B-spline: Difference between revisions

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Outputs a graphical representation of a B-spline.
Outputs a graphical representation of a B-spline.

=={{header|Phix}}==
{{trans|Wren}}
{{libheader|Phix/pGUI}}
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/bspline.htm here].
<!--<lang Phix>(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\B-spline.exw
-- =========================
--
-- Use +/- to change the order between k = 1 and k = 4.
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">ctrl_points</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">171</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">171</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">185</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">111</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">202</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">109</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">202</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">189</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">328</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">160</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">208</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">254</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">241</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">330</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">164</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">252</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">69</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">278</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">139</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">208</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">72</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">148</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">168</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">172</span><span style="color: #0000FF;">}}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">t</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">// B-spline helper function</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">?</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])/(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">0</span> <span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">// B-spline function</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">==</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<=</span><span style="color: #000000;">x</span> <span style="color: #008080;">and</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">w</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">))*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">b_spline</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ctrl_points</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">// use a uniform knot vector, delta = 1</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"k (= %d) cannot be more than %d or less than 1."</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">px</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000000;">py</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">to</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">sumX</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">sumY</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sumX</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ctrl_points</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">sumY</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ctrl_points</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">px</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sumX</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">py</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sumY</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">xtick</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">ytick</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">xmin</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trunc</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">px</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">xtick</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">xtick</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">xmax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">ceil</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">px</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">xtick</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">xtick</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">ymin</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trunc</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">py</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">ytick</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">ytick</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">ymax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">ceil</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">py</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">ytick</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">ytick</span>
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XTICK"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xtick</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XMIN"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xmin</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XMAX"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xmax</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YTICK"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ytick</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YMIN"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ymin</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YMAX"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ymax</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">graphdata</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">px</span><span style="color: #0000FF;">,</span><span style="color: #000000;">py</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_BLUE</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">graphdata</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">set_title</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetStrAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"B-spline curve (order k = %d)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">k</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">key_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #004600;">K_ESC</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_CLOSE</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'+'</span> <span style="color: #008080;">then</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">set_title</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupRedraw</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_IGNORE</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b_spline</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`RASTERSIZE=600x600`</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"KEY_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"key_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">set_title</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</lang>-->


=={{header|Wren}}==
=={{header|Wren}}==