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  "body": "\n## Summary\n\nThe convex join of two sets is the union of all [[line segments|VQ4Q2V45RP]] that start in the first set and end in the second.\nWhen both sets are [[convex|02AS45T3H9]] and nonempty, the convex join is the [[convex hull|0FQSDC2EQ2]] of their union.\nSo it gives a concrete way to build the hull of two convex pieces from segments alone.\n\n## Explanations\n\n### L1 human\n\nTake two shapes and join every point of the first to every point of the second by a straight segment.\nThe region covered by all these segments is the convex join.\nFor a point $p$ and a disc, the join is a cone shape: the disc together with all segments from $p$ to it.\nFor the two points $(0, 0)$ and $(1, 0)$ of the plane, the join is just the segment between them.\n",
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