Update README.md

README.md

@@ -9,7 +9,13 @@ Module for plotting complex-valued functions of complex variable using different
 
 ## Examples gallery
 
-The code for generating the following examples can be found at [`examples.py`](examples.py).
+A script for generating the following examples can be found at [`examples.py`](examples.py).
+
+To use this module just place the script [`cplotting_tools.py`](cplotting_tools.py) in your working directory. It can be imported like this:
+
+```python
+import cplotting_tools as cplt
+```
 
 ### Examples 1 
 
@@ -18,22 +24,54 @@ In this first set of examples the test function is the following one:
 <img src="https://render.githubusercontent.com/render/math?math=f(z)%20%3D%20%5Cfrac%7B(z%5E2-1)(z-2-i)%5E2%7D%7Bz%5E2%2B2%2B2i%7D">
 </p>
 
-![](cplotting-images/domain_coloring.png) |  ![](cplotting-images/domain_coloring_cmap.png)
-| ------------- | ------------- |
-![](cplotting-images/domain_coloring_illum.png)  |  ![](cplotting-images/domain_coloring_illum_logbrightness.png)
-![](cplotting-images/plot3D_logmodeFalse.png)  |  ![](cplotting-images/plot3D.png)
-![](cplotting-images/re_im.png)  |  ![](cplotting-images/re_im_contour.png)
-![](cplotting-images/streamplot.png)  |  ![](cplotting-images/streamplot_modulus_lines.png)
-![](cplotting-images/real_contour.png)  |  ![](cplotting-images/imag_contour.png)
-![](cplotting-images/mod_contour.png)  |  ![](cplotting-images/both_contour.png)
+We start defining the variables and parameters for these first examples:
+
+```python
+N = 100
+lim = 3
+x, y = np.meshgrid(np.linspace(-lim,lim,N), 
+                   np.linspace(-lim,lim,N))
+z = x + 1j*y
+```
+
+The code of the function <img src="https://render.githubusercontent.com/render/math?math=f">, `f`, and its set of poles and zeros, `pts`, looks like this:
 
+```python
+f = (z**2-1)*(z-2-1j)**2/(z**2+2+2j)
+pts = [-1, 1, 2+1j, 2**(3/4)*np.exp(1j*(5*np.pi/8)), 2**(3/4)*np.exp(1j*(5*np.pi/8+np.pi))]
+```
+
+Then, we can use the functions defined in [`cplotting_tools.py`](cplotting_tools.py) to generate, for example, the following plots:
+
+![](cplotting-images/domain_coloring.png) <br> `cplt.domain_coloring(x, y, f, cmap="hsv")` |  ![](cplotting-images/domain_coloring_cmap.png) <br> `cplt.domain_coloring(x, y, f, cmap="twilight_r")`
+| :-------------: | :-------------: |
+![](cplotting-images/domain_coloring_illum.png) <br> **`cplt.domain_coloring_illuminated(x, y, f, log_brightness=False)`** |  ![](cplotting-images/domain_coloring_illum_logbrightness.png) <br> **`cplt.domain_coloring_illuminated(x, y, f)`**
+![](cplotting-images/plot3D_logmodeFalse.png)  <br> **`cplt.complex_plot3D(x, y, f, log_mode=False)`** |  ![](cplotting-images/plot3D.png) <br> **`cplt.complex_plot3D(x, y, f, log_mode=True)`**
+![](cplotting-images/re_im.png) <br> **`cplt.plot_re_im(x, y, f, cmap="twilight", contour=False, alpha=0.9)`** |  ![](cplotting-images/re_im_contour.png) <br> **`cplt.plot_re_im(x, y, f, cmap="twilight", contour=True, alpha=0.9)`**
+![](cplotting-images/streamplot.png) <br> **`cplt.complex_streamplot(x, y, f, mod_as_linewidths=False, cmap="twilight_r", density=2, scatterpoints=pts)`** |  ![](cplotting-images/streamplot_modulus_lines.png) <br> **`cplt.complex_streamplot(x, y, f, mod_as_linewidths=True, cmap="twilight_r", density=2, scatterpoints=pts)`**
+![](cplotting-images/real_contour.png) <br> **`cplt.complex_contour(x, y, f, mode="real", levels=np.arange(0,21,1), lw=2, cmap="coolwarm", scatterpoints=pts)`** |  ![](cplotting-images/imag_contour.png) <br> **`cplt.complex_contour(x, y, f, mode="imag", levels=np.arange(0,21,1), lw=2, cmap="coolwarm", scatterpoints=pts)`**
+![](cplotting-images/mod_contour.png) <br> **`cplt.complex_contour(x, y, f, mode="modulus", levels=np.arange(0,21,1), lw=2, cmap="coolwarm", scatterpoints=pts)`** |  ![](cplotting-images/both_contour.png) <br> **`cplt.complex_contour(x, y, f, mode="both", levels=np.arange(0,21,1), lw=2, cmap="coolwarm", scatterpoints=pts)`**
+
+
 ### Examples 2 
 
 In this second set of examples the test function is:
 <p align="center">
 <img src="https://render.githubusercontent.com/render/math?math=f(z)%20%3D%20%5Ccos%20z">
 </p>
 
-![](cplotting-images/vector_cos.png)  |  ![](cplotting-images/vector_cmap_cos.png)
-| ------------- | ------------- |
-![](cplotting-images/vector_normalized_cos.png)  |  ![](cplotting-images/vector_cmap_normalized_cos.png)
+As we did in the first set of examples, we start defining the variables, the parameters and the function:
+
+```python
+N = 40
+lim = 6
+x, y = np.meshgrid(np.linspace(-lim,lim,N), 
+                    np.linspace(-lim,lim,N))
+z = x + 1j*y
+f = np.cos(z)
+```
+Then, we could obtain the following plots:
+
+![](cplotting-images/vector_cos.png) <br> `cplt.complex_vector_field(x, y, f, norm=False)`  |  ![](cplotting-images/vector_cmap_cos.png) <br> `cplt.complex_vector_field(x, y, f, cmap="hsv", norm=False)`
+| :-------------: | :-------------: |
+![](cplotting-images/vector_normalized_cos.png) <br> **`cplt.complex_vector_field(x, y, f, norm=True)`** |  ![](cplotting-images/vector_cmap_normalized_cos.png) <br> **`cplt.complex_vector_field(x, y, f, cmap="hsv", norm=True)`**