The first reaction the word “Maths” is generally one of fear and loathing. Whilst science has recently been given a media makeover with the likes of Brian Cox and Dara O’Briain both presenting prime time TV shows in what had previously been considered terminally dull subject areas, Maths still remains deeply unglamorous. Of course the interesting thing is that maths, perhaps more than any other subject, has the capacity to illuminate, inspire and astound.

We wanted to make a maths game with allure; something you wanted to touch, something that had the capacity to surprise and, crucially, something that didn’t instantly cause students to put up the shutters. One of the problems is that when you think of maths most people instantly default to imagining a sea of numbers. Maths can, however, encompass more than abstract numbers- it can include the wonders of geometry and this was where we found our ‘eureka’ moment.
Focussing on Geometry

The idea that 2D shapes can be found within 3D shapes is interesting enough on its own but when you begin to see some examples of what this means it becomes quite an eye-opener. Slice a cylinder at a jaunty angle and you reveal an unexpected ellipse shape which looks as if it could never fit inside the starting object.

Early video prototype of Crafty Cut

Geometry is traditionally a difficult area of maths to teach and immediately we could feel a synergy between the notion of geometry and the tactile nature of a touchscreen device. By using such an interface we felt we could finally offer the students a maths theme game that is almost devoid of numbers.

Crafty Cut was now taking shape, the principles were clear; it’s an experiential game, one which encourages success through experimentation rather than cold calculation. The aim is to find a 2D shape within a 3D shape. So far, so good – on paper…

Taking the design from the drawing board to the tablet was a huge technical challenge. Essentially we needed to create a program capable of accurately rendering 3D objects, which can then be manipulated in any direction and sliced into pieces by a player trying to reveal a very precise 2D face. It then had to judge how successful a match the revealed shape was to the target shape, something much easier to ask for than to code.

We had to think very carefully about the presentation of the shapes: part of the challenge was that your mind expects to see an object in perspective rather than as an orthographic depiction (the kind you see on 2D blueprints and plans). The problem is that this same perspective makes it very difficult to accurately cut through an object. The angle of the planned cut doesn’t take into account the fact that the far side of the object ‘shrinks’ as it nears the vanishing point.

After much experimentation we developed a way to show a visual projection of your intended cut running through the object and that really helped. This sort of help was vital because we found that for many players this was the first time they had even thought about cutting 3D objects to reveal 2D faces – conceptually it was a leap of faith.

Once we had a system that allowed you to make an accurate cut we had to find a reliable way of judging the revealed face against the target shape. We couldn’t just drop the target shape over the new face – that would require a level of accuracy that simply wasn’t possible when you are using your fingers to make a cut. We needed to measure ‘relative success’ or the game would be too hard to play.

In the end we settled on a three star rating system:
The first star would relate to the number of sides the freshly revealed shape had in comparison with the target.
The second would look at the angles between each side.
The final star measured the length of each of the sides.

Result screen featuring three star rating system

Now we had all the mechanics in place it was simply a matter of selecting a number of 3D objects and target shapes to find. The difficulty curve across the game hinged on the type of shapes we used. We started with a set of primitive shapes familiar to any gamer, the standard role-playing dice shapes; 4 sided, 6 sided, 8 sided, 10 sided, 12 sided and 20 sided. These shapes already gave us plenty of choice but for the later levels we started to look at more outlandish geometry including our favourite ‘Great Stellated Dodecahedron’.

'Fiendish' level featuring a Stellated Dodechedron

We finally had an original and challenging game that brought the world of geometry to your hands. This was a product aimed at peaking the player’s curiosity about geometry and it seemed only fair that we allowed them to ‘play’ as well as just play, so we included a simple sandbox mode in which you could cut and sculpt all of the shapes just for fun.

Freeform sculpting in Create Mode

We like to think that Crafty Cut is a well-polished, solid game but we are never happy just to rest on our laurels. Our work with Amplify is all about iteration and subtle evolution over time so we will continue to try and improve upon the design. We love to test our products and listen carefully to the feedback we receive. Designing games in an ivory tower is a dangerous business; in the end you learn the most from watching how people play the game and listening to their experiences. The final shape of Crafty Cut will be hewn by the people who play it.

Find out more about Crafy Cut on the case study.