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Author Topic: Miranda's cheapskate Steampunk apparel  (Read 33201 times)
J. Wilhelm
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« Reply #125 on: March 20, 2021, 01:08:12 am »

Well, it's been a vey long time since I last posted here! Back in 2019 there were so many events happening I was so busy putting outfits together (to avoid the shame of being seen in th same outfit twice in a season) to write about them, and of course in 2020 it was the exact opposite...

I did start a new project in the first lockdown in 2020, but then a stream of family difficulties including damed Covid doing its worst, as it has for so many other families, removed any enthusiasm I had for any such frivolities. Now though I feel I need to pull myself back to a point where I'm enjoying life again, and part of that is getting back to being creative. So, time to revisit the aforementioned project.

At the start of lockdown, before everything became so awful, there were plenty of social media posts (at least in the social media I frequent) suggesting exceptionally large crinolines to encourage social distancing. I took this as a challenge to make an outfit inspired by 'peak crinoline', which as far as I can tell was mid 1860s. It seems the largest they every actually got (not counting the 'spoof' ones for satirical images) was about six feet in diameter. So, I dissassembed my existing crinoline (diameter as then four feet), added expansion panels and re-worked the hoops. Now depending on the hoops inserted it can be the original size (using clips to pull in the additional fabric) or expanded to slightly over the six foot mark. In the process I also made up two petticoat layers to go over it from some old net curtains:



The only problem was then how to make a frock when no pattern I knew of actually went to that size. Clearly it was time to brush up on my 3D geometry and fire up the speadsheet!

To be continued...

Yours,
Miranda,

Would that be a solid of revolution, like an ellipsoid? Or more like a paraboloid?  Grin
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Miranda.T
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« Reply #126 on: March 21, 2021, 10:59:55 pm »



Would that be a solid of revolution, like an ellipsoid? Or more like a paraboloid?  Grin

Close - I went with elliptical in the end.

As the esteemed Admiral has noted, I needed to decide on a shape for the crinolines`, and hence skirts', cross sections. One constraint was that for both four foot and six foot widths it had to be about the same vertical fall as I couldn't easily alter its length. So after some experimentation I found elliptical sections worked best. Here are the two cross-sections compared:



Generating pattern pieces from this was made easier by the circular symmetry of the crinoline; for each height-step down the skirt I treated the circle at that level as the base of a cone; I used a spreadsheet to find the radius at each height which it then 'flattened' to and arc and from this found the x & y coordinates of the pattern piece's side (I've four sections around the skirt, with as usual each pattern piece being half of a section for cutting on the fold). Once cut and sewn I was very pleased to see it fitted the cage perfectly.

Skirts of this era typically had several layers giving a tiered effect, but rather than just adding an over-skirt that was just shorter, I decided I'd use the spreadsheet to give the second a bit more interest in the from of a wavy edge. I added a cosine variation along both sides (trough at back and front centres) but with half the amplitude on the front sections compared to the back to give a rise across the profile. The pattern pieces are below, with the shorter ones for the over-skirt:



Again, when cut and sewn the fit was perfect. Unfortunately I didn't get any pictures of the skirt on the crinoline as at this point we'd all moved to working from home in lockdown and I had to quickly 'take down' the skirt to free up the sewing room (our conservatory) to make some extra workspace. And of course right now we're pretty much in the same situation...

I've of course done a lot of pattern adjustment before, but having the result fit first time without a load of time-consuming adjustment was rather pleasing. So it got me wondering, could I do the same for the bodice? It would mean making a 3D model of a (my) torso, 'fitting' material on it and generating pattern pieces from this. Clearly a spreadsheet was not going to be up to this task, so it was time to start coding...

To be continued...

Yours,
Miranda.
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J. Wilhelm
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« Reply #127 on: March 22, 2021, 10:17:40 am »

Sartorial Maths  Grin I love it!
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« Reply #128 on: March 22, 2021, 12:30:48 pm »

And I'm very impressed! Cheesy
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Miranda.T
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« Reply #129 on: March 22, 2021, 11:34:37 pm »

Sartorial Maths  Grin I love it!
had cause

What an excellent title for this endeavor!  Smiley

And I'm very impressed! Cheesy

Thank you!

To produce pattern pieces I'd need to code up a model of a torso, but before that I'd need a way to visualise the result. I suppose I could have done this using OpenGL functions, but that would mean learning how to use the OpenGL framework (of which I have no experience) and besides which I'd often wondered how 3D imagery worked, so now was the ideal time to satisfy that curiosity. So with a free couple of hours I sat down with pencil and paper to work through the maths.
Imagine x, y z axes, and you are looking along a line towards their origin which is rotated in the xy plane at a given angle to the x axis and then rotated again up or down from this plane. By varying the angles you can now look into the space from any direction. Pick a fairly arbitrary distance along this line from the origin and at that point add a plane perpendicular to the observation line; this will be the 2D plane with x' and y' axes onto which the 3D image will be projected. I made the x' axis of this parallel to the xy plane; I didn't implement any rotation about the observation line as I don't need it for this application, but if I ever wanted to add it I'd just do a 2D rotation in the x'y' plane. Now for any point in the xyz space I just need to find out how far this is perpendicularly from the observation line in the x' and y' directions using trig and 3D Pythagarus. Once coded as a function, I just needed to pass the angles and z,y,z to get back x' y' ready to plot. Now onto the torso model.

Obviously the front and back needed separate models, and due to symmetry just one half of each needed to be generated. The results look like this:



The trunk is made up of ellipses in both the horizontal and veritical planes. The breast (just one so singular) is hemispherical below the centre line and elliptical above. Once the breast is added smoothing is applied to even off the breast-torso join and the profile from the vertiucal centre of the breast is taken back to the torso centre to model the drape of material (at least for a roughly period correct Victorian outfit; if I want to make something a bit more Steamy than period I could leave the edges unsmoothed and generate pattern pieces for the cups). There are variable parameters for all the dimensions; I should stress the current model is not my body but just a set of sensible working values. I suspect when I rework it for myself the waist will become rather chunkier  Roll Eyes. The model is generated as a set of points by stepping up and down vertically from the waist and at each height stepping around from 0 to 90 degrees giving a set of horizontal slices stacked on top of each other, a bit like those 3D jigsaws made up of planes of card.

The coloured lines represent the seams, neck hole and arm hole. These are variable so I can add different styles. For this one I'm going for an elliptical neck-line (I'll be adding a flounced bertha) and straight seams in a V to the waist (to give the illusion it's smaller than reality - the Victorian's knew a thing or two about body-con!)

So the next challenge is to turn the model into actual pattern pieces...

To be continued.

Yours,
Miranda.
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J. Wilhelm
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« Reply #130 on: March 23, 2021, 06:50:06 am »

I knew at some point there's be an excuse to create a Steampunk Sartorial Plotter app.
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Miranda.T
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« Reply #131 on: March 29, 2021, 11:20:12 pm »

Didn't Thomas Edison, on talking about the difficulties of how to make an electric light bulb, say something like "I have not failed. I've just found 10,000 ways that won't work"? Maybe he should have just asked Swan... Anyway, I've found lots of ways to not generate pattern pieced from my 3D model, but I hope I may have now found one that works.

Here's the rationale. Firstly, set a couple of straight datum lines - one along the waist, another straight up the centre of the front/back or along the side seam (depending on the piece being generated). Generate x & y coordinates for the points on these lines by finding the distance between them in the 3D grid using Pythagoras.

Then work above the waist one layer of points at a time, and in each layer run around the points from centre or seam, again depending on the piece. For each point, in the 3D model find the horizontal and diagonal distances from the previous point on this line and the previous point on the line below. Combine these with the distance between these previous points in the pattern xy plane to make a triangle; use this to find the position of the new point in the pattern xy plane and add it. Continue with next point. Obviously this distorts the grid of points, but hopefully the give in the material compensates for this. Repeat down below the waist.

I found you have to stop at the seam or the level of distortion beyond it is so great it ruins the pattern piece the further you move up it. Also the position of the seam is important; in the wrong place you find towards the top you get elements that cannot be formed into triangles (the sum of two sides is less than the length of the third), which I'm taking to mean that transposition is geometrically not possible.

The pieces generated (both for the front) look like:





The next thing to do is feed in the parameters for my mannequin (that should be a lot easier than testing it out on myself), generate the pieces for it and see if they fit.

To be continued...

Yours,
Miranda.
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J. Wilhelm
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« Reply #132 on: March 30, 2021, 08:58:41 am »

I understood the first part of your previous post as being the projection of a 3D surface onto a plane of the screen with primarily pitch and yaw angles. That's basically the same thing I did to visualize 3D surfaces when trying to plot in my old HP 28s calculator back in 1989,before the HP 48 could plot in 3D (that was for my maths class in college).

The second part of the same post deals with the generation of elliptical cross sections parallel to the xy plane, does it not? In what format is your data, (x,y,z)? Because I was going to suggest mapping the (x, y, z) coordinates into polar coordinates, that is, (x, y, z) → (r, θ, z), where r² = x²+y², and θ = arc tan y/x, and that way you can work with a protractor and a ruler to build a "mannequin" layer by layer using horizontal disks of cardboard, Styrofoam or similar. θ=0 is defined as the seam. The z coordinates are the same for each plotted ellipse. Then just drape the cloth over the mannequin and cut!

Now, if building a mannequin is not an option (you have one) and you want to plot the cloth pattern itself on paper directly , the you "unwrap" the polar angle θ=0 to 90 degrees on a flat plane (like unrolling a rolled sheet of paper) and calculate the perimeter, s, from θ=0 at the seam by writing the integral

s=∫0θrdθ,

noting that an ellipse is defined as

r=√(a²cos²θ+b²sin²θ) where I assume you know a and b for that particular ellipse at height z over the waist.

So, the partial perimeter of the ellipse from θ=0 at the seam to some angle θ=θ (90 degrees in your case) is

S(θ)= ∫0θ  √( a²cos²θ+b²sin²θ) dθ

This integral doesn't have a solution except by approximation, that is using a quadrature method. Fairly easy to do as a sum of differential rectangles or triangles, like

S(θ)= Σi=1n  √( a²cos²θi+b²sin²θi) Δθ

Where Δθ is some arbitrary small angle equal to 90 degrees divided by the number, n, of angle slices you want, like so:

Δθ=θ/n

This could be programmed in a spreadsheet quite easily.

Or are we making things too complicated?  Grin

Actually you don't need to calculate the quadrature. You can get one of those flexible rulers used for architecture and work by measuring the perimeter of each of your cardboard plates (even a piece of string will do) and use the seam as your zero displacement datum.
« Last Edit: March 30, 2021, 09:05:59 am by J. Wilhelm » Logged
Miranda.T
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« Reply #133 on: March 30, 2021, 01:34:24 pm »

Dear Admiral Wilhelm,
In the full detail it's pretty much as you surmised. The 'virtual mannequin' does indeed consist of stacked layers each separated by the same vertical distance (1 mm); I made this the y-axis. For each layer the radial distance to the 'surface' is found for each degree between 0 and 90 and converted to x & z coordinates, these are stored in an array indexed on y and angle theta.

The elliptical integration approximation was used for the skirt, but the bodice is more complex, varying in each plane (xz, xy and yz) both elliptically for the trunk and additionally for the front the breast shape is added on top and then and a smoothing routine applied to remove sharp transitions between the two (as a material would when draped across them). Hence an algebraic integral is not an option leading me to essentially numerically integrate in 2D across the surface. I'll find out if my method of doing this is correct when I try cutting out he pattern and fitting it to a real body rather than a virtual one...

Yours,
Miranda.
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J. Wilhelm
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« Reply #134 on: March 30, 2021, 07:25:00 pm »

Dear Admiral Wilhelm,
In the full detail it's pretty much as you surmised. The 'virtual mannequin' does indeed consist of stacked layers each separated by the same vertical distance (1 mm); I made this the y-axis. For each layer the radial distance to the 'surface' is found for each degree between 0 and 90 and converted to x & z coordinates, these are stored in an array indexed on y and angle theta.

The elliptical integration approximation was used for the skirt, but the bodice is more complex, varying in each plane (xz, xy and yz) both elliptically for the trunk and additionally for the front the breast shape is added on top and then and a smoothing routine applied to remove sharp transitions between the two (as a material would when draped across them). Hence an algebraic integral is not an option leading me to essentially numerically integrate in 2D across the surface. I'll find out if my method of doing this is correct when I try cutting out he pattern and fitting it to a real body rather than a virtual one...

Yours,
Miranda.

The Great Steampunk Sartorial Guide - with software included.  Grin
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« Reply #135 on: March 31, 2021, 10:30:01 am »

Dear Admiral Wilhelm,
In the full detail it's pretty much as you surmised. The 'virtual mannequin' does indeed consist of stacked layers each separated by the same vertical distance (1 mm); I made this the y-axis. For each layer the radial distance to the 'surface' is found for each degree between 0 and 90 and converted to x & z coordinates, these are stored in an array indexed on y and angle theta.

The elliptical integration approximation was used for the skirt, but the bodice is more complex, varying in each plane (xz, xy and yz) both elliptically for the trunk and additionally for the front the breast shape is added on top and then and a smoothing routine applied to remove sharp transitions between the two (as a material would when draped across them). Hence an algebraic integral is not an option leading me to essentially numerically integrate in 2D across the surface. I'll find out if my method of doing this is correct when I try cutting out he pattern and fitting it to a real body rather than a virtual one...

Yours,
Miranda.

My virtual body is WAY better than my real one... Wink
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Miranda.T
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« Reply #136 on: March 31, 2021, 11:01:11 pm »

I've now added the export routine for the pattern pieces, put out as A4 'tiles' ready for printing & sticky-taping together (a couple of tiles below). Next is to feed in the mannequin's parameters, print off & cut the pattern pieces and see how well or badly they fit. I'm anticipating quite a bit of fiddling with the code to get a proper fit; for example, I wonder if I need to add an 'ease' parameter to make the exact fit a bit less critical. Anyway, trial run first.

Yours,
Miranda.





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Miranda.T
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« Reply #137 on: April 02, 2021, 12:02:54 am »

The pattern pieces do indeed come together to produce something that looks like it could make a garment  Smiley. I have discovered though that it's quite difficult to measure the parameters even on a static mannequin; my first attempt was way off. After a couple of iterations tweaking the parameters, I've got something which is a fit, but still could be better (still a bit baggy about the boobs, but to be fair the mannequin has pretty small ones).

Anyway, as I'm not making clothes for the mannequin so I think I'll leave that experiment there. I need to give some thought as to how to measure the parameters more accurately and then check them without the tedious process of printing out the patterns pieces and assembling them. I might try outputting out the circumference of the virtual model's body at various heights which can then be compared to the real body to see how closely they match.

Yours,
Miranda.

Edit: I think I know how to improve the parameter measuring. Stripped down to my unmentionables, I'll take front and side photos whilst holding a metre rule. I'll import these into my DTP program and, using its measuring tools and the metre rule for scale, I should be able to get pretty accurate values. Then I can export front and side projections from the 3D model, overlay onto the real photos and see how well they fit. If it works, it will be a virtual fitting room, which of course given the pandemic is the only form of fitting room one can go into at the moment...
« Last Edit: April 02, 2021, 10:01:59 am by Miranda.T » Logged
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