Question

I’m currently trying to implement a silhouette algorithm in my project (using Open GLES, it’s for mobile devices, primarily iPhone at the moment). One of the requirements is that a set of 3D lines be drawn. The issue with the default OpenGL lines is that they don’t connect at an angle nicely when they are thick (gaps appear). Other subtle artifacts are also evident, which detract from the visual appeal of the lines.

Now, I have looked into using some sort of quad strip as an alternative to this. However, drawing a quad strip in screen space requires some sort of visibility detection – lines obscured in the actual 3D world should not be visible.

There are numerous approaches to this problem – i.e. quantitative invisibility. But such an approach, particularly on a mobile device with limited processing power, is difficult to implement efficiently, considering raycasting needs to be employed. Looking around some more I found this paper, which describes a couple of methods for using z-buffer sampling to achieve such an effect. However, I’m not an expert in this area, and while I understand the theory behind the techniques to an extent, I’m not sure how to go about the practical implementation. I was wondering if someone could guide me here at a more technical level – on the OpenGLES side of things. I’m also open to any suggestions regarding 3D line visibility in general.

Answer 1

I have worked out a solution that works nicely on an iPhone 4S (not tested on any other devices). It builds on the idea of rendering world-space quads, and does the silhouette detection all on the GPU. It works along these lines (pun not intended):

• We generate edge information. This consists of a list of edges/”lines” in the mesh, and for each we associate two normals which represent the tris on either side of the edge.
• This is processed into a set of quads that are uploaded to the GPU – each quad represents an edge. Each vertex of each quad is accompanied by three attributes (vec3s), namely the edge direction vector and the two neighbor tri normals. All quads are passed w/o “thickness” – i.e. the vertices on either end are in the same position. However, the edge direction vector is opposite for each vertex in the same position. This means they will extrude in opposite directions to form a quad when required.
• We determine whether a vertex is part of a visible edge in the vertex shader by performing two dot products between each tri norm and the view vector and checking if they have opposite signs. (see standard silhouette algorithms around the net for details)
• For vertices that are part of visible edges, we take the cross product of the edge direction vector with the view vector to get a screen-oriented “extrusion” vector. We add this vector to the vertex, but divided by the w value of the projected vertex in order to create a constant thickness quad.

This does not directly resolve the gaps that can appear between neighbor edges but is far more flexible when it comes to combating this. One solution may involve bridging the vertices between large angled lines with another quad, which I am exploring at the moment.