Orbital Motion

15 May 2011 00:09
Last Modified
13 Jan 2013 17:34

Rather than simply using a fixed set of positions for planatary bodies, I wanted to calculate their positions. My initial apprach would only calculate approximate positions, however it was important to consider the following, regardless of the position algorithm used:

Position calculation

My first approach to optimising calculating positions is to only process items which may be visible in the current view. For items in an elliptical orbit, the item may be visible if the orbit is greater than a certain size in the current field of view. The semi-major axis is used to estimate orbital size.

An additional problem which arises is the requirement to correctly draw orbits, which are pre-calculated using a specified number of points. As a body moves around the orbit, drawing the orbit so a vertex exactly coincides with the selected object requires dynamically calculating vertices, at least near to the selected object in each frame.

Time display and control

Date and time is shown using a digital clock. The orientation of the time display is dertermined from the system orientation, rounded to the nearest 90° (i.e. aligned with an edge of the screen).

A dial menu is used to specify a positive or negative factor for adjusting time. A button on the menu can also be used to reset the time display to real-time (i.e. the current time and a factor of +1).

Time control and display

Figure 1. Time control and display.

Camera behaviour

The first consideration was how to adjust the absolute position of each camera type with respect to a moving body. For orbital cameras, the same relative position between the camera and the selected body is maintained. This also has the effect of keeping the background stars fixed. A free camera can operate with or without tracking the current point of interest (if any). When tracking is enabled, the camera maitains its position in space, but adjusts its orientation to keep the point of interest fixed.

Another implication for camera behaviour concerns how a camera transitions from one object to another. Previously the objects were fixed and a linear interpolation between initial and target positions could be used. When the target is moving a velocity-based approach can be used, which accelerates the camera towards the target while tracking its current position, until the camera has reached a given distance from the target and has synchronised velocity. Another option is a distance-based linear interpolation, which reduces the distance to the target over a specified time. While less physically realistic, it is easy to implement and has the benefit of a fixed time to move between objects. I am initially using the latter approach, combined with a simple SLERP of orientation.

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