So I have a sun object in a flat world. By flat world, I mean that it is like a snow globe, where the ground is flat and there is an arc around the top. I want to have a sun go from one end, to the other, naturally.

So my world's time is represented in percentages. I have a floating point value, from 0.0 to 0.999999, whcih represents the percentage of the day that has passed. from 0.3 to 0.7, the sun should be up. It should start at one end of the world at 0.3, orbit to a place somewhere in the middle (in an arc motion) for 0.5 and finish at the other end at 0.7. At 0.7, the moon should come in from where the sun started. At 0.0, it should be at the center, where the sun was, and at 0.3, it should be at the end.

This does not need to be exact, just a decent simulation that will be relatively smooth. I will give it three points, a starting point, middle point, and end point. I need an equation taht will use the percentage of the day passed, along with the 3 points I am providing, to create a smooth movement along this path.