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57 lines
5.5 KiB
Markdown
57 lines
5.5 KiB
Markdown
---
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title: "Guessing Vinyl Colours"
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emoji: 🎨
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date: 2024-05-07T15:13:43+01:00
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draft: false
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summary: I used my Nix Mini colorimeter & a bit of maths to estimate transparency for some adhesive vinyl I bought.
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tags:
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- maths
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- colour
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- vinyl
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- SilhouetteCameo
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topics:
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- Creativity
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- Maths
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math: true
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---
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I've been getting a lot more use from my [Silhouette Cameo 4](https://www.silhouetteamerica.com/featured-product/cameo) plotter/cutter recently, and I've been using a couple of different vinyls to make things. I found it annoying that I couldn't get a good read on what the colour was before I purchased them, so here's the readings I've taken for the vinyls I bought & where I bought them in case any one else finds them useful!
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I took readings for their colour on both black and white card to try and estimate transparency — the process I followed is below. You can see the cheaper "IModeur" yellow vinyl is thinner, and transparent enough to make a difference!
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| Vinyl colour | Approx colour | On top of {{< swatch "239,236,230" >}} | On top of {{< swatch "64,63,66" >}} |
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|-------------------------------------------------------------------------------------------------------------------|-----------------------------------|----------------------------------------|-------------------------------------|
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| [Oracal 651 sample](https://www.gmcrafts.co.uk/product/sampler-pack-basic-oracal-651-for-silhouette/): Red | {{< swatch "185,0,9,0.98" >}} | {{< swatch "194,0,11" >}} | {{< swatch "174,0,13" >}} |
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| [Oracal 651 sample](https://www.gmcrafts.co.uk/product/sampler-pack-basic-oracal-651-for-silhouette/): Yellow | {{< swatch "254,192,0,0.99" >}} | {{< swatch "255,192,0" >}} | {{< swatch "251,191,0" >}} |
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| [IModeur Glossy Yellow](https://www.amazon.co.uk/dp/B09JG886SK) | {{< swatch "219,196,11,0.83" >}} | {{< swatch "248,212,14" >}} | {{< swatch "167,165,55" >}} |
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| [Oracal 651 sample](https://www.gmcrafts.co.uk/product/sampler-pack-basic-oracal-651-for-silhouette/): Lime Green | {{< swatch "100,164,43,0.99" >}} | {{< swatch "101,164,44" >}} | {{< swatch "100,163,44" >}} |
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| [IModeur Glossy Green](https://www.amazon.co.uk/dp/B09JG7Y1Y4) | {{< swatch "0,119,47,0.99" >}} | {{< swatch "0,122,48" >}} | {{< swatch "0,116,49" >}} |
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| [Oracal 651 sample](https://www.gmcrafts.co.uk/product/sampler-pack-basic-oracal-651-for-silhouette/): Azure Blue | {{< swatch "0,90,173,1" >}} | {{< swatch "0,90,173" >}} | {{< swatch "0,90,173" >}} |
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| [IModeur Glossy Blue](https://www.amazon.co.uk/dp/B09JGBNNCT) | {{< swatch "0,137,206,0.99" >}} | {{< swatch "0,138,209" >}} | {{< swatch "0,136,202" >}} |
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| [Oracal 651 sample](https://www.gmcrafts.co.uk/product/sampler-pack-basic-oracal-651-for-silhouette/): Ice Blue | {{< swatch "59,159,211,1" >}} | {{< swatch "58,159,212" >}} | {{< swatch "60,158,209" >}} |
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| [Oracal 651 sample](https://www.gmcrafts.co.uk/product/sampler-pack-basic-oracal-651-for-silhouette/): Lilac | {{< swatch "187,147,186,1" >}} | {{< swatch "188,146,186" >}} | {{< swatch "187,147,186" >}} |
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| [IModeur Glossy White](https://www.amazon.co.uk/dp/B09MHNX66S) | {{< swatch "238,236,237,0.95" >}} | {{< swatch "239,236,236" >}} | {{< swatch "228,229,230" >}} |
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| [IModeur Glossy Black](https://www.amazon.co.uk/dp/B09MH8GL3N) | {{< swatch "5,0,8,1.0" >}} | {{< swatch "4,0,8" >}} | {{< swatch "6,0,7" >}} |
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_I'll keep an up-to-date list of vinyl I buy and their colours in my [memex page on plotting](/memex/art-design/plotting/)._
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### Colorimetric process
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I measured these by putting two squares of the vinyl on black card and on white card, then using the difference between their measured colours (using my trusty [Nix Mini 2](https://www.nixsensor.com/mini-3-color-sensor/)) to deduce their colour _including_ transparency.
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This process isn't perfect, in the real world a material can be differently transparent at different frequencies. My process was:
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1. Measure the sRGB values for both the plain white ($R_c^w$, $G_c^w$, $B_c^w$) and black ($R_c^b$, $G_c^b$, $B_c^b$) card I'm using as backing paper (values in the table headers above).
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2. Measure the sRGB values for the vinyl being tested on both black and white card (in the right-most two columns above).
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3. Calculate the [colorimetric greyscale](https://en.wikipedia.org/wiki/Grayscale#Colorimetric_(perceptual_luminance-preserving)_conversion_to_grayscale) value for both the white and black card ($Y_c^w$, $Y_c^b$), and the vinyl on both black and white card ($Y_v^w$, $Y_v^b$), from their measured RGB values
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$$Y = 0.2126R + 0.7152G + 0.0722B$$
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4. Calculate the alpha value for the vinyl from the greyscale values:
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$$A = 1 - \frac{Y_v^w - Y_v^b}{Y_c^w - Y_c^b}$$
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5. Use the calculated alpha to find the 'true' red, green, and blue values for the vinyl, averaging the results from the black and white backing card:
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$$R = \frac{R_c^w + R_c^b}{2} + \frac{R_c^w + R_c^b - R_v^w - R_v^b}{2 A}$$
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6. Clip the calculated sRGB values to be within [0, 255], for the oddities!
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