How do I render thick 2D lines as polygons?

Question

I have a path made up of a list of 2D points. I want to turn these into a strip of triangles in order to render a textured line with a specified thickness (and other such th

Answer 1

I ended up having to get my hands dirty and write a small ribbonizer to solve a similar problem.

For me the issue was that I wanted fat lines in OpenGL that did not have the kinds of artifacts that I was seeing with OpenGL on the iPhone. After looking at various solutions; bezier curves and the like - I decided it was probably easiest to just make my own. There are a couple of different approaches.

One approach is to find the angle of intersection between two segments and then move along that intersection line a certain distance away from the surface and treat that as a ribbon vertex. I tried that and it did not look intuitive; the ribbon width would vary.

Another approach is to actually compute a normal to the surface of the line segments and use that to compute the ideal ribbon edge for that segment and to do actual intersection tests between ribbon segments. This worked well except that for sharp corners the ribbon line segment intersections were too far away ( if the inter-segment angle approached 180' ).

I worked around the sharp angle issue with two approaches. The Paul Bourke line intersection algorithm ( which I used in an unoptimized way ) suggested detecting if the intersection was inside of the segments. Since both segments are identical I only needed to test one of the segments for intersection. I could then arbitrate how to resolve this; either by fudging a best point between the two ends or by putting on an end cap - both approaches look good - the end cap approach may throw off the polygon front/back facing ordering for opengl.

See http://paulbourke.net/geometry/lineline2d/

See my source code here : https://gist.github.com/1474156