Merge pull request #570 from rtoy/131-setvaluecurveattime-linear-interp

Fix #131: specify linear interpolation for setValueCurveAtTime

index.html

@@ -1762,18 +1762,19 @@ <h2 id="AudioParam">The AudioParam Interface</h2>
         </dd>
       </dl>              
       <p>
-        During the time interval: <code>startTime</code> &lt;= t &lt;
-        <code>startTime</code> + <em>duration</em>, values will be calculated:
-      </p>
-      <pre>
-        v(t) = values[N * (t - startTime) / duration]
-      </pre>
-      <p>
-        where <em>N</em> is the length of the <em>values</em> array.
+        Let \(T_0\) be <code>startTime</code>, \(T_D\) be <code>duration</code>, \(V\) be the
+        <code>values</code> array, and \(N\) be the length of the <code>values</code> array.  Then,
+        during the time interval: \(T_0 \le t &lt; T_0 + T_D\), let
+        $$
+          \begin{align*}
+              k &= \big\lfloor \frac{N}{T_D}(t-T_0) \big\rfloor \\
+          \end{align*}
+        $$
+        Then \(v(t)\) is computed by linearly interpolating between \(V[k]\) and \(V[k+1]\),
       </p>
       <p>
-        After the end of the curve time interval (t &gt;= <code>startTime</code> +
-        <em>duration</em>), the value will remain constant at the final curve
+        After the end of the curve time interval (\(t \ge T_0 + T_D\)),
+        the value will remain constant at the final curve
         value, until there is another automation event (if any).
       </p>
     </dd>