Uniform discretization of Bezier curve
<p>I need to discretise a 3rd order Bezier curve with points equally distributed along the curve. The curve is defined by four points p0, p1, p2, p3 and a generic point p(t) with 0 &lt; t &lt; 1 is given by: </p>

<pre><code>point_t = (1 - t) * (1 - t) * (1 - t) * p0 + 3 * (1 - t) * (1 - t) * t * p1 + 3 * (1 - t) * t * t * p2 + t * t * t * p3;
</code></pre>

<p>My first idea was to discretise t = 0, t_1, ... t_n, ..., 1 </p>

<p>This doesn't work as, in general, we don't end up with a uniform distance between the discretised points.</p>

<p>To sum up, what I need is an algorithm to discretise the parametric curve so that: </p>

<pre><code>|| p(t_n) - p(t_n_+_1) || = d
</code></pre>

<p>I thought about recursively halving the Bezier curve with the <a href="https://en.wikipedia.org/wiki/De_Casteljau&#39;s_algorithm" rel="nofollow">Casteljau algorithm</a> up to required resolution, but this would require a lot of distance calculations. </p>

<p>Any idea on how to solve this problem analytically?</p>