let rotX =0, rotY =0,
perspective =500,
depth,
currX, currY;// learned something like this at Andries Odendaal's www.wireframe.co.za function point3d(x, y, z){
let cosX = Math.cos(rotX),
cosY = Math.cos(rotY),
sinX = Math.sin(rotX),
sinY = Math.sin(rotY),
posX, posY, posZ;
posZ = z * cosX - x * sinX,
posX = z * sinX + x * cosX,
posY = y * cosY - posZ * sinY,
posZ = y * sinY + posZ * cosY;
depth =1/ (posZ / perspective +1);
currX = posX * depth;
currY = posY * depth;return[ currX, currY, depth ];}
Here’s is an example of it in action:
I’ve used this code many many times, it’s just easy to throw into any language and instantly get 3d points rendered in 2d. Here is a short video of a Java applet from 2003 called “Catch Env” that made use of it:
You’ll notice in that source, that I nested the equation to allow for local and global transformations. It was around that time that I learned the ins and outs of real 2D and 3D matrix transformation math… Ken Perlin’s classfiles from NYU were a real help when I was learning that stuff. I don’t think this was the exact file I was working with, but it was definitely on his site somewhere.
Before all that, during my junior year in college I created a 3d engine based off Odendaal’s code in Director (Lingo). Here is a video of some of the demos for it:
…and here is a strange screenshot from my personal website at the time:
Just an example of a powerful snippet and a gateway to learning matrix transformation math. When I first really dug in to html5 canvas - before WebGL was supported so widely - having this trick up my sleeve was great. As you can see in the below link, I used it more than a few times back then:
Around 2015 I had the idea for a PRNG that would clamp itself and have moments of “smoothness”. When I got around to trying to create such a thing, the result was something I jokingly called the “Hermit Crab Curve”. I also called it the “Shard Curve”.
The equation for the curve defines a radius in polar coordinates:
Where a and d are paramters that control the detail of the curve. o is a rotation and offset value for the angle and s is a scalar. Note the use of rem. The resulting curve is much less interesting if a standard modulo is used in place of a remainder:
The above variable values were found using this interactive version of the equation:
To illustrate how you might use this as a PRNG I created this fork of the above pen:
Circle fitting is one of those things I've never bothered to do... today I figured I'd give it a try and this is what I came up with. I posted it on wonderfl: