1. The endpoint of the stroke doesn't need to be exacly on the line. Depending on the size of the object (you don't give any indication), this might be good enough, not visible.
2. If this is something important and will be visible while zoomed in, you could use a distorted black rectangle, of which the points can align perfectly with the outline.
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will_f wrote:
1. Place another point on the same black line, about a millimeter or two from the point in question.
2. Then select the hide line segment tool (H) and click on the segment closest to the edge.
3. You may have to slide the new point you created a bit to one side or the other, in order to get it to line up correctly.
Woah, that's a nice little trick! Still, the angle of the end will not necessarily correspond to the outline.
AS 9.5 MacPro Quadcore 3GHz 16GB OS 10.6.8 Quicktime 7.6.6
AS 11 MacPro 12core 3GHz 32GB OS 10.11 Quicktime 10.7.3
Moho 13.5 iMac Quadcore 2,9GHz 16GB OS 10.15
Moho 14.1 Mac Mini Plus OS 13.5
you could use the Bezier handles to adjust the precise shapes of the lines if the exact shape isn't critical (and maybe add a point or two to the outline and/or the traversing line to help you to make a right-angled connection - no need in this case to hide short line segments)...