This is Ren from the Shopify support team, thanks for your question!
You can absolutely achieve this by adding custom fields to your product page. One way to do it is through the custom code of the theme using line item properties. This will allow your customer to specify the dimensions needed for their custom cut glass. Pay careful attention to the type of theme you have as the tutorial differs depending on whether it's sectioned or non-sectioned. You can find the tutorials below:
Another option would be with the use of a product customizer app.
We have a lot of different options from very advanced customizations to simply input text boxes. Check out Infinite Product Options which boasts a free plan, free installation support, and the ability to assign price mark-ups if necessary.
For something a little more advanced, check out Bold Product Options. This app is fully customizable, allowing for a wide variety of options such as:
Apps are a great option if you're not comfortable installing your own code. Either way, both options will get you what you need to collect the necessary details from customers when they're placing their orders. How are you finding Shopify so far? If there's anything else I can do to assist, just let me know!