How to make an irregular quadrilateral shaped button in kivy python?

You can extend Button to behave as though it is two Buttons:

class MyButton(Button):
    my_state = StringProperty('')  # this will be 'b1' or 'b2', even when button is not down
    my_down_image = StringProperty('')
    def on_touch_down(self, touch):
        if self.collide_point(*touch.pos):
            rx, ry = self.to_widget(*touch.pos, relative=True)
            if ry > self.height/2.0:  # more complex geometry calculation required
                self.my_down_image = 'B2Down.png'
                self.my_state = 'b2'
            else:
                self.my_down_image = 'B1Down.png'
                self.my_state = 'b1'
        return super(MyButton, self).on_touch_down(touch)

The MyButton class adds two properties to Button, the my_state andmy_down_image properties. The my_state property will be b1 or b2 depending on which sub-button was pressed (set by on_touch_down()). The my_down_image property is set to either B1Down.png or B2Down.png which depict what we want the MyButton to look like when B1 or B2 is pressed. The simple y-coordinate compare that is in the above code will not work, and must be more complicated to correctly determine which sub-button was pressed. The MyButton can be used in kv like this:

MyButton:
    background_normal: 'B1andB2.png'
    on_press: app.do_butt_press(self)
    on_release: app.do_butt_release(self)

where the app methods look like:

def do_butt_press(self, button):
    print('on_butt_press', button.state, button.my_state)

def do_butt_release(self, button):
    print('on_butt_release', button.state, button.my_state)

and in kv:

<-MyButton>:
    state_image: self.background_normal if self.state == 'normal' else self.my_down_image
    disabled_image: self.background_disabled_normal if self.state == 'normal' else self.background_disabled_down
    canvas:
        Color:
            rgba: self.background_color
        BorderImage:
            border: self.border
            pos: self.pos
            size: self.size
            source: self.disabled_image if self.disabled else self.state_image
        Color:
            rgba: 1, 1, 1, 1
        Rectangle:
            texture: self.texture
            size: self.texture_size
            pos: int(self.center_x - self.texture_size[0] / 2.), int(self.center_y - self.texture_size[1] / 2.)

The above kv rule is mostly just a copy of the default Button rule used by Kivy. The only change is the use of my_down_image in the state_image definition.

For this example, the B1andB2.png can be:

B1Down.png:

and B2Down.png: