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<a name="math_toolkit.cardinal_quadratic_b"></a><a class="link" href="cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation">Cardinal Quadratic B-spline
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<h4>
<a name="math_toolkit.cardinal_quadratic_b.h0"></a>
<span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.synopsis"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.synopsis">Synopsis</a>
</h4>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">cardinal_quadratic_b_spline</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">interpolators</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">cardinal_quadratic_b_spline</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="comment">// If you don't know the value of the derivative at the endpoints, leave them as NaNs and the routine will estimate them.</span>
<span class="comment">// y[0] = y(a), y[n - 1] = y(b), step_size = (b - a)/(n -1).</span>
<span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Real</span><span class="special">*</span> <span class="keyword">const</span> <span class="identifier">y</span><span class="special">,</span>
<span class="identifier">size_t</span> <span class="identifier">n</span><span class="special">,</span>
<span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
<span class="identifier">Real</span> <span class="identifier">h</span> <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
<span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
<span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
<span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span>
<span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
<span class="identifier">Real</span> <span class="identifier">h</span> <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
<span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
<span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
<span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>
<span class="special">}}}</span>
</pre>
<h4>
<a name="math_toolkit.cardinal_quadratic_b.h1"></a>
<span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte">Cardinal
Quadratic B-Spline Interpolation</a>
</h4>
<p>
The cardinal quadratic B-spline interpolator is very nearly the same as the
cubic B-spline interpolator, with the modification that the basis functions
are constructed by convolving a box function with itself twice, rather than
three times as is done with the cubic B-spline.
</p>
<p>
Since the basis functions are less smooth than the cubic B-spline, you will
nearly always wish to use the cubic B-spline interpolator rather than this.
However, this interpolator is occasionally useful for approximating functions
of reduced smoothness, as hence finds use internally in the Boost.Math library.
</p>
<p>
It is reasonable to test this interpolator against the cubic b-spline interpolator
when you are approximating functions which are two or three times continuously
differentiable, but not three or four times differentiable.
</p>
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