2D outline algorithm for projected 3D mesh

Question

Given: A 3D mesh defined with a set of vertices and triangles building up the mesh with these points.

Problem: Find the 2d outline of the projected arbitrarily rotated m

Answer 1

The alpha shapes technique mentioned in this question handles a general set of points where the vertex connections are not known:

Is there an efficient algorithm to generate a 2D concave hull?

However, since you already know "face" information which can be preserved through the projection, it is probably not the best approach.

A brute force algorithm might feasible, especially if spatial sorting structures where used. eg for each facet:

1. Project facet on to the plane
2. Check if projected facet is completely enclosed by existing geometry, if yes: done (no need to expand projected silhouette)
3. If points fall outside the existing geometry, do triangle-triangle intersections to determine which portions fall outside, build an arbitrary n-gon (possibly concave) to fill the missing space, then chop the n-gon in to triangles

Another idea, depending on the fidelity you require, is just shoot a bunch of rays normal from your projection plane to your original geometry. Create a 2d hit/miss and use that to determine your extents.