Here is a convex object and an origin point outside it.

V_0 is an arbitrary point in the boundary. Find the farthest point on the boundary along the vector \overrightarrow{v_0o}. Name the farthest point w_0.

We get a new vector \overrightarrow{w_0o} to find the farthest point on the boundary along the direction \overrightarrow{w_0o}. The point w_1 is added to the simple vertices set S_2 = {w_0, w_1}.

Connect points w_0 and w_1, find the closet point v_2 on the line segment to the origin O. Find the farthest point w_2 on the boundary with direction \overrightarrow{v_2o}. The point w_2 is added to the simple vertices set S_3 = {w_0, w_1, w_2}.

Find the closest point v_3 on the triangle (w_0, w_1, w_2). We can find the farthest point w_3 on the boundary along direction \overrightarrow{v_3o}. Now we focus on the new convex hull S_4 = <w_0, w_3, w_2>.

The length of the W triangle will become smaller as we continue these steps. For convex faceted objects, the closest point will be found in a finite number of steps.


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3D Model Viewer: add grid plane and convex hull.
Add google translate tool at right-bottom position.

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