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<li class="nav-item" data-level="1"><a href="#interpolatorslib" class="nav-link">interpolators.lib</a>
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<li class="nav-item" data-level="2"><a href="#two-points-interpolation-functions" class="nav-link">Two points interpolation functions</a>
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<li class="nav-item" data-level="3"><a href="#itinterpolate_linear" class="nav-link">(it.)interpolate_linear</a>
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<h1 id="interpolatorslib">interpolators.lib</h1>
<p>A library to handle interpolation. Its official prefix is <code>it</code>.</p>
<p>This library provides several basic interpolation functions as well as interpolators
taking a <code>gen</code> circuit of N outputs producing values to be interpolated, triggered
by a <code>idv</code> read index signal. Two points and four points interpolations are implemented.</p>
<p>The <code>idv</code> parameter is to be used as a read index. In float (= singleprecision) mode,
a technique based on 2 signals with the pure integer index and a fractional part in the [0,1]
range is used to avoid accumulating errors. In -double (= doubleprecision)/-quad (= quadprecision) modes,
a standard implementation with a single fractional index signal is used.
Three functions <code>int_part</code>, <code>frac_part</code> and <code>mak_idv</code> are available to manipule the read index signal.</p>
<p>Use-case with <code>waveform</code>. Here the signal given to <code>interpolator_XXX</code> uses the <code>idv</code> model.</p>
<pre><code>waveform_interpolator(wf, step, interp) = interp(gen, idv)
with {
gen(idx) = wf, (idx:max(0):min(size-1)) : rdtable with { size = wf:(_,!); }; /* waveform size */
index = (+(step)~_)-step; /* starting from 0 */
idv = it.make_idv(index); /* build the signal for interpolation in a generic way */
};
waveform_linear(wf, step) = waveform_interpolator(wf, step, it.interpolator_linear);
waveform_cosine(wf, step) = waveform_interpolator(wf, step, it.interpolator_cosine);
waveform_cubic(wf, step) = waveform_interpolator(wf, step, it.interpolator_cubic);
waveform_interp(wf, step, selector) = waveform_interpolator(wf, step, interp_select(selector))
with {
/* adapts the argument order */
interp_select(sel, gen, idv) = it.interpolator_select(gen, idv, sel);
};
waveform and index
waveform_interpolator1(wf, idv, interp) = interp(gen, idv)
with {
gen(idx) = wf, (idx:max(0):min(size-1)) : rdtable with { size = wf:(_,!); }; /* waveform size */
};
waveform_linear1(wf, idv) = waveform_interpolator1(wf, idv, it.interpolator_linear);
waveform_cosine1(wf, idv) = waveform_interpolator1(wf, idv, it.interpolator_cosine);
waveform_cubic1(wf, idv) = waveform_interpolator1(wf, idv, it.interpolator_cubic);
waveform_interp1(wf, idv, selector) = waveform_interpolator1(wf, idv, interp_select(selector))
with {
/* adapts the argument order */
interp_select(sel, gen, idv) = it.interpolator_select(gen, idv, sel);
};
</code></pre>
<p>Some tests here:</p>
<pre><code>wf = waveform {0.0, 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 50.0, 40.0, 30.0, 20.0, 10.0, 0.0};
process = waveform_linear(wf, step), waveform_cosine(wf, step), waveform_cubic(wf, step) with { step = 0.25; };
process = waveform_interp(wf, 0.25, nentry("algo", 0, 0, 3, 1));
process = waveform_interp1(wf, idv, nentry("algo", 0, 0, 3, 1))
with {
step = 0.1;
idv_aux = (+(step)~_)-step; /* starting from 0 */
idv = it.make_idv(idv_aux); /* build the signal for interpolation in a generic way */
};
/* Test linear interpolation between 2 samples with a `(idx,dv)` signal built using a waveform */
linear_test = (idx,dv), it.interpolator_linear(gen, (idx,dv))
with {
/* signal to interpolate (only 2 points here) */
gen(id) = waveform {3.0, -1.0}, (id:max(0)) : rdtable;
dv = waveform {0.0, 0.25, 0.50, 0.75, 1.0}, index : rdtable;
idx = 0;
/* test index signal */
index = (+(1)~_)-1; /* starting from 0 */
};
/* Test cosine interpolation between 2 samples with a `(idx,dv)` signal built using a waveform */
cosine_test = (idx,dv), it.interpolator_cosine(gen, (idx,dv))
with {
/* signal to interpolate (only 2 points here) */
gen(id) = waveform {3.0, -1.0}, (id:max(0)) : rdtable;
dv = waveform {0.0, 0.25, 0.50, 0.75, 1.0}, index : rdtable;
idx = 0;
/* test index signal */
index = (+(1)~_)-1; /* starting from 0 */
};
/* Test cubic interpolation between 4 samples with a `(idx,dv)` signal built using a waveform */
cubic_test = (idx,dv), it.interpolator_cubic(gen, (idx,dv))
with {
/* signal to interpolate (only 4 points here) */
gen(id) = waveform {-1.0, 2.0, 1.0, 4.0}, (id:max(0)) : rdtable;
dv = waveform {0.0, 0.25, 0.50, 0.75, 1.0}, index : rdtable;
idx = 0;
/* test index signal */
index = (+(1)~_)-1; /* starting from 0 */
};
</code></pre>
<h2 id="two-points-interpolation-functions">Two points interpolation functions</h2>
<hr />
<h3 id="itinterpolate_linear"><code>(it.)interpolate_linear</code></h3>
<p>Linear interpolation between 2 values.</p>
<h4 id="usage">Usage</h4>
<pre><code>interpolate_linear(dv,v0,v1) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>dv</code>: in the fractional value in [0..1] range</li>
<li><code>v0</code>: is the first value</li>
<li><code>v1</code>: is the second value</li>
</ul>
<h4 id="reference">Reference:</h4>
<ul>
<li><a href="https://github.com/jamoma/JamomaCore/blob/master/Foundation/library/includes/TTInterpolate.h">https://github.com/jamoma/JamomaCore/blob/master/Foundation/library/includes/TTInterpolate.h</a></li>
</ul>
<hr />
<h3 id="itinterpolate_cosine"><code>(it.)interpolate_cosine</code></h3>
<p>Cosine interpolation between 2 values.</p>
<h4 id="usage_1">Usage</h4>
<pre><code>interpolate_cosine(dv,v0,v1) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>dv</code>: in the fractional value in [0..1] range</li>
<li><code>v0</code>: is the first value</li>
<li><code>v1</code>: is the second value</li>
</ul>
<h4 id="reference_1">Reference:</h4>
<ul>
<li><a href="https://github.com/jamoma/JamomaCore/blob/master/Foundation/library/includes/TTInterpolate.h">https://github.com/jamoma/JamomaCore/blob/master/Foundation/library/includes/TTInterpolate.h</a></li>
</ul>
<h2 id="four-points-interpolation-functions">Four points interpolation functions</h2>
<hr />
<h3 id="itinterpolate_cubic"><code>(it.)interpolate_cubic</code></h3>
<p>Cubic interpolation between 4 values.</p>
<h4 id="usage_2">Usage</h4>
<pre><code>interpolate_cubic(dv,v0,v1,v2,v3) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>dv</code>: in the fractional value in [0..1] range</li>
<li><code>v0</code>: is the first value</li>
<li><code>v1</code>: is the second value</li>
<li><code>v2</code>: is the third value</li>
<li><code>v3</code>: is the fourth value</li>
</ul>
<h4 id="reference_2">Reference:</h4>
<ul>
<li><a href="https://www.paulinternet.nl/?page=bicubic">https://www.paulinternet.nl/?page=bicubic</a></li>
</ul>
<h2 id="two-points-interpolators">Two points interpolators</h2>
<hr />
<h3 id="itinterpolator_two_points"><code>(it.)interpolator_two_points</code></h3>
<p>Generic interpolator on two points (current and next index), assuming an increasing index.</p>
<h4 id="usage_3">Usage</h4>
<pre><code>interpolator_two_points(gen, idv, interpolate_two_points) : _,_... (equal to N = outputs(gen))
</code></pre>
<p>Where:</p>
<ul>
<li><code>gen</code>: a circuit with an 'idv' reader input that produces N outputs</li>
<li><code>idv</code>: a fractional read index expressed as a float value, or a (int,frac) pair</li>
<li><code>interpolate_two_points</code>: a two points interpolation function</li>
</ul>
<hr />
<h3 id="itinterpolator_linear"><code>(it.)interpolator_linear</code></h3>
<p>Linear interpolator for a 'gen' circuit triggered by an 'idv' input to generate values.</p>
<h4 id="usage_4">Usage</h4>
<pre><code>interpolator_linear(gen, idv) : _,_... (equal to N = outputs(gen))
</code></pre>
<p>Where:</p>
<ul>
<li><code>gen</code>: a circuit with an 'idv' reader input that produces N outputs</li>
<li><code>idv</code>: a fractional read index expressed as a float value, or a (int,frac) pair</li>
</ul>
<hr />
<h3 id="itinterpolator_cosine"><code>(it.)interpolator_cosine</code></h3>
<p>Cosine interpolator for a 'gen' circuit triggered by an 'idv' input to generate values.</p>
<h4 id="usage_5">Usage</h4>
<pre><code>interpolator_cosine(gen, idv) : _,_... (equal to N = outputs(gen))
</code></pre>
<p>Where:</p>
<ul>
<li><code>gen</code>: a circuit with an 'idv' reader input that produces N outputs</li>
<li><code>idv</code>: a fractional read index expressed as a float value, or a (int,frac) pair</li>
</ul>
<h2 id="four-points-interpolators">Four points interpolators</h2>
<hr />
<h3 id="itinterpolator_two_points_1"><code>(it.)interpolator_two_points</code></h3>
<p>Generic interpolator on interpolator_four_points points (previous, current and two next indexes), assuming an increasing index.</p>
<h4 id="usage_6">Usage</h4>
<pre><code>interpolator_four_points(gen, idv, interpolate_four_points) : _,_... (equal to N = outputs(gen))
</code></pre>
<p>Where:</p>
<ul>
<li><code>gen</code>: a circuit with an 'idv' reader input that produces N outputs</li>
<li><code>idv</code>: a fractional read index expressed as a float value, or a (int,frac) pair</li>
<li><code>interpolate_four_points</code>: a four points interpolation function</li>
</ul>
<hr />
<h3 id="itinterpolator_cubic"><code>(it.)interpolator_cubic</code></h3>
<p>Cubic interpolator for a 'gen' circuit triggered by an 'idv' input to generate values</p>
<h4 id="usage_7">Usage</h4>
<pre><code>interpolator_cubic(gen, idv) : _,_... (equal to N = outputs(gen))
</code></pre>
<p>Where:</p>
<ul>
<li><code>gen</code>: a circuit with an 'idv' reader input that produces N outputs</li>
<li><code>idv</code>: a fractional read index expressed as a float value, or a (int,frac) pair</li>
</ul>
<hr />
<h3 id="itinterpolator_select"><code>(it.)interpolator_select</code></h3>
<p>Generic configurable interpolator (with selector between in [0..3]). The value 3 is used for no interpolation.</p>
<h4 id="usage_8">Usage</h4>
<pre><code>interpolator_select(gen, idv, sel) : _,_... (equal to N = outputs(gen))
</code></pre>
<p>Where:</p>
<ul>
<li><code>gen</code>: a circuit with an 'idv' reader input that produces N outputs</li>
<li><code>idv</code>: a fractional read index expressed as a float value, or a (int,frac) pair</li>
<li><code>sel</code>: an interpolation algorithm selector in [0..3] (0 = linear, 1 = cosine, 2 = cubic, 3 = nointerp)</li>
</ul></div>
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