Density and Contour Plots

Density and Contour Plots

• It is useful to display three-dimensional data in two dimensions using contours or color- coded regions. Three Matplotlib functions are used for this purpose. They are :

a) plt.contour for contour plots,

b) plt.contourf for filled contour plots,

c) plt.imshow for showing images.

1. Contour plot :

• A contour line or isoline of a function of two variables is a curve along which the function has a constant value. It is a cross-section of the three-dimensional graph of the function f(x, y) parallel to the x, y plane.

• Contour lines are used e.g. in geography and meteorology. In cartography, a contour line joins points of equal height above a given level, such as mean sea level.

• We can also say in a more general way that a contour line of a function with two variables is a curve which connects points with the same values.

import numpy as np

xlist = np.linspace(-3.0, 3.0, 3)

ylist = np.linspace(-3.0, 3.0, 4)

X, Y = np.meshgrid(xlist, ylist

print(xlist)

print(ylist)

print(X)

print(Y)

Output:

Changing the colours and the line style

importmatplotlib.pyplot as plt

plt.figure()

cp = plt.contour(X, Y, Z, colors='black', linestyles='dashed')

plt.clabel(cp, inline=True,

fontsize=10)

plt.title('Contour Plot')

plt.xlabel('x (cm))

plt.ylabel('y (cm)')

plt.show()

Output:

• When creating a contour plot, we can also specify the color map. There are different classes of color maps. Matplotlib gives the following guidance :

a) Sequential: Change in lightness and often saturation of color incrementally, often using a single hue; should be used for representing information that has ordering.

b) Diverging: Change in lightness and possibly saturation of two different colors that meet in the middle at an unsaturated color; should be used when the information being plotted has a critical middle value, such as topography or when the data deviates around zero.

c) Cyclic : Change in lightness of two different colors that meet in the middle and beginning/end at an unsaturated color; should be used for values that wrap around at the endpoints, such as phase angle, wind direction, or time of day.

d) Qualitative: Often are miscellaneous colors; should be used to represent information which does not have ordering or relationships.

• This data has both positive and negative values, which zero representing a node for the wave function. There are three important display options for contour plots: the undisplaced shape key, the scale factor, and the contour scale.

a) The displaced shape option controls if and how the deformed model is shown in comparison to the undeformed (original) geometry. The "Deformed shape only" is the default and provides no basis for comparison.

b) The "Deformed shape with undeformed edge" option overlays the contour plot on an outline of the original model.

c) The "Deformed shape with undeformed model" option overlays the contour plot on the original finite element model.