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Daniel Weschke
2026-01-22 18:50:07 +01:00
parent d0eabd3252
commit 22cc4f2943
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docs/build/html/pylib.function.html vendored
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@@ -47,26 +47,29 @@
<dt id="pylib.function.b_spline_basis">
<code class="sig-name descname">b_spline_basis</code><span class="sig-paren">(</span><em class="sig-param">knots</em>, <em class="sig-param">knot_span</em>, <em class="sig-param">degree</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#b_spline_basis"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.b_spline_basis" title="Permalink to this definition"></a></dt>
<dd><p>Cox-de Boor algorithm / recursion formula.</p>
<p>Calculate the i-th B-spline basis function of degree p: N_{i,p}(u)</p>
<p>Calculate the i-th B-spline basis function of degree p:
<span class="math notranslate nohighlight">\(N_{i,p}(u)\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>knots</strong> (<em>list</em>) – Knot vector U. m + 1 non-decreasing numbers / knots,
<span class="math notranslate nohighlight">\(u_0 &lt;= u_1 &lt;= u_2 &lt;= ... &lt;= u_m\)</span></p></li>
<span class="math notranslate nohighlight">\(u_0 \le u_1 \le u_2 \le \dots \le u_m\)</span></p></li>
<li><p><strong>knot_span</strong> (<em>int</em>) – i-th knot span</p></li>
<li><p><strong>degree</strong> (<em>int</em>) – degree of B-spline basis function</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>B-spline basis function using variable, u in [u_0, u_m]</p>
<dd class="field-even"><p>B-spline basis function using variable,
<span class="math notranslate nohighlight">\(u \in [u_0, u_m]\)</span></p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>function</p>
</dd>
</dl>
<div class="math notranslate nohighlight">
\[\begin{split}N_{i,0}(u) &amp;= \begin{cases} 1 &amp; \text{if } u_i \le u \lt u_{i+1} \\
0 &amp; \text{otherwise}\end{cases} \\
\[\begin{split}N_{i,0}(u) &amp;= \begin{cases}
1 &amp; \text{if } u_i \le u \lt u_{i+1} \\
0 &amp; \text{otherwise}\end{cases} \\
N_{i,p}(u) &amp;= \frac{u - u_i}{u_{i+p} - u_i} N_{i,p-1}(u) +
\frac{u_{i+p+1} - u}{u_{i+p+1} - u_{i+1}} N_{i+1,p-1}(u)\end{split}\]</div>
</dd></dl>
@@ -82,11 +85,11 @@ N_{i,p}(u) &amp;= \frac{u - u_i}{u_{i+p} - u_i} N_{i,p-1}(u) +
<li><p><strong>degree</strong> (<em>int</em>) – degree of B-spline basis functions</p></li>
<li><p><strong>control_points</strong> (<em>list</em>) – control points P, n + 1 control points</p></li>
<li><p><strong>knots</strong> (<em>list</em>) – Knot vector U. m + 1 non-decreasing numbers / knots,
<span class="math notranslate nohighlight">\(u_0 &lt;= u_1 &lt;= u_2 &lt;= ... &lt;= u_m\)</span></p></li>
<span class="math notranslate nohighlight">\(u_0 \le u_1 \le u_2 \le \dots \le u_m\)</span></p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>B-spline curve using variable, u in [u_0, u_m]</p>
<dd class="field-even"><p>B-spline curve using variable, <span class="math notranslate nohighlight">\(u \in [u_0, u_m]\)</span></p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>function</p>
@@ -100,10 +103,11 @@ N_{i,p}(u) &amp;= \frac{u - u_i}{u_{i+p} - u_i} N_{i,p-1}(u) +
<li><p>the curve will not touch the first and last legs of the
control polyline</p></li>
<li><p>the knot vector does not have any particular structure</p></li>
<li><p>for degree p, intervals [u_0, u_p) and [u_{n-p}, u_n) will not
have “full support” of basis functions and are ignored when a
B-spline curve is open. For open B-spline curves, the domain
is inteval [u_p, u_{n-p}]</p></li>
<li><p>for degree p, intervals <span class="math notranslate nohighlight">\([u_0, u_p)\)</span> and
<span class="math notranslate nohighlight">\([u_{n-p}, u_n)\)</span> will not have “full support” of basis
functions and are ignored when a B-spline curve is open. For
open B-spline curves, the domain is inteval
<span class="math notranslate nohighlight">\([u_p, u_{n-p}]\)</span></p></li>
</ul>
</li>
<li><p>clamped B-spline curves, nonperiodic B-spline curves</p>
@@ -118,7 +122,7 @@ a Bézier curve</p></li>
<ul>
<li><p>the start and the end of the generated curve join together
forming a closed loop</p></li>
<li><p>repeating some knots and control points # TODO: which?</p></li>
<li><p>repeating some knots and control points (TODO: which?)</p></li>
</ul>
</li>
<li><p>uniform B-spline curves</p>
@@ -202,10 +206,10 @@ y(\theta) = r\sin\theta \\
<dt id="pylib.function.cosine_wave">
<code class="sig-name descname">cosine_wave</code><span class="sig-paren">(</span><em class="sig-param">A=1</em>, <em class="sig-param">k=1</em>, <em class="sig-param">f=1</em>, <em class="sig-param">phi=0</em>, <em class="sig-param">D=0</em>, <em class="sig-param">degree=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#cosine_wave"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.cosine_wave" title="Permalink to this definition"></a></dt>
<dd><p>A cosine wave is said to be sinusoidal, because,
<span class="math notranslate nohighlight">\(\cos(x) = \sin(x + \pi/2)\)</span>, which is also a sine wave with a
phase-shift of π/2 radians. Because of this head start, it is often
said that the cosine function leads the sine function or the sine
lags the cosine.</p>
<span class="math notranslate nohighlight">\(\cos(x) = \sin(x + \pi/2)\)</span>, which is also a sine wave with
a phase-shift of π/2 radians. Because of this head start, it is
often said that the cosine function leads the sine function or
the sine lags the cosine.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
@@ -363,9 +367,9 @@ y(\theta) = (R - r)\sin\theta - d\sin\left(\frac{R-r}{r}\theta\right) \\
<span class="o">*</span> <span class="o">*</span> <span class="o">*</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">hyotrochoid</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)[:</span><span class="mi">2</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">hyotrochoid</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">interval</span> <span class="o">=</span> <span class="n">hyotrochoid</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">hypotrochoid</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)[:</span><span class="mi">2</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">hypotrochoid</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">interval</span> <span class="o">=</span> <span class="n">hypotrochoid</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
</pre></div>
</div>
<div class="admonition seealso">
@@ -625,7 +629,28 @@ Example of 3 columns and 3 rows (upside down view of ‘normal’ braille/drawil
<p class="caption"><span class="caption-text">Contents:</span></p>
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="pylib.html#subpackages">Subpackages</a></li>
<li class="toctree-l3 current"><a class="reference internal" href="pylib.html#submodules">Submodules</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="pylib.data.html">pylib.data module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.data_step.html">pylib.data_step module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.data_step_std.html">pylib.data_step_std module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.date.html">pylib.date module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.drawblock.html">pylib.drawblock module</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">pylib.function module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.geometry.html">pylib.geometry module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.geometry2d.html">pylib.geometry2d module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.geometry2d_plot.html">pylib.geometry2d_plot module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.geometry_plot.html">pylib.geometry_plot module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.geometry_plot_pylab.html">pylib.geometry_plot_pylab module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.helper.html">pylib.helper module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.mathematics.html">pylib.mathematics module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.time_of_day.html">pylib.time_of_day module</a></li>
<li class="toctree-l4"><a class="reference internal" href="pylib.tui.html">pylib.tui module</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>