So… Remember how the players use glorified minimaps to actually play?
One of the main features of the minimap is the compass – icons, showing direction to points of interest.
Easy enough to do it on a circular compass. Found a way to do it also on a square one. The main concern is that the circle does not cover space well and I would be happier if I can allow the players top see more of their surroundings. Here comes the square minimap. However, square is not… friendly. I kind of don’t like the sharp corners. This can be, of course, mitigated, by designing the whole UI to accept such corners, but why mitigate a problem when you can resolve it?
Enter squircle – a square with rounded corners. It would look well and give more visibility than a circle with same radius as it’s side length. But how do you project icons on the compass?
The way the compass works is simple – you get the angle between the player forward direction and the direction to the object, translate that angle on the minimap and place the icon the right amount away from the center of the minimap. Yeah, that’s the problem. For the circle it’s basically a non-problem. For a square – I found a solution online (see below).
But a squircle? I think I found the correct road to a solution, but it’s still a rocky road for a person how has not practice any meaningful math for decades.
Here’s the construction:
The shape goes between two extremes. You have two governing variables – the radius of the corner circles and the length of the straight intervals between the corner circles. So the whole shape has two extremes:
- it’s a circle if the intervals have length of 0
- it’s a square if the radiuses are 0
What is given:
- the radius of the circle
- the length of the interval
- the angle between (any) axis (IE) and the line passing through the center of the compass and the target icon (BJ)
What I need to find:
- The angle between (any) axis (IE) and the line that connects the center of the circle and the crossection of the circle and the line from the center of the compass and the icon (IK)