method using numpy's linspace coupled with matplotlib's cm-type object. It's possible that the above solution is for an older version. I am using the python 3.4.3, matplotlib 1.4.3, and numpy 1.9.3., and my solution is as follows.
import matplotlib.pyplot as plt
from matplotlib import cm
from numpy import linspace
start = 0.0
stop = 1.0
number_of_lines= 1000
cm_subsection = linspace(start, stop, number_of_lines)
colors = [ cm.jet(x) for x in cm_subsection ]
for i, color in enumerate(colors):
plt.axhline(i, color=color)
plt.ylabel('Line Number')
plt.show()
This results in 1000 uniquely-colored lines that span the entire cm.jet colormap as pictured below. If you run this script you'll find that you can zoom in on the individual lines.
Now say I want my 1000 line colors to just span the greenish portion between lines 400 to 600. I simply change my start and stop values to 0.4 and 0.6 and this results in using only 20% of the cm.jet color map between 0.4 and 0.6.
So in a one line summary you can create a list of rgba colors from a matplotlib.cm colormap accordingly:
colors = [ cm.jet(x) for x in linspace(start, stop, number_of_lines) ]
In this case I use the commonly invoked map named jet but you can find the complete list of colormaps available in your matplotlib version by invoking:
>>> from matplotlib import cm
>>> dir(cm)
A combination of line styles, markers, and qualitative colors from matplotlib:
import itertools
import matplotlib as mpl
import matplotlib.pyplot as plt
N = 8*4+10
l_styles = ['-','--','-.',':']
m_styles = ['','.','o','^','*']
colormap = mpl.cm.Dark2.colors # Qualitative colormap
for i,(marker,linestyle,color) in zip(range(N),itertools.product(m_styles,l_styles, colormap)):
plt.plot([0,1,2],[0,2*i,2*i], color=color, linestyle=linestyle,marker=marker,label=i)
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.,ncol=4);
UPDATE: Supporting not only ListedColormap, but also LinearSegmentedColormap
import itertools
import matplotlib.pyplot as plt
Ncolors = 8
#colormap = plt.cm.Dark2# ListedColormap
colormap = plt.cm.viridis# LinearSegmentedColormap
Ncolors = min(colormap.N,Ncolors)
mapcolors = [colormap(int(x*colormap.N/Ncolors)) for x in range(Ncolors)]
N = Ncolors*4+10
l_styles = ['-','--','-.',':']
m_styles = ['','.','o','^','*']
fig,ax = plt.subplots(gridspec_kw=dict(right=0.6))
for i,(marker,linestyle,color) in zip(range(N),itertools.product(m_styles,l_styles, mapcolors)):
ax.plot([0,1,2],[0,2*i,2*i], color=color, linestyle=linestyle,marker=marker,label=i)
ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.,ncol=3,prop={'size': 8})
U may do as I have written from my deleted account (ban for new posts :( there was). Its rather simple and nice looking.
Im using 3-rd one of these 3 ones usually, also I wasny checking 1 and 2 version.
from matplotlib.pyplot import cm
import numpy as np
#variable n should be number of curves to plot (I skipped this earlier thinking that it is obvious when looking at picture - sorry my bad mistake xD): n=len(array_of_curves_to_plot)
#version 1:
color=cm.rainbow(np.linspace(0,1,n))
for i,c in zip(range(n),color):
ax1.plot(x, y,c=c)
#or version 2: - faster and better:
color=iter(cm.rainbow(np.linspace(0,1,n)))
c=next(color)
plt.plot(x,y,c=c)
#or version 3:
color=iter(cm.rainbow(np.linspace(0,1,n)))
for i in range(n):
c=next(color)
ax1.plot(x, y,c=c)
example of 3:
Ship RAO of Roll vs Ikeda damping in function of Roll amplitude A44