Vector Adventure Lab Finished Product: http://f.cl.ly/items/2U1q1r1o2d1a0q2I453S/12.10.04%20Vector%20Adventure%20Lab.pdf

12.10.04 Vector Adventure Lab.py

# Included in LaTeX document, but also I put it here for better code highlighting

import math
import operator
import itertools
import numpy


def polar_to_cartesian(point):
    r, theta = point
    theta = 90 - theta
    x = r * math.cos(math.radians(theta))
    y = r * math.sin(math.radians(theta))
    return (x, y)


def cartesian_to_polar(point):
    x, y = point
    theta = 90 - numpy.angle(complex(x,y), deg=True)
    r = numpy.hypot(x, y)
    return (r, theta)


def add_points(points):
    return sum(map(numpy.array, map(polar_to_cartesian, points)))


def draw_vector(old_coordinate, polar_vector, label, style='', position='above'):
    old_coordinate = numpy.around(old_coordinate, 2)
    cartesian_vector = numpy.around(polar_to_cartesian(polar_vector), 2)
    new_coordinate = numpy.around(old_coordinate + cartesian_vector, 2)
    halfway_coordinate = numpy.around(old_coordinate + (cartesian_vector / 2), 2)
    polar_vector = numpy.around(polar_vector, 2)
    print(r'''
    \addplot[
        quiver={{
            u={cartesian_v[0]},
            v={cartesian_v[1]},
            every arrow/.append style={{
                line width=2pt,{style}
            }},
        }},
        -stealth
    ]
    coordinates {{ ({old_c[0]}, {old_c[1]})}};
    \addlegendentry{{$\vec{{{label}}}={polar_v[0]}\unit{{ft}}; {polar_v[1]}\degree$}}
    \node[coordinate, pin={position}:$\vec{{{label}}}$]
        at (axis cs:{halfway_c[0]},{halfway_c[1]}) {{}};
    '''.format(old_c=old_coordinate, cartesian_v=cartesian_vector,
               polar_v=polar_vector, new_c=new_coordinate, label=label,
               style=style, position=position, halfway_c=halfway_coordinate))

polar_vectors = [
    (0, 0),
    (17, 290),
    (24, 155),
    (24, 65),
    (8.5, 290)]
vector_names = ['A', 'B', 'C', 'D']
for n in range(1, len(polar_vectors)):
    old_coordinate = add_points(polar_vectors[:n])
    label = vector_names[n - 1]
    draw_vector(old_coordinate, polar_vectors[n], label=label)

displacement_vector = numpy.array((12.5 * 2.08, 28))
draw_vector(numpy.array((0, 0)),
            displacement_vector,
            label='displacement',
            position='left')

last_calculate_point = add_points(polar_vectors)
displacement_to_last_calculate_vector = polar_to_cartesian(displacement_vector) - last_calculate_point
draw_vector(last_calculate_point,
            cartesian_to_polar(displacement_to_last_calculate_vector),
            'error',
            'style={loosely dashed}',
            'right')

12.10.04 Vector Adventure Lab.tex

\documentclass[11pt, oneside]{article}      % use "amsart" instead of "article" for AMSLaTeX format
\usepackage{geometry}                       % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                          % ... or a4paper or a5paper or ...
\geometry{landscape}                       % Activate for for rotated page geometry
%\usepackage[parfill]{parskip}          % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}               % Use pdf, png, jpg, or eps§ with pdflatex; use eps in DVI mode
                                % TeX will automatically convert eps --> pdf in pdflatex
\usepackage{amssymb}
\usepackage{python}
\usepackage{units}


\usepackage{pgfplots}
\usepgfplotslibrary{polar}
\newcommand{\degree}{\ensuremath{^\circ}}
\usepgfplotslibrary{units}

\title{Vector Adventure Lab}
\author{Saul Shanabrook}
%\date{}                            % Activate to display a given date or no date
\pgfplotsset{width=6in,compat=1.6}
\begin{document}
\maketitle
\begin{figure}
    \centering
    \begin{tikzpicture}
        \begin{axis}[use units,
            scale only axis,
            xmin=-20,xmax=20,
            axis y line*=left,
            title=North,
            xlabel=South,ylabel=West,
            x unit=ft, y unit=ft,
            legend style={
                cells={anchor=east},
                legend pos=outer north east,
            }]

\begin{python}
import math
import operator
import itertools
import numpy


def polar_to_cartesian(point):
    r, theta = point
    theta = 90 - theta
    x = r * math.cos(math.radians(theta))
    y = r * math.sin(math.radians(theta))
    return (x, y)


def cartesian_to_polar(point):
    x, y = point
    theta = 90 - numpy.angle(complex(x,y), deg=True)
    r = numpy.hypot(x, y)
    return (r, theta)


def add_points(points):
    return sum(map(numpy.array, map(polar_to_cartesian, points)))


def draw_vector(old_coordinate, polar_vector, label, style='', position='above'):
    old_coordinate = numpy.around(old_coordinate, 2)
    cartesian_vector = numpy.around(polar_to_cartesian(polar_vector), 2)
    new_coordinate = numpy.around(old_coordinate + cartesian_vector, 2)
    halfway_coordinate = numpy.around(old_coordinate + (cartesian_vector / 2), 2)
    polar_vector = numpy.around(polar_vector, 2)
    print(r'''
    \addplot[
        quiver={{
            u={cartesian_v[0]},
            v={cartesian_v[1]},
            every arrow/.append style={{
                line width=2pt,{style}
            }},
        }},
        -stealth
    ]
    coordinates {{ ({old_c[0]}, {old_c[1]})}};
    \addlegendentry{{$\vec{{{label}}}={polar_v[0]}\unit{{ft}}; {polar_v[1]}\degree$}}
    \node[coordinate, pin={position}:$\vec{{{label}}}$]
        at (axis cs:{halfway_c[0]},{halfway_c[1]}) {{}};
    '''.format(old_c=old_coordinate, cartesian_v=cartesian_vector,
               polar_v=polar_vector, new_c=new_coordinate, label=label,
               style=style, position=position, halfway_c=halfway_coordinate))

polar_vectors = [
    (0, 0),
    (17, 290),
    (24, 155),
    (24, 65),
    (8.5, 290)]
vector_names = ['A', 'B', 'C', 'D']
for n in range(1, len(polar_vectors)):
    old_coordinate = add_points(polar_vectors[:n])
    label = vector_names[n - 1]
    draw_vector(old_coordinate, polar_vectors[n], label=label)

displacement_vector = numpy.array((12.5 * 2.08, 28))
draw_vector(numpy.array((0, 0)),
            displacement_vector,
            label='displacement',
            position='left')

last_calculate_point = add_points(polar_vectors)
displacement_to_last_calculate_vector = polar_to_cartesian(displacement_vector) - last_calculate_point
draw_vector(last_calculate_point,
            cartesian_to_polar(displacement_to_last_calculate_vector),
            'error',
            'style={loosely dashed}',
            'right')
\end{python}
        \end{axis}
        \begin{axis}[
scale only axis,
xmin=-20,xmax=20,
axis y line*=right,
axis x line=none,
ylabel=West,
yticklabel=\empty];
\end{axis}
    \end{tikzpicture}
\end{figure}

\end{document}