The Gender Politics of 1+1=2

Last weekend, I tried making a little romance game for a game jam. Surprisingly, the hardest part in the design was avoiding all sorts of gender politics minefields that I didn't realize were there. I guess there are so few games centered around romances, that I didn't understand that it's really easy to make an insensitive romance model. There are so many games centered on violence that the minefields in those games are well known: make sure your game isn't exclusively about white people killing non-white people and throw in a token mix of genders and you're generally pretty safe. With romance games, these sorts of politics haven't been worked out yet.

Terminology
Even figuring out something as basic as terminology was really difficult. I wanted to make a regency romance game, with Darcys and Elizabeth Bennets, who you are trying to get married. So the two types of characters in the romance simulation would most easily be named men and women. Of course, a computer simulation doesn't really care about genders, and given my proximity to San Francisco, there's no reason that my simulation shouldn't support the option of men-men, women-women, men-women, women-men, ?-? pairings. But what terms should I use for the two types of characters then? One way to get around this problem would be to only have one type of character, but I was making a tower defence game where the "attacking" characters are distinct from the "defence" characters. I decided to call the "attacking" characters suitors. But what would an appropriate term for the "defence" characters be? After much digging online, I couldn't find anything good. Terms like defendant, target, or wooed just seemed too adversarial or awkward. It's weird that I couldn't find a nice simple term to express the object of one's affections. Finally, after an hour of searching, I just gave up and decided to move on.

Romance Statistics
Since I was building a tower defence romance, the romances needed to be represented numerically so they could be simulated instead of using a hand-crafted narrative that might be possible in a work of interactive fiction. Now in a traditional tower defence, the units have various stats like hit points, attack power, defence power, etc. But what are appropriate stats for a romance? Some stats like social station or income level are considered politically incorrect today, but they can be included in an ironic sort of way. But if you look at a novel like Jane Eyre, beauty and looks do influence romances, so that should be modeled in the simulation somehow. But is it really politically correct to have a game that gives advantages to the good-looking in romances? On the other hand, people would object if someone made a Jane Eyre game where she were depicted as beautiful instead of as plain. After much brainstorming, I figured out that I could use "fashion" as a statistic instead of "looks." Although fashion can be used to model the difference between a plain Jane Eyre and a handsome Emma Woodhouse, it's considered palatable to modern sensibilities because "fashion" is something that can potentially be changed whereas "looks" are considered as more innate.

Romance Model: 1+1=2
After coming up with a few basic stats for the characters in the game, I then had to come up with a model for how romances would work in the simulation. In real-life, romances are quite complicated. Since my tower defence game was intended as a silly little casual game, I wanted to find as simple a romance model as possible.

So suppose you have two characters attending a music concert.
Character A has a music rating of 5.
Character B has a music rating of 3.
How much should the love between A and B increase during the concert?

A*B: Initially, I was thinking of multiplying the two numbers together. The most obvious interpretation of this romance model is that A's interest in music is 5/5, and B's music ability is 3/5. Multiplying 5/5 by 3/5 gives you the amount that B's music ability is able to satisfy A's interest in music. Although the math is symmetric, the interpretation is not. It seems like B exists solely to satisfy the interests of A. I didn't want people to come away with the idea that the "wooed" existed solely to catch the interests of the "suitors."

A+B: Adding the numbers does result in a stretched, but plausible interpretation that's also symmetric. Love between the two characters increases by A+B because their enjoyment of the music concert is dictated by their combined backgrounds in music. By sharing this enjoyable experience, their love for each other increases. The problem with this model is that it results in weird characters statistics as the game progresses. As players get deeper into the game, the game should get harder. You want to make it harder for characters to fall in love as the game progresses to increase the challenge. Characters fall in love slower if their stats are lower. So as players go deeper into the game, they will end up encountering lamer and lamer characters, which doesn't seem right. The characters should get more interesting and have higher statistics as the game progresses not have lower statistics and become less interesting.

-abs(A-B): Taking the negative delta of the two numbers results in a symmetric interpretation that doesn't require characters in later levels to have lower statistics. The interpretation of this approach is that two people who share a similar interest and background in music will fall in love. People who have a disparity in their interests will not. This works, but I was worried that this interpretation might be too complicated for casual gameplayers to understand.

Overall, this whole game ended up being complicated in a way that is more annoying than fun for me. Perhaps my underlying approach to modelling romances in fundamentally wrong. Perhaps I should have gone for a like/dislike model instead like Miss Management. Ugh. Very frustrating.

Gradients 1: The Problem of Gradients

When I learned math and geometry in school, I always got the impression that it was invented by the Greeks hundreds of years old. So when I got to university, I was fascinated by the fact that many mathematical concepts that we were taught in schools were actually fairly recent discoveries. Then, as I studied things even more, I discovered that there are some pretty basic geometry operations that we still don't know how to do. It boggled my mind that researchers were still trying to work out how certain key building blocks of computer graphics should work. One of those areas is gradients.

Gradients sound like they should be simple. How do we shade in a shape? If we assign colours to the different points on a polygon, how do we colour in the inside of that polygon?

For triangles, we can use barycentric coordinates. If we want to colour a point in a triangle, we draw lines from the corners of the triangle to this point. That creates different areas. The ratio of the sizes of these areas gives us the ratio we should mix the colours at the corners. The bigger the area, the more of the colour at the opposite corner should be used. This technique for colouring triangles is so simple and so elegant that modern computer hardware is designed specifically to draw these gradient-shaded triangles.

Just moving to four sided shapes immediately causes problems. You would think that you could simply cut a four-sided shape into two triangles, and then use barycentric coordinates to colour the two triangles. Unfortunately, this leads to inconsistent results. Depending on how you cut a four-sided shape into triangles, you get different colourings. Below, in the center square, the middle of the square is a mix of red and blue with no yellow nor green: a purple. In the square on the right, the middle of the square is a mix of green and yellow with no red nor blue: a light-green.

Once you move to five-sided shapes or shapes with curvy sides, things become even more complicated. Gradients should be a basic building block for 2d graphics, but in most computer programs only support simple gradients like linear gradients where one side of a shape is one colour that smoothly blends to another colour on the other side of the shape. So that is the gradient problem that still needs solving: how do we colour a multi-sided shape with different colours at its corners?