tl;dr, how do we go from the Q matrix for a given edge to the edge's cost?
Long from of question: I understand how each point has a quadric error matrix Q_v, and each edge has a quadratic error matrix Q_e (from summing the matrices from both endpoints).
From this, how do we "find the point at each edge minimizing quadric error"? I believe this is looking at the Q_e for each edge, and choosing some query point u s.t. (u_TQu) is minimized, but where is this query point located then? If the query point is on the edge itself, then I feel all this stuff wouldn't make much sense since all points on the edge lie on the planes of the two triangles that make up the edge -> plane distances are zero.
tl;dr, how do we go from the Q matrix for a given edge to the edge's cost?
Long from of question: I understand how each point has a quadric error matrix Q_v, and each edge has a quadratic error matrix Q_e (from summing the matrices from both endpoints).
From this, how do we "find the point at each edge minimizing quadric error"? I believe this is looking at the Q_e for each edge, and choosing some query point u s.t. (u_TQu) is minimized, but where is this query point located then? If the query point is on the edge itself, then I feel all this stuff wouldn't make much sense since all points on the edge lie on the planes of the two triangles that make up the edge -> plane distances are zero.