2025-03-14

Last modified: 2025-03-15 08:09:04

• PolarPattern domain repetition
• Using Vec3s
• Developing SDFs
• Todo

PolarPattern domain repetition

I am having some trouble getting either my or Cursor's head around the mathematics.

I think we need to firstly rotate into "axis space" (so that our pattern rotates around Z), and rotate back at the end. That's fine.

And then with our pattern rotating around Z, we need to work out the angle to instance 0 and make sure our pattern segments are centered around the centre of instance 0.

And then work out what pattern segment the point is in.

And then rotate the point around Z so that it is in the first segment.

OK, finally got it.

Now just need fillet/chamfer.

Woo, check this out:

That is a PolarPattern of 40 cubes, with fillets on the joins. Domain repetition with 7 overlaps in each direction.

Using Vec3s

Currently lots of code does ad-hoc vector handling, even though I have a Vec3 class.

Firstly I should make .cursorrules tell it to use the Vec3 class, and secondly I should make it change everything to use Vec3s.

Where we have GLSL code like:

vec3 axis = vec3(${normalizedAxis.x.toFixed(16)}, ${normalizedAxis.y.toFixed(16)}, ${normalizedAxis.z.toFixed(16)});

We should maybe make Vec3 have a toFixed() function and then:

vec3 axis = vec3(${normalizedAxis.toFixed(16)});

Or maybe just glsl():

vec3 axis = ${normalizedAxis.glsl()};

Which gives you a string like "vec3(0.0, 0.0, 0.0)" but 16 decimal places or whatever.

Developing SDFs

I think the way to develop SDFs is in 2d in shadertoy. This is so blatantly obvious that I don't know why I didn't work it out before.

Instead of writing JavaScript code to make 3d SDFs, and then loading the app up in Firefox and manipulating the document tree to put objects where I want them, and then trying to work out if the SDF is broken by applying roughness/thickness/etc., I should just make a 2d version in shadertoy and show the actual distance field.

(And, further, I should add a "field cross section" mode to Isoform that will plot a cross section of the scene as a 2d field).

Here is a field cross section view:

You can see that the chamfer causes a warped interior SDF, which then causes a broken "thickness".

Todo

• can we interrupt shader compilation?
• make the axis indicator more clearly show whether something is pointing towards or away
• don't recompile the shader twice when we add a new node and then immediately start editing it (once for the new tree, once for the new secondary - just do the new secondary the first time around)
• move static matrix calculations etc. out of the shader code into JavaScript
• recompile shader if "bound" mode does not match what it was, and we need to draw a secondary
• calculate bounding spheres for more node types
• check bounding boxes in Union etc. in the shader? to avoid calculating parts that can't contribute
• how harmful is branching in shaders? how does it actually work? https://docs.unity3d.com/6000.0/Documentation/Manual/shader-branching.html - sounds like it might run both branches and discard one result, in which case branching based on bounding spheres is totally useless because it has to evaluate the worst-case branch anyway? or is it still helpful because if every "warp" takes the same branch then we do get to skip the slow path? https://shader-tutorial.dev/advanced/branching/
• how could we do tests? have some basic parts and octree of SDF samples, check that they're all within limits, flag parts that are wrong? compute it for each node in the tree and only show the user the smallest incorrect subtree; we could initialise it with randomly-combined parts to sort of "fuzz test" the combinations
• plot a cross section as a 2d field
• cooler-looking lighting
• worldtoScreen/screenToWorld broken
• infinite extrusion, infinite pattern
• choose whether extrusions are reversed, midplane, different length in each direction
• "Clone" or "Reference" node that is a shallow reference to another node
• copy or duplicate subtree
• Linear Pattern with domain repetition along X axis is reversed (rotateToAxis/rotateFromAxis issues?)