Since R = 10000 m in this model, the following values of s in meters (as well as A) may be obtained by plugging the given camera settings into this formula:
Apply the formula, s = 2 * 10000 * tan [atan (17.5 / f) / W], directly to obtain star size values for camera settings not covered by this table. The resolution, W, is the largest dimension of the rendered frame, so if you're rendering in portrait format instead of landscape, you should consider W to be the height instead of the width.
Note that if you actually try to use the obtained value of s to set the pose slider in the choreography, the starfield may appear to be too bright because of the oversized stars produced by the random scaling distribution in the model. You can make the starfield dimmer by lowering the value of the pose slider to about 80% of the original value -- this is why in the default choreography, where the camera has a focal length of 35 mm and a resolution of 640 pixels, I have made the star size 12 m instead of 14.49 as given by the formula. However, reducing the size of the stars may cause flickering when panning the camera with antialiasing turned on. As an alternative to lowering the pose slider value, you can make the overall color of the star sphere model a shade of gray instead of white.
Another advantage of the scalable star sphere is the ability to animate the star size to stay in sync with the animation of the camera's focal length. If the camera will be making a zoom move in the course of the choreography, you will need to keyframe the "Median star size in meters" pose slider on the same frames as the keyframes you set for the beginning and end of the zoom. The new value of the pose slider at the end of the zoom will need to be calculated using the formula or the table, based on the new focal length.
If the camera will be moving a considerable distance away from the center of the star sphere during the choreography, as it approaches the edge of the sphere it will become apparent that some of the stars are closer to the camera, and therefore brighter, than others. You can remedy this either by constraining the star sphere to translate to the camera, or by scaling up the entire star sphere from its model bone. It will also be necessary to scale up the star sphere if the objects included in the scene are too big to fit into the existing volume. Scaling the star sphere will not affect the angular size of the stars, and the replicated action objects will follow the translation and scaling of the parent object.
Fixed-size star spheres are best suited for applications where you don't expect to be animating the camera's focal length, and you can't afford to wait for the scalable star sphere to load. Consult the formula and table above to determine which star size is best suited for your camera's settings.
A choreography and a replication action are provided using the sphere with 12-meter stars. If you want to use them with a different fixed-size sphere, you will need to open StarSphere Fixed Replicate.act in a text editor. Search for "StarSphere-12m" and replace it with the filename of the sphere you want to use. Once you have resaved the action, open StarSphere_fixed.cho in A:M. In the Project Workspace, expand the choreography and select Shortcut to StarSphere-12m. In its "Shortcut To" property, click on StarSphere-12m and choose the new star sphere from the pull-down menu.
If none of the included fixed-size spheres have the right star size for your needs, you can create a new fixed-size sphere yourself. Create a new action and edit it using the scalable star sphere (StarSphere.mdl). Set the pose slider to the desired size. Right-click on the action in the PWS, select Export > Model (*.MDL), and save the model under a new name; this may take some time. Close the action and open the model you just created. Expand it using its + button in the PWS. Select the Bones and Relationships folders and delete them. Save the model.
The star sphere concept was inspired by a model by Carmen Rizzolo, available at AnimationPitStop.com. Grateful acknowledgement is made to Yves Poissant and Anders Averö for their valuable programming advice.
Focal length
(f)Angle of view
(A)Resolution (W) in pixels
320
640
720
800
1024
1280
30 mm
60.51°
33.00
16.50
14.67
13.20
10.31
8.25
35 mm
53.13°
28.98
14.49
12.88
11.59
9.06
7.24
50 mm
38.58°
21.04
10.52
9.35
8.42
6.58
5.26
70 mm
28.07°
15.31
7.66
6.80
6.12
4.78
3.83
100 mm
19.85°
10.83
5.41
4.81
4.33
3.38
2.71
Using the fixed-size star spheres
Acknowledgements