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jupytersketcher
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                  <h1>Sketcher definition</h1>
                
                <h2 id="a-language-to-describe-a-sketch">A language to describe a sketch</h2>
<p>Pysketcher initial version <a href="">HPL Pysketcher</a> enable sketch definition in python. HPL is showing the hierachical nature of sketches. This is implemented via the Composition function. One can further grasp this using the graphviz_dot function applied to discover the composition herarchy implemented as a graphviz image <a href="#the-hierarchy-of-the-friction-main-object">see The hierarchy of the "friction" main object</a> at the end of this page.</p>
<p>Due to the hierarchical nature of sketches, it is quite straightforward to think about using yaml as the syntax for defining a sketch.</p>
<p>The benefits are as follow:</p>
<ul>
<li>A leaner presentation of the sketch as only the data making sense is going to be used</li>
<li>A more straightforward reading of the composition hierachy</li>
<li>A more robust sketch definition as only a set of rules will be applied to define a sketch and no further python idiom will be intermingled</li>
</ul>
<h2 id="example">Example</h2>
<p>This example provides the yaml content to define the Dry Friction case</p>
<h3 id="the-final-sketch">The final sketch</h3>
<p><img alt="" src="../images/dryfriction.png" /></p>
<p>An inclined plan (the A-B edge) supports a blue rectangle which is pulled donward by the gravity. The plan makes an angle <span><span class="MathJax_Preview">\theta</span><script type="math/tex">\theta</script></span>. The sketch design enable the <span><span class="MathJax_Preview">\theta</span><script type="math/tex">\theta</script></span> angle to change. The whole plan including the body can rotate arround the point B.</p>
<h3 id="the-yaml-definition">The yaml definition</h3>
<p>Sketcher language is defined as a yaml compliant file or string. The yaml file is a dictionnary of </p>
<ul>
<li>functionnal objects (leaf objects, like Rectangle, Circle, Line etc or composition)</li>
<li>extended with object style (line or fill colors, line stroke...)</li>
<li>to which transformation are applied (translation, rotation...)</li>
</ul>
<p>As a general rule, a new object suppose all parameters to be defined before they are used to construct it.</p>
<p><strong>For example, you can create a circle if the center and the radius have been defined earlier in the file.</strong></p>
<p>The general layout of a sketcher file is as follow:</p>
<ul>
<li><strong>Libraries, Construction Variables, Frame</strong><ul>
<li>declaration of the libraries used by the objects further declared: at least pysketcher is mandatory</li>
<li>various global variable which encompass the "Construction" variables which define the object main physical dimensions, positions...</li>
<li>some "actions" corresponding to executable python sentences<ul>
<li>One mandatory action is the setting of the drawing frame (drawing_tool.set_coordinate_system): it must be declared before any other pysketcher object is used.</li>
<li>Other use case of action is the setting of global parameters like default line color: (drawing_tool.set_linecolor('black')) for example</li>
</ul>
</li>
</ul>
</li>
<li><strong>Objects</strong><ul>
<li>Usually starting with the declaration of leaf simple objects</li>
<li>then aggregated using the composition object</li>
<li>Composition can be made of composition object</li>
<li>grouping leafs and composition will be further used to apply transformation latter on (based on the "physics")</li>
<li>The example presents three group of objects<ul>
<li>The body object</li>
<li>The plan object</li>
<li>The friction main object</li>
</ul>
</li>
<li>The plan includes the body</li>
<li>The friction includes the plan (that will be able to rotate as a group) and the ground (will stay fixed)</li>
</ul>
</li>
</ul>
<h4 id="libraries-construction-variables-frame">Libraries, Construction Variables, Frame</h4>
<pre><code class="yaml">libraries: [&quot;from math import tan, radians, sin, cos&quot;,
            &quot;from pysketcher import *&quot;]
fontsize: 18
g: 9.81              # constant gravity
theta: 30.0          # inclined plane angle
L: 10.0              # sketch sizing parameter
a: 1.0               #
xmin: 0.0            # sketech min Abscissa
ymin: -3.0           # sketech min Ordinate     
rl: 2.0              # rectangle width
rL: 1.0              # rectangle length
setframe:            # sketch setup
    action: &quot;drawing_tool.set_coordinate_system(xmin=xmin-L/5, xmax=xmin+1.5*L,ymin=ymin, ymax=ymin+1.5*L,instruction_file='tmp_mpl_friction.py')&quot;
setblackline:        # default frame values and actions
    action: &quot;drawing_tool.set_linecolor('black')&quot;
B: point(a+L,0)                      # wall right end
A: point(a,tan(radians(theta))*L)    # wall left end
normal_vec: point(sin(radians(theta)),cos(radians(theta)))     # Vector normal to wall
tangent_vec: point(cos(radians(theta)),-sin(radians(theta)))   # Vector tangent to wall
help_line: Line(A,B)                 # wall line
x: a + 3*L/10.
y: help_line(x=x)    
contact: point(x, y)    
c: contact + rL/2*normal_vec
</code></pre>

<h4 id="the-body-object">The body object</h4>
<pre><code class="yaml">rectangle: 
    formula: Rectangle(contact, rl, rL)
    style:
        linecolor: blue
        filled_curves: blue
    transform: [&quot;rotate(-theta, contact)&quot;,
                &quot;translate(-rl/2*tangent_vec)&quot;]
N: 
    formula: Force(contact - rl*normal_vec, contact, r'$N$', text_pos='start')
    style:
        linecolor: black
mg: 
    formula: Gravity(c, rl, text='$Mg$')
    style:
        linecolor: black
wheel: 
    formula: &quot;Composition({'outer': rectangle})&quot;   
    style:
        shadow: 1
body: 
    formula: &quot;Composition({'wheel': wheel, 'N': N, 'mg': mg})&quot;
    style:
        linecolor: black
</code></pre>

<h4 id="the-plan-object">The plan object</h4>
<pre><code class="yaml">mB:
    formula: Text(r'$B$',B)
mA:
    formula: Text(r'$A$', A)
wall: 
    formula: Wall(x=[A[0], B[0]], y=[A[1], B[1]], thickness=-0.25,transparent=False)
    style:
        linecolor: black    
angle: 
    formula: &quot;Arc_wText(r'$&lt;bslash&gt;theta$', center=B, radius=3, start_angle=180-theta, arc_angle=theta, fontsize=fontsize)&quot;
    style:
        linecolor: black
        linewidth: 1
ground: 
     formula: Line((B[0]-L/10., 0), (B[0]-L/2.,0))
     stlye:
         linecolor: black
         linestyle: dashed
         linewidth: 1
x_const: 
    formula: Line(contact, contact + point(0,4))
    style:
        linestyle: dotted
    transform: rotate(-theta, contact)
x_axis: 
    formula: &quot;Axis(start=contact+ 2*rl*normal_vec, length=2*rl,label='$x$', rotation_angle=-theta)&quot;
plan: 
    formula: &quot;Composition({'body': body, 'angle': angle, 'inclined wall': wall, 'x start': x_const, 'x axis': x_axis, 'mA': mA, 'mB': mB})&quot;
</code></pre>

<h4 id="the-friction-main-object">The friction main object</h4>
<pre><code class="yaml">
friction: 
    formula: &quot;Composition({'plan': plan, 'ground': ground})&quot;
</code></pre>

<h3 id="the-hierarchy-of-the-friction-main-object">The hierarchy of the "friction" main object</h3>
<p><img alt="" src="../images/dotfriction.png" /></p>
                
              
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