3D graphics have appeared on the web in a few different forms over the years, but there never seems to be an industry-standard system or browser plugin that everyone can agree on. Some systems are long gone - does anyone still remember VRML?
So what's available now, and is it any good?
Build your own
Yes, it's possible to build your own 3D engine. My music video Dark Matter features 2D and 3D animations created in many different ways. Here's a looped version of part of it. Click on it to play/stop the video:
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The swirly patterns in this section of the video are Roessler and Lorenz attractors. This is right at the extreme DIY end of the scale - I created a small piece of software in C++ that calculates the 3D differential equations that define the shapes you see, and renders the result, frame by frame, onto a predefined background image. Because of the time taken by the computer to draw each frame of animation, the only way you can put this on the web is as a series of pre-rendered frames - a video. So there's no interactivity; all you can do is watch it.
Fine for data visualisations and for art's sake, but of limited commercial use. Those attractors need hundreds of millions of 3D points to be calculated for each frame of animation. Maybe we could cut that down to, say, fewer than twenty?