# 3D in D3

I have spent some time lately with D3. It’s a lot of fun to build interactive graphs. See for instance this demo (will provide a longer writeup soon).

D3 doesn’t have support for 3D but you can do projections into 2D pretty easily. It’s just old school computer graphics. I ended up adding an animated background to this blog based on an experiment. The math is simple.

First, there’s the rotation. Given a bunch of 3D coordinates, how do you rotate them in 3D space? The cleanest way is to define angles $\alpha, \beta, \gamma$ and use them for rotation in the yz-plane, xz-plane, and xy-plane, respectively. Each of them define a rotation matrix. For the xy-plane, we get the rotation matrix $R_{xy}$ (see code):

We get three of these matrices in total: $R_{yz}, R_{xz}, R_{xy}$ .

The rotation of any vector $\mathbf{v}$ can now be described as $R_{yz} R_{xz} R_{xy}\mathbf{v}$ . The nice thing is we can precompute the product of these matrices $R$ (see code). Math porn:

Now going forward we can use the matrix $R$ to rotate any vector $\mathbf{v}$ (see code).

The other thing you want to do is to make distant objects look further away. Thinking through proportionalities you can derive a pretty simple equation (see code). $% $ , and same for $y$ . The constant $d$ is just a hack to scale down the $z$ values.

Not sure whether the 3D animation is cool or just annoying, but I’ll prob keep it for a bit – enjoy!