The question at
the end of Part I was simple:
What if I built the Guilloché model with Python instead?
I am not a professional
programmer. However, in 2026, when we want to build a small and highly
specialised tool for a particular workflow, AI-assisted coding has become a
practical way to turn a technical idea into a working prototype.
This was how I began
developing my own parametric Guilloché Generator.
I first explained to ChatGPT how Guilloché is produced in
the physical world: how the workpiece rotates, how the path changes
periodically, how the cutting tool creates a V-shaped groove, and which
parameters should influence the resulting pattern.
I then asked it to convert those manufacturing principles
into mathematical equations and executable Python code.
The program was not completed through a single prompt.
The development process was closer to iterative AI vibe
coding. I was responsible for explaining the craft, evaluating the geometric
results, identifying problems and introducing new constraints. AI helped
translate these ideas into a working software structure and revise the code
after each round of testing.
The earliest version could only draw a simple
two-dimensional path.
I gradually introduced parameters such as Diameter,
Amplitude, Frequency, Phase, Pattern Count, Groove Width and Groove Depth.
Later, I added a user interface so that the values could
be adjusted without directly editing the code. I also added a Preview window,
allowing the basic path and overall pattern to be inspected before generating a
high-resolution model.
Eventually, I asked the program to project the pattern
onto a simply defined domed surface.
If the dial radius is (a), and the height difference
between the centre and the outer edge is (h), a simplified parabolic dome can
be described as:
$\rho=\sqrt{x^2+y^2}$
$z_{\text{base}}(\rho)=h\left(1-\frac{\rho^2}{a^2}\right)$
The program first calculates the flat (x) and (y)
coordinates from the Guilloché equation. It then calculates the radial distance
(\rho) from the centre and uses this value to determine the corresponding dome
height.
Conceptually, if the shortest distance between a mesh
vertex and the engraved path is (D), the groove width and depth can be used to determine
how far that point should move downward.
A simplified V-shaped groove can be written as:
$z=z_{\text{base}}-d\max\left(0,1-\frac{D}{w}\right)$
Here, (d) represents the engraving depth, while (w)
represents half of the groove width.
The program then connects the calculated vertices into a
large number of triangular faces, creating a 3D mesh that can be exported as
OBJ or STL.
It can also export DXF, SVG and PNG height maps for CAD
reference, vector paths, rendering and future manufacturing experiments.
In other words, I am no longer asking the CAD software to
understand and calculate one hundred Guilloché cuts.
Instead, I complete the repetitive calculations outside
the CAD environment and import the already-generated result.
What Did This Tool Actually Change?
The most immediate benefit of the Guilloché Generator is
design efficiency.
I can change the frequency, amplitude, line count or dome
height within seconds, generate a new version, and import it into CAD or
rendering software to evaluate how it works on the dial.
Previously, comparing two Guilloché patterns might have
required two separate collections of sketches, sweeps and pattern features.
Now, I only need to change a small number of values.
However, the value of the tool goes beyond producing
attractive patterns more quickly.
Because every pattern is generated from clearly defined
and controllable parameters, it allows me to ask questions that are closer to
formal research:
Does increasing
the number of lines make a dial appear more refined while reducing its sense of
calmness?
Does a higher level of rotational symmetry make the
pattern feel more classical, formal or orderly?
Does a larger amplitude increase the sense of movement
and ornamentation, or does it make the surface appear visually chaotic?
How do groove width, groove depth and dome curvature
interact to influence light reflection and the perceived material quality of
the dial?
From Parametric Design to Kansei
Engineering
These questions made me realise that the Guilloché
Generator may be more than a modeling tool.
It could also become an experimental tool for Kansei
Engineering research.
The central idea of Kansei Engineering is to translate
users’ impressions, feelings and emotional responses into design and
engineering elements that can be measured and controlled.
In other words, it attempts to establish relationships
between subjective impressions such as “refined,” “calm,” “classical,” “modern”
or “luxurious,” and objective characteristics such as dimensions, proportions,
materials and geometry.
With a traditional Guilloché design process, every
experimental sample would require considerable manual modification, making it
difficult to change only one geometric factor at a time.
With a parametric generator, the dial diameter, material,
colour and lighting conditions can remain unchanged while only one selected
variable is modified.
A structured series of patterns could then be generated
and evaluated using semantic differential scales.
Participants might rate each design between pairs of
terms such as:
refined and rough, calm and dynamic, classical and
modern, formal and casual, luxurious and industrial.
Existing research into product surfaces has already
explored quantitative relationships between colour, texture, gloss, roughness and
human visual, tactile and emotional responses.
Research has also suggested that the expectations people
form by looking at a surface may not always match their impressions after
physically touching or handling it.
This is especially relevant to Guilloché.
The appeal of Guilloché does not come from geometry
alone. It also comes from the way microscopic grooves capture and reflect
light.
The same pattern may produce completely different
impressions when displayed on a computer screen, engraved into polished brass,
plated with another metal, or covered with transparent lacquer.
A possible next stage would therefore be to produce the
same set of patterns in two forms:
a group of computer-rendered images, and a group of
physically manufactured dial or metal samples.
Participants’ Kansei evaluations of the two formats could
then be compared.
Can computer rendering accurately predict the perceived
refinement, classical character or luxury of a physical Guilloché surface?
Which impressions can be predicted through geometry and
rendering, and which impressions only emerge through real materials, lighting
conditions and viewing angles?
This comparison could help validate the reliability of
computer visualization and also reveal how much designers should depend on rendered
images when making aesthetic decisions during the early stages of product
development.
A Generator Is Not the Same as Real
Guilloché
I do not believe that a Python generator can replace the
work of a skilled Guilloché craftsman.
A mathematical model can define an ideal engraving path,
but the physical result is still influenced by the shape of the tool, cutting
depth, material hardness, machine rigidity, surface finishing, plating, lacquer
and the operating technique of the craftsman.
A 3D rendering can only reproduce the material and
lighting conditions that have been defined within the software.
The purpose of this tool is therefore not to prove that a
computer can completely reproduce traditional craftsmanship.
Its purpose is to allow different design directions to be
explored systematically before committing to physical prototypes.
It turns patterns that would otherwise be compared mainly
through experience and intuition into a set of design parameters that can be
modified, recorded, reproduced and tested.
Conclusion: When Aesthetics Become
Computable
Looking back, this entire process began because CAD
software could not efficiently model a Guilloché surface.
That limitation forced me to move from CAD modeling to
mathematical curves, and from mathematical curves to Python, mesh modeling, AI
vibe coding and Kansei Engineering.
My engineering background once led me to believe that
everything should be accurate and precisely defined.
Over time, I began to understand that aesthetics can be
rational, but they can also contain qualities that cannot be fully explained
through rationality alone.
Parametric design is not intended to eliminate subjective
or irrational responses.
Instead, it gives us a method for studying how those
responses are created.
For me, the most valuable feature of this Guilloché
Generator is not the number of complex patterns it can produce.
Its real value is that it transforms a question such as:
“Which one looks better?”
into a more researchable question:
“Which geometric parameter changed the way we feel about
it?”
Once an aesthetic language can be translated into
parameters, it is no longer only a decorative pattern.
It begins to become a system that can be designed, tested
and studied.
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