<story><title>Parallel Curves of Cubic Béziers</title><url>https://raphlinus.github.io/curves/2022/09/09/parallel-beziers.html</url></story><parent_chain><item><author>version_five</author><text>If you&amp;#x27;re like me and first got hung up on the difference between a parallel curve and a translation of the curve, the wikipedia article (literally the first link) explains it.&lt;p&gt;My understanding is that a parallel curve is what you get if you dilate the curve with a circle, ie the curve along the furthest extent of the dilation (see the picture in the wikipedia article) which evidently is not the same as just translating the curve down.&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Parallel_curve&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Parallel_curve&lt;/a&gt;</text></item></parent_chain><comment><author>upwardbound</author><text>Yep.  A way that helps me visualize it is that a parallel curve is what you need to make a set of railroad tracks.  The tracks have to always be a constant distance apart &lt;i&gt;when measured along the direction locally perpendicular to the tracks - i.e. the direction of the train&amp;#x27;s axle&lt;/i&gt;.</text></comment>
<story><title>Parallel Curves of Cubic Béziers</title><url>https://raphlinus.github.io/curves/2022/09/09/parallel-beziers.html</url></story><parent_chain><item><author>version_five</author><text>If you&amp;#x27;re like me and first got hung up on the difference between a parallel curve and a translation of the curve, the wikipedia article (literally the first link) explains it.&lt;p&gt;My understanding is that a parallel curve is what you get if you dilate the curve with a circle, ie the curve along the furthest extent of the dilation (see the picture in the wikipedia article) which evidently is not the same as just translating the curve down.&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Parallel_curve&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.m.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Parallel_curve&lt;/a&gt;</text></item></parent_chain><comment><author>Jasper_</author><text>A simple counterexample to imagine is a curve that represents a circle (or a circular arc). The parallel curve to this is a scaling of the circle, with a bigger&amp;#x2F;smaller radii, not a translation.</text></comment>