$$ \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\rpos}{\boldsymbol{r}} \newcommand{\ii}{\boldsymbol{i}} \newcommand{\jj}{\boldsymbol{j}} \newcommand{\ir}{\boldsymbol{i}_r} \newcommand{\ith}{\boldsymbol{i}_{\theta}} $$
Using Pysketcher to Create Principal Sketches of Physics Problems

 

 

 

Basic shapes

This section presents many of the basic shapes in Pysketcher: Axis, Distance_wText, Rectangle, Triangle, Arc, Spring, Dashpot, and Wavy. Each shape is demonstrated with a figure and a unit test that shows how the figure is constructed in Python code. These demos rely heavily on the method draw_dimensions in the shape classes, which annotates the basic drawing of the shape with the various geometric parameters that govern the shape.

Axis

The Axis object gives the possibility draw a single axis to notify a coordinate system. Here is an example where we draw \( x \) and \( y \) axis of three coordinate systems of different rotation:





The corresponding code looks like this: 

def test_Axis():
    drawing_tool.set_coordinate_system(
        xmin=0, xmax=15, ymin=-7, ymax=8, axis=True,
        instruction_file='tmp_Axis.py')
    # Draw normal x and y axis with origin at (7.5, 2)
    # in the coordinate system of the sketch: [0,15]x[-7,8]
    x_axis = Axis((7.5,2), 5, 'x', rotation_angle=0)
    y_axis = Axis((7.5,2), 5, 'y', rotation_angle=90)
    system = Composition({'x axis': x_axis, 'y axis': y_axis})
    system.draw()
    drawing_tool.display()

    # Rotate this system 40 degrees counter clockwise
    # and draw it with dashed lines
    system.set_linestyle('dashed')
    system.rotate(40, (7.5,2))
    system.draw()
    drawing_tool.display()

    # Rotate this system another 220 degrees and show
    # with dotted lines
    system.set_linestyle('dotted')
    system.rotate(220, (7.5,2))
    system.draw()
    drawing_tool.display()

    drawing_tool.display('Axis')

Distance with text

The object Distance_wText is used to display an arrow, to indicate a distance in a sketch, with an additional text in the middle of the arrow.

The figure





was produced by this code: 

def test_Distance_wText():
    drawing_tool.set_coordinate_system(
        xmin=0, xmax=10, ymin=0, ymax=6,
        axis=True, instruction_file='tmp_Distance_wText.py')

    fontsize=14
    t = r'$ 2\pi R^2 $'  # sample text
    examples = Composition({
        'a0': Distance_wText((4,5), (8, 5), t, fontsize),
        'a6': Distance_wText((4,5), (4, 4), t, fontsize),
        'a1': Distance_wText((0,2), (2, 4.5), t, fontsize),
        'a2': Distance_wText((0,2), (2, 0), t, fontsize),
        'a3': Distance_wText((2,4.5), (0, 5.5), t, fontsize),
        'a4': Distance_wText((8,4), (10, 3), t, fontsize,
                             text_spacing=-1./60),
        'a5': Distance_wText((8,2), (10, 1), t, fontsize,
                             text_spacing=-1./40, alignment='right'),
        'c1': Text_wArrow('text_spacing=-1./60',
                          (4, 3.5), (9, 3.2),
                          fontsize=10, alignment='left'),
        'c2': Text_wArrow('text_spacing=-1./40, alignment="right"',
                          (4, 0.5), (9, 1.2),
                          fontsize=10, alignment='left'),
        })
    examples.draw()
    drawing_tool.display('Distance_wText and text positioning')

Note the use of Text_wArrow to write an explaining text with an associated arrow, here used to explain how the text_spacing and alignment arguments can be used to adjust the appearance of the text that goes with the distance arrow.

Rectangle



The above figure can be produced by the following code. 

def test_Rectangle():
    L = 3.0
    W = 4.0

    drawing_tool.set_coordinate_system(
        xmin=0, xmax=2*W, ymin=-L/2, ymax=2*L,
        axis=True, instruction_file='tmp_Rectangle.py')
    drawing_tool.set_linecolor('blue')
    drawing_tool.set_grid(True)

    xpos = W/2
    r = Rectangle(lower_left_corner=(xpos,0), width=W, height=L)
    r.draw()
    r.draw_dimensions()
    drawing_tool.display('Rectangle')

Note that the draw_dimension method adds explanation of dimensions and various important argument in the construction of a shape. It adapts the annotations to the geometry of the current shape.

Triangle



The code below produces the figure. 

def test_Triangle():
    L = 3.0
    W = 4.0

    drawing_tool.set_coordinate_system(
        xmin=0, xmax=2*W, ymin=-L/2, ymax=1.2*L,
        axis=True, instruction_file='tmp_Triangle.py')
    drawing_tool.set_linecolor('blue')
    drawing_tool.set_grid(True)

    xpos = 1
    t = Triangle(p1=(W/2,0), p2=(3*W/2,W/2), p3=(4*W/5.,L))
    t.draw()
    t.draw_dimensions()
    drawing_tool.display('Triangle')

Here, the draw_dimension method writes the name of the corners at the position of the corners, which does not always look nice (the present figure is an example). For a high-quality sketch one would add some spacing to the location of the p1, p2, and even p3 texts.

Arc



An arc like the one above is produced by 

def test_Arc():
    L = 4.0
    W = 4.0

    drawing_tool.set_coordinate_system(
        xmin=-W/2, xmax=W, ymin=-L/2, ymax=1.5*L,
        axis=True, instruction_file='tmp_Arc.py')
    drawing_tool.set_linecolor('blue')
    drawing_tool.set_grid(True)

    center = point(0,0)
    radius = L/2
    start_angle = 60
    arc_angle = 45
    a = Arc(center, radius, start_angle, arc_angle)
    a.draw()

    R1 = 1.25*radius
    R2 = 1.5*radius
    R = 2*radius
    a.dimensions = {
        'start_angle':
        Arc_wText(
            'start_angle', center, R1, start_angle=0,
            arc_angle=start_angle, text_spacing=1/10.),
        'arc_angle':
        Arc_wText(
            'arc_angle', center, R2, start_angle=start_angle,
            arc_angle=arc_angle, text_spacing=1/20.),
        'r=0':
        Line(center, center +
             point(R*cos(radians(start_angle)),
                   R*sin(radians(start_angle)))),
        'r=start_angle':
        Line(center, center +
             point(R*cos(radians(start_angle+arc_angle)),
                   R*sin(radians(start_angle+arc_angle)))),
        'r=start+arc_angle':
        Line(center, center +
             point(R, 0)).set_linestyle('dashed'),
        'radius': Distance_wText(center, a(0), 'radius', text_spacing=1/40.),
        'center': Text('center', center-point(radius/10., radius/10.)),
        }
    for dimension in a.dimensions:
        if dimension.startswith('r='):
            dim = a.dimensions[dimension]
            dim.set_linestyle('dashed')
            dim.set_linewidth(1)
            dim.set_linecolor('black')

    a.draw_dimensions()
    drawing_tool.display('Arc')

Spring



The code for making these two springs goes like this: 

def test_Spring():
    L = 5.0
    W = 2.0

    drawing_tool.set_coordinate_system(
        xmin=0, xmax=7*W, ymin=-L/2, ymax=1.5*L,
        axis=True, instruction_file='tmp_Spring.py')
    drawing_tool.set_linecolor('blue')
    drawing_tool.set_grid(True)

    xpos = W
    s1 = Spring((W,0), L, teeth=True)
    s1_title = Text('Default Spring',
                    s1.geometric_features()['end'] + point(0,L/10))
    s1.draw()
    s1_title.draw()
    #s1.draw_dimensions()
    xpos += 3*W
    s2 = Spring(start=(xpos,0), length=L, width=W/2.,
                bar_length=L/6., teeth=False)
    s2.draw()
    s2.draw_dimensions()
    drawing_tool.display('Spring')

Dashpot



This dashpot is produced by 

def test_Dashpot():
    L = 5.0
    W = 2.0
    xpos = 0

    drawing_tool.set_coordinate_system(
        xmin=xpos, xmax=xpos+5.5*W, ymin=-L/2, ymax=1.5*L,
        axis=True, instruction_file='tmp_Dashpot.py')
    drawing_tool.set_linecolor('blue')
    drawing_tool.set_grid(True)

    # Default (simple) dashpot
    xpos = 1.5
    d1 = Dashpot(start=(xpos,0), total_length=L)
    d1_title = Text('Dashpot (default)',
                    d1.geometric_features()['end'] + point(0,L/10))
    d1.draw()
    d1_title.draw()

    # Dashpot for animation with fixed bar_length, dashpot_length and
    # prescribed piston_pos
    xpos += 2.5*W
    d2 = Dashpot(start=(xpos,0), total_length=1.2*L, width=W/2,
                 bar_length=W, dashpot_length=L/2, piston_pos=2*W)
    d2.draw()
    d2.draw_dimensions()

    drawing_tool.display('Dashpot')

Wavy

Looks strange. Fix x axis.

Stochastic curves

The StochasticWavyCurve object offers three precomputed graphics that have a random variation:





The usage is simple. The construction 

curve = StochasticWavyCurve(curve_no=1, percentage=40)

picks the second curve (the three are numbered 0, 1, and 2), and the first 40% of that curve. In case one desires another extent of the axis, one can just scale the coordinates directly as these are stored in the arrays curve.x[curve_no] and curve.y[curve_no].