Transformation matrix app created

- Can display the app with pyqt5
- It can show the plot of a 3d grid with colors
- It can transform the space with a given transformation matrix

TODO:
- Default colors and alpha when the PlotWidget class is created (maybe)
- Create a way to replot the grid while the app is running

Author: alhazacod

Plotting.py

@@ -0,0 +1,48 @@
+import PyQt5.QtWidgets as QtWidgets
+from matplotlib.figure import Figure
+from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
+
+"""
+TODO:
+    - I should add the option of default colors and alpha but i couldn't, it's something to fix
+"""
+class PlotWidget(QtWidgets.QWidget):
+    """
+
+    Widget for PyQt5 with the plot
+
+    ...
+
+    Parameters
+    ----------
+    x: list
+        List with the x values
+    y: list
+        List with the y values
+    z: list
+        List with the z values
+    colors: tuple
+        Tuple with the RGB colors
+    alpha: float
+        The transparency of the plot
+
+    ...
+
+    Attributes
+    ----------
+    fig: matplotlib.figure
+
+    axes:  matplotlib.axes
+
+    canvas: matplotlib.backends.backend_qt5agg.FigureCanvasQTAgg
+    """
+    def __init__(self, x: list, y: list, z: list, colors: tuple, alpha: float):
+        super().__init__()
+        self.fig = Figure()
+        self.canvas = FigureCanvas(self.fig)
+        self.axes = self.fig.add_subplot(111,projection='3d')
+
+        layout = QtWidgets.QVBoxLayout(self)
+        layout.addWidget(self.canvas)
+
+        self.axes.scatter(x, y, z, c = colors, alpha = alpha)

main.py

@@ -0,0 +1,78 @@
+"""
+Visualization of the tranformation matrix
+Author: Manuel Garcia
+Date: January 27 2021
+"""
+from sympy.matrices import Matrix       #It's easier work with matrices in sympy than numpy
+from sympy import sin,cos,pi            #Trigonometric functions
+import matplotlib.pyplot as plt         #Plotting
+from numpy import linspace,column_stack,array #For create the linspace for the plotting
+
+import PyQt5.QtWidgets as QtWidgets     #Python GUI
+
+from Plotting import PlotWidget         #The plot object
+
+"""Transformation matrix"""
+transformationMatrix = Matrix([[1, 0, 0],
+                               [0, 0.5, 0],
+                               [0, 0, 1]])
+
+def transformPoint(x,y,z):
+    """Return the vector transformed
+    
+    """
+    return transformationMatrix*Matrix([x,y,z])
+
+def colorizer(x, y,z):
+    """Color the points in the space by their position
+    
+    """
+    r = min(1, 1-y/3)
+    g = min(1, 1+y/3)
+    b = 1/4 + x/16
+    return (r, g, b)
+
+
+def get_grid(min,max):
+    """Return a grid in x, y and z
+    
+    ...
+
+    Parameters
+    ----------
+    min
+        minimum value in the x,y and z axes
+    max
+        maximum value in the x,y and z axes
+    """
+    xvals = linspace(min, max, abs(min-max)+1)
+    yvals = linspace(min, max, abs(min-max)+1)
+    zvals = linspace(min, max, abs(min-max)+1)
+    xyzgrid = column_stack([[x, y,z] for x in xvals for y in yvals for z in zvals])
+    return xyzgrid
+
+if __name__ == "__main__":
+
+    originalGrid = get_grid(-2,2)
+    transformedGrid = transformPoint(originalGrid[0],originalGrid[1],originalGrid[2])
+    xyzgrid = array([transformedGrid[0,:][0,:],     #
+                     transformedGrid[1,:][0,:],     # Save the transformed grid as a numpy array 
+                     transformedGrid[2,:][0,:]])    #
+
+    colors = list(map(colorizer, originalGrid[0], originalGrid[1], originalGrid[2])) # Asign the colors to the points
+
+    app = QtWidgets.QApplication([])
+    plot = PlotWidget(xyzgrid[0], xyzgrid[1], xyzgrid[2], colors = colors, alpha = 0.7)
+
+    plot.axes.set_xlim([-2, 2]) #
+    plot.axes.set_ylim([-2, 2]) # Set the limits of the plot
+    plot.axes.set_zlim([-2, 2]) #
+    plot.axes.axis('on')        # Show the axis
+    plot.axes.set_xlabel('x')   #
+    plot.axes.set_ylabel('y')   # Axes names
+    plot.axes.set_zlabel('z')   #
+    plot.axes.grid(False)       # Don't show the grid
+    plot.axes.view_init(10,5)   # View init at 15 and 5 degrees
+
+    plot.show()
+    app.exec()