Merge pull request #1 from alhazacod/adding_interactive_functions

Now this is usable lol

Author: alhazacod

.pylintrc

@@ -0,0 +1 @@
+extension-pkg-whitelist=PyQt5

MatrixButtons.py

@@ -0,0 +1,67 @@
+import PyQt5.QtWidgets as QtWidgets
+from matplotlib.figure import Figure
+from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
+from sympy import Matrix
+
+class MatrixButtons(QtWidgets.QWidget):
+    """Widget for PyQt5 with the Matrix input and the buttons
+
+    ...
+
+    Attributes
+    ----------
+    layout: QtWidgets.QGridLayout
+    """
+    def __init__(self):
+        super().__init__()
+        self.layout = QtWidgets.QGridLayout(self) # Set the layout
+
+        #First row
+        self.matrix00 = QtWidgets.QLineEdit()
+        self.matrix10 = QtWidgets.QLineEdit()
+        self.matrix20 = QtWidgets.QLineEdit()
+        self.addToLayout(self.matrix00,[0,0],[1,1])
+        self.addToLayout(self.matrix10,[1,0],[1,1])
+        self.addToLayout(self.matrix20,[2,0],[1,1])
+
+        # Second row
+        self.matrix01 = QtWidgets.QLineEdit()
+        self.matrix11 = QtWidgets.QLineEdit()
+        self.matrix21 = QtWidgets.QLineEdit()
+        self.addToLayout(self.matrix01,[0,1],[1,1])
+        self.addToLayout(self.matrix11,[1,1],[1,1])
+        self.addToLayout(self.matrix21,[2,1],[1,1])
+
+        # Third row
+        self.matrix02 = QtWidgets.QLineEdit()
+        self.matrix12 = QtWidgets.QLineEdit()
+        self.matrix22 = QtWidgets.QLineEdit()
+        self.addToLayout(self.matrix02,[0,2],[1,1])
+        self.addToLayout(self.matrix12,[1,2],[1,1])
+        self.addToLayout(self.matrix22,[2,2],[1,1])
+
+        # Button for plot the grid transformed by the matrix
+        self.plotButton = QtWidgets.QPushButton('Plot')
+        self.addToLayout(self.plotButton,[1,3],[1,1])
+
+        
+    def addToLayout(self, widget, position:list, size:list):
+        self.layout.addWidget(widget,position[1],position[0],size[1],size[0])
+
+    def setMatrix(self,matrix):
+        """Add widget to layout
+        """
+        # First row
+        self.matrix00.setText(str(matrix[0,0]))
+        self.matrix10.setText(str(matrix[0,1]))
+        self.matrix20.setText(str(matrix[0,2]))
+
+        # Second row
+        self.matrix01.setText(str(matrix[1,0]))
+        self.matrix11.setText(str(matrix[1,1]))
+        self.matrix21.setText(str(matrix[1,2]))
+
+        # Third row
+        self.matrix02.setText(str(matrix[2,0]))
+        self.matrix12.setText(str(matrix[2,1]))
+        self.matrix22.setText(str(matrix[2,2]))

Plotting.py

@@ -4,12 +4,10 @@
 
 """
 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
+    """Widget for PyQt5 with the plot
 
     ...
 
@@ -36,13 +34,37 @@ class PlotWidget(QtWidgets.QWidget):
 
     canvas: matplotlib.backends.backend_qt5agg.FigureCanvasQTAgg
     """
-    def __init__(self, x: list, y: list, z: list, colors: tuple, alpha: float):
+    def __init__(self):
         super().__init__()
-        self.fig = Figure()
-        self.canvas = FigureCanvas(self.fig)
-        self.axes = self.fig.add_subplot(111,projection='3d')
+        self.fig = Figure() # Create a matplotlib figure
+        self.canvas = FigureCanvas(self.fig) # Get the plot image
+        self.axes = self.fig.add_subplot(111,projection='3d') # Create matpotlib axes
+
+        self.setWindowTitle('Linear transformations')
+
+        self.layout = QtWidgets.QGridLayout(self) # Set the layout
+
+        self.addToLayout(self.canvas, [0,0],[10,10]) # add the plot to the layout
+
+    def scatter(self,xyzgrid:list,colors:list):
+        """Scatter the data
+    
+        ...
 
-        layout = QtWidgets.QVBoxLayout(self)
-        layout.addWidget(self.canvas)
+        Parameters
+        ----------
+        xyzgrid:list
+            data for plotting
+            xyzgrid[0] the x data
+            xyzgrid[1] the y data
+            xyzgrid[2] the z
+        colors:list
+            colors
+        """
+        self.axes.clear()
+        self.axes.scatter(xyzgrid[0],xyzgrid[1],xyzgrid[2],c = colors,alpha=0.7)
 
-        self.axes.scatter(x, y, z, c = colors, alpha = alpha)
+    def addToLayout(self, widget, position:list = [0,0], size:list = [1,1]):
+        """Add widget to layout
+        """
+        self.layout.addWidget(widget,position[1],position[0],size[1],size[0])

README.md

@@ -0,0 +1,41 @@
+# Linear transformation visualization in 3D
+
+## Why?
+
+A linear transformation is a function from one vector space to another that respects the linear structure of each vector space ([Learn more](https://brilliant.org/wiki/linear-transformations/)). For visualizing this we can transform a vector as we can see in the Fig. 1. 
+
+<figure>
+  <img src="vector_linearTransformation.png" alt="vector transformed" style="width:40%;
+                                                                             display: block;
+                                                                             margin-left: auto;
+                                                                             margin-right: auto;">
+  <figcaption  style="text-align: center;">Fig.1 - Vector transformed with a transformation matrix</figcaption>
+</figure>
+
+But it has an obvious problem, because the linear transformation transform the whole space, not just the vector, in other words it transforms the basis vectors thus every vector in the space gets transformed too. That's why i created this app so everyone can see how a transformation matrix change the whole space.
+
+## Installation guide
+
+### With the executable file
+
+1. Install Python from the [python web](https://www.python.org/).
+2. Download the executable file for your OS (Linux or Windows).
+3. Execute the file.
+4. Start using.
+
+The executable was created with [PyInstaller](http://www.pyinstaller.org/).
+
+### Manual installation
+
+1. Install Python from the [python web](https://www.python.org/).
+2. Install pip from the [pip web](https://pip.pypa.io/en/stable/installing/)
+3. Install the dependences using pip.
+   - pip install sympy
+   - pip install pyqt5
+   - pip install numpy
+4. Download the main.py, Plotting.py and Matrix.py files.
+5. In the console go to the files location
+6. Run the main file with <code>python3.8 main.py</code>
+
+## How to use
+

main.py

@@ -4,20 +4,18 @@
 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
+from sympy import sin,cos,pi,N          #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 PyQt5.QtGui import QFont           #Pyqt5 fonts
 
 from Plotting import PlotWidget         #The plot object
 
-"""Transformation matrix"""
-transformationMatrix = Matrix([[1, 0, 0],
-                               [0, 0.5, 0],
-                               [0, 0, 1]])
+from MatrixButtons import MatrixButtons # Interface class
 
-def transformPoint(x,y,z):
+def transformPoint(x,y,z,transformationMatrix):
     """Return the vector transformed
     
     """
@@ -28,11 +26,10 @@ def colorizer(x, y,z):
     
     """
     r = min(1, 1-y/3)
-    g = min(1, 1+y/3)
+    g = min(1, 1+x/3)
     b = 1/4 + x/16
     return (r, g, b)
 
-
 def get_grid(min,max):
     """Return a grid in x, y and z
     
@@ -51,28 +48,120 @@ def get_grid(min,max):
     xyzgrid = column_stack([[x, y,z] for x in xvals for y in yvals for z in zvals])
     return xyzgrid
 
+def get_transformedGrid(originalGrid, transformationMatrix):
+    """Return a grid in x, y and z transformed
+    
+    ...
+
+    Parameters
+    ----------
+    originalGrid
+        
+    transformationMatrix
+        
+    """
+    transformedGrid = transformPoint(originalGrid[0],originalGrid[1],originalGrid[2],transformationMatrix)
+
+    return array([transformedGrid[0,:][0,:],     #
+                  transformedGrid[1,:][0,:],     # Save the transformed grid as a numpy array 
+                  transformedGrid[2,:][0,:]])    #
+
+def adjust_plot(axes):
+    axes.set_xlim([-2, 2]) #
+    axes.set_ylim([-2, 2]) # Set the limits of the plot
+    axes.set_zlim([-2, 2]) #
+    axes.axis('on')        # Show the axis
+    axes.set_xlabel('x')   #
+    axes.set_ylabel('y')   # Axes names
+    axes.set_zlabel('z')   #
+    axes.grid(True)       # Don't show the grid
+
+def exceptionDialog(msg):
+    dlg = QtWidgets.QErrorMessage()
+    dlg.showMessage(msg)
+    dlg.exec_()
+
+def transformAndPlot(plot,matrix):
+    
+    try:
+        matrix = array(matrix)
+        print(matrix)
+        interface.setMatrix(matrix)
+        xyzgrid = get_transformedGrid(originalGrid, Matrix([[N(matrix[0,0]),N(matrix[0,1]),N(matrix[0,2])],
+                                                            [N(matrix[1,0]),N(matrix[1,1]),N(matrix[1,2])],
+                                                            [N(matrix[2,0]),N(matrix[2,1]),N(matrix[2,2])]])) # get a transformed grid
+        plot.scatter(xyzgrid,colors)
+        adjust_plot(plot.axes)
+        plot.fig.canvas.draw()
+        plot.fig.canvas.flush_events()
+    except:
+        exceptionDialog('An error has ocurred. Remember that you only can write operations between numbers or trigonometric functions in the matrix boxes. ex. sin(3*pi/2) or sqrt(2)/2+5')
+
+def examplesComboBox(window,comboBox):
+    examples = {
+        'Original Grid' :[[1, 0, 0],[0, 1, 0],[0, 0, 1]],
+        'Personalized matrix' :[[1, 0, 0],[0, 1, 0],[0, 0, 1]],
+        'Reflect in X' :[[-1, 0, 0],[0, 1, 0],[0, 0, 1]],
+        'Reflect in Y' :[[1, 0, 0],[0, -1, 0],[0, 0, 1]],
+        'Reflect in Z' :[[1, 0, 0],[0, 1, 0],[0, 0, -1]],
+        'Stretch in Y' :[[1, 0, 0],[0, 2, 0],[0, 0, 1]],
+        'Compact in Y' :[[1, 0, 0],[0, '1/2', 0],[0, 0, 1]],
+        'X rotation 45º' :[[1, 0, 0],[0, 'cos(45*pi/180)', '-sin(45*pi/180)'],[0, 'sin(45*pi/180)', 'cos(45*pi/180)']],
+        'Y rotation 45º' :[['cos(45*pi/180)', '-sin(45*pi/180)', 0],['sin(45*pi/180)', 'cos(45*pi/180)', 0],[0, 0, 1]],
+        'Z rotation 45º' :[['cos(45*pi/180)', 0, '-sin(45*pi/180)'],[0, 1, 0],['sin(45*pi/180)', 0, 'cos(45*pi/180)']],
+        'X-Y rotation 45º-10º':[['cos(45*pi/180)*cos(10*pi/180)','cos(45*pi/180)*sin(10*pi/180)-sin(45*pi/180)','cos(45*pi/180)*sin(10*pi/180)+sin(45*pi/180)*sin(10*pi/180)'],['sin(45*pi/180)*cos(10*pi/180)','sin(45*pi/180)*sin(10*pi/180)+cos(45*pi/180)','sin(45*pi/180)*sin(10*pi/180)-cos(45*pi/180)'],['-sin(10*pi/180)','cos(10*pi/180)','cos(10*pi/180)']],
+        'Only XY dimension' :[[1, 0, 0],[0, 1, 0],[0, 0, 0]],
+        'Only YZ dimension' :[[0, 0, 0],[0, 1, 0],[0, 0, 1]],
+        'Only XZ dimension' :[[1, 0, 0],[0, 0, 0],[0, 0, 1]]
+    }
+    for key in examples:
+        examplesWidget.addItem(key)
+
+    examplesWidget.activated[str].connect(lambda str: transformAndPlot(window,examples.get(str)))
+
+    window.addToLayout(examplesWidget, [13,2],[3,1])
+
+def plotButton(plot,matrix):
+    transformAndPlot(plot,matrix)
+    examplesWidget.setCurrentIndex(1)
+
 if __name__ == "__main__":
+    """Transformation matrix"""
+    transformationMatrix = [[1, 0, 0],
+                            [0, 1, 0],
+                            [0, 0, 1]]
 
-    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,:]])    #
+    originalGrid = get_grid(-2,2) # Create a straigh grid
+    xyzgrid = get_transformedGrid(originalGrid, Matrix(transformationMatrix)) # get a transformed grid
 
     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
+    app = QtWidgets.QApplication([]) # Create the app
+    plot = PlotWidget() # Get the widget where the plot is
+
+    plot.scatter(xyzgrid,colors) # Scatter
+
+    adjust_plot(plot.axes) # Set the limits of the axes
     plot.axes.view_init(10,5)   # View init at 15 and 5 degrees
+    
+    examples_label = QtWidgets.QLabel('Examples')
+    examples_label.setFont(QFont('Sans Serif', 20))
+    plot.addToLayout(examples_label,[12,2],[1,1])
+    examplesWidget = QtWidgets.QComboBox()
+    examplesComboBox(plot,examplesWidget)
+
+    matrix_label = QtWidgets.QLabel('Transformation Matrix')
+    matrix_label.setFont(QFont('Sans Serif', 20))
+    plot.addToLayout(matrix_label,[12,4],[2,1])
+    interface = MatrixButtons() # Get the interface
+    plot.addToLayout(interface,[11,5],[10,2]) # add the interface to the plot layout
+
+    interface.setMatrix(array(transformationMatrix))
+
+    interface.plotButton.clicked.connect(
+        lambda: plotButton(plot,[[interface.matrix00.text(), interface.matrix10.text(), interface.matrix20.text()],
+                                 [interface.matrix01.text(), interface.matrix11.text(), interface.matrix21.text()],
+                                 [interface.matrix02.text(), interface.matrix12.text(), interface.matrix22.text()]]))
 
-    plot.show()
+    plot.show() 
     app.exec()