AS3 with Nape physics: How can I find a tangent from a point to a body?

Question

The short question: Is there any simple way in Nape to calculate the points of tangency with a Nape body object or shape given a point outside that body?

What I'm trying to do is create Worms-style rope physics. It basically works as an extendable line/distance joint that automatically breaks into segments when it comes in contact with the level geometry. I do this by raycasting from the most recent pivot point; if there is a collision I offset from the collision point by a couple of pixels, create a new rope segment, and make that point the new pivot. In case my character is swinging around a sharp corner, I then recast from that point, looping as necessary, until I'm clear of the level geometry.

It works amazingly well given my lack of experience, but there's one little cosmetic glitch. The rope won't wrap "tightly" around a horn-shaped protrusion. It's pretty easy to see why this is happening. Refer to the figure below.

I cast a ray each time I step the Nape world at 60 frames/second. Figure 1 shows the difference between two example raycasts. The character (not pictured) is at the end of the line, and he's fallen past the cliff "edge" in relation to the pivot in one step, so the collision point falls short of the desired point of tangency.

Figure 2 is what I end up with. The wraparound logic still works, by offsetting from the surface and recasting, but it doesn't appear "taut."

What I want is something like Figure 3, which corrects the angle to find the actual point of tangency with the body and creates the new pivot from that.

My planned fallback is to offset the angle of the raycast by small increments and recast until I no longer strike the level geometry, then back up one and use that as the collision point. Even that will probably require fewer computations than "curving" around like in Figure 2, but I'm still wondering: is there an even simpler way?

Answer 1

Excuse me for not commenting, but I don't have needed points for that :)

I've used something similar before (not exactly the same) and I think the way to go is to save the points of each cast, get the one with highest difference from the starting point, based on the y axis (if the rope goes up, then you get the point with smallest y and vice versa (rope going down from starting point)). Then you can fix the angle to point to this specific point, marked as an "edge". Later you can continue with the common pattern, as the rope will go in the other direction (exactly like the edge of a cliff).