Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43
Design of a Skeletal Animation System – Aimless Development
Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138
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Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 43

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

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Design of a Skeletal Animation System

When I explained the evolution of John Smith’s animation system, I provided the broad strokes of the system and the overall feature set. This article is mainly focused on the technical aspects of the system, and will include a fair amount of source code snippets. I’ll be publishing snippets of the source code to get the thrust across, because the code is dependant on the graphics and physics engines used in my game, making the full source pretty much useless without substantial work. I developed this system in C++, so that’s what I’ll be presenting it in, but it shouldn’t be too hard to replicate in another OO language. However, if you’re still interested in looking at the full source as well as the source to the editor, pop me an email at ian@aimlessdevelopment.com and I’ll pack it up and send it your way, along with the instructions on how to get it going..

Without further babbling on my part, let’s dig in.

Overview of design

AnimationSystemEntities

Definition Classes

The definition classes are essentially object factories. Each SkeletonDefinition and the SkeletonJointDefinitions that it contains store the necessary information to build a skeleton, its joints, and all the constraints from scratch. They also contain data that doesn’t change between instances of the same skeleton, like animation data. Within the editor, this is where all the changes are made.

The SkeletonJointDefinition class is pretty much the same, except that it has even less information to deal with. The joints contain the basic information required for setting up the constraints later, such as angle relative to the parent joint, rotation range, and the allowable distance range from the parent. As well, they contain the necessary information for rendering the skin sprite attached to the joint in the form of a SkeletonSkinElement.

The SkeletonSkinElement will contain either one or two SkeletonSkinData objects (collections of texture coordinates, attachment information, z-value, and blending modes), depending on whether the “flippedIsDifferent” flag is set. This functionality is crucial because often, when the skeleton is flipped around to face the right instead of the left, a different image or z-ordering will need to be displayed. Since I’m doing a sidescroller with human characters, the right arm is going to be behind the character when facing one way and in front when facing the other, requiring different z-values.

AnimationSystemFlippedSkeleton

Fortunately, the other aspects of flipping the skin around—flipping the image and ensuring the attachment is correct—can be computed automatically:

if(flipped)
    hx = 1-hx; //Mirror the anchor point position horizontally

 //Set anchor point
skin.SetHotSpot(skinWidth*tw*hx, skinHeight*th*hy); 

/*
   ...
*/
if(flipped)
{

    //Mirror the attachment angle on the y-axis
    attachmentAngle = Pi() - attachmentAngle;

    //Flip around the anchor point horizontally
    skin.SetFlip(true,false,true);
}

With the obvious exception of the animations themselves, that sums up the definition elements. Lets move on to the skeleton itself.

Skeleton, Constraints, and Joints

The Skeleton class is the workhorse of the system. It serves as a container for joints and constraints and negotiates between them, manages rendering the skeleton, and contains the interface for applying animations to the whole lot of them. Internally, it will reference the appropriate skeleton definition when finding animations, determining skin information, and any other sort of data that all skeletons of the same type might share.

Applying animations takes several steps:

  1. Reset the skeleton and remove animation data from the joints.
  2. Apply all the animations you’re interested in, accumulating their joint offsets.
  3. Compose the animation, taking the accumulated values and determining their position relative their parents.
  4. Flip the skeleton if necessary.

Animations are specified as offsets from the default position of bones, and when two animations attempt to affect the same joint they simply sum their contributions, allowing very cheap layering and mixing of animations. It’s trivial to implement blending functionality as all you’d need to do is specify a floating point multiplication factor to apply to all of the offsets. If you apply two animations at the same time such that their factors add up to 1, they can be considered blended.

Another important function of the skeleton is to store all the constraints on the skeleton and resolve them when called to do so. This is necessary for inverse kinematics and ragdolls, and I’ll get back to it when I get to the constraints!

The SkeletonJoint class manages a single joint. This includes position, orientation, and rendering. There is no information about the relationship between a joint and its parent, since this is managed entirely by the constraint system. However, joints do accumulate animation data for the composition step.

Finally, after much waffling, the constraints; Without constraints, unanimated joints would move around unhindered, shapeless, and—quite frankly—be very boring. I work with two types of constraints, of which the typical joint will have both: an angular constraint, and a distance constraint. The angular constraints force a joint to keep the angle between its current position and its default position (relative the parent) within certain bounds. The distance constraint is more straightforward, and forces it to stay within a certain distance range. These two in combination are sufficient for pretty much anything you might want to do with a skeleton.

The funny thing is, if you’re only applying animations, you don’t need these constraints, really. After all, the position and angle offsets of the bones are already recorded for you in the animations, so you presumably don’t need to worry about invalid positions being held. The first version of my skeletal animation system didn’t have the idea of constraints for this reason. However, constraints are crucial for inverse kinematics, which makes editing animations faster and more accurate, and are similarly necessary for ragdoll physics, which I only managed to make work before with a series of hacks.

Now, resolving a list of constraints can be hairy. The reason for this is that when one constraint is resolved, it is almost guaranteed to upset others. If one were to simply iterate through the constraints and resolve each in turn, you’d probably only be satisfying the last of the constraints. Now, there’s probably a more elegant way to resolve constraints efficiently, but the method I use (and which appears to be most common) is to resolve all constraints several times over a set number of iterations (10 seems like a good number). The end result, while not guaranteed to be perfect, will get closer and closer to something acceptable with each new iteration. Another wrinkle you can add to it is to apply the constraints at a certain strength with each generation. For instance, if you needed to move both joints 10 units towards each other to resolve the constraint, you instead move each 7 units. It takes longer to converge, but makes the entire process more stable.The constraints resolution is something that has a lot of uses. The biggest one is to allow inverse kinematics during the editing phase. One does that by setting the position of the join being manipulated (and usually all its children as well) and then running the constraint resolution until the rest of the skeleton has adjusted to compensate.

An addition required to make inverse kinematics useful as an editing tool is a “lock” flag on each SkeletonJoint. When a joint is locked, constraints are not allowed to change it. Using this, you can lock a shoulder joint then move the hand around, and then ONLY the joints in the hand and arm will be moving. Without the lock, dragging the hand would drag the torso and legs along for the ride, knocking everything out of position.

To use constraints for ragdolls, you must turn each joint into a physically simulated particle, and then attempt to resolve constraints after doing the physics updates. It takes a lot of trial and error, but eventually you’ll have a skeleton that flops around while maintaining the overall form of the skeleton.

Animations

The Animation class contains all its information within a two layer hierarchy. Animations contain tracks, which contain keyframes. In this way, a track can concern itself with a certain aspect of the animation without interfering with one another (for instance, one track can be concerned with the large strokes of the motion while another deals with details.) Each track is just a container for its keyframes, which are interpolated between to get the exact pose at any position between the start and end of the animation. Animations are assigned names and are tied to a specific skeleton definition to make them easy to reference via script. They also have a default animation length specified, though it’s a trivial matter to increase or decrease the speed in-game. The default speed is mainly there for convenience. Beyond that, most of the data that the animation class contains lies in a vector of AnimationTracks.

The AnimationTrack class holds Keyframes in a vector, much like the Animation class holds tracks. Like animations, tracks are named, though it’s primarily for the animator’s benefit to distinguish between them. Tracks can be turned on or off at a whim, stopping them from contributing to the final animation, which is very useful during editing.

Keyframes are the basis of any animation. They contain JointStates for every joint in the skeleton, specifying a pose. The position, a float from 0-1, is the fraction of the distance between the start and the end of the animation that the keyframe is supposed to lie on. They also contain events, which are optional strings that are meant to be sent to an event handler somewhere when the keyframe is passed over in the animation. Finally, every keyframe can also store a “position offset” in a 2D vector, which is used to encode movement into animations.

The JointState class is used to specify what kind of offset will be applied to the joint at a specific keyframe. Each one specifies an offset from the default angle relative the parent, and an offset from the default distance to the parent. These offsets can be added on top of one another, which is what allows multiple tracks and even multiple animations to be layered and blended on top of each other without “masking” specific joints for each one.

There’s also an optional pointer to a SkinState class, a wrapper around a SkeletonSkinElement that will signal that the animation should override the default skin settings for the joint. Unlike the angle and distance offsets, it cannot be blended between animations or tracks. Instead, if two animations want to affect the same joint they compete on a first-come-first-serve basis. However, skin states can be blended along the same track if flagged to interpolate between one another, allowing texture coordinates, z values, and achor points on the sprites to move smoothly over an animation.

Conclusion

AnimationSystemEditor

This is by no means a battle tested system. It hasn’t gone through the rigorous in-game use that its predecessor had, and the skin animation is awkward (if functional). It isn’t the be-all-end-all mechanism for 2D animation by any stretch of the imagination. It is, however, highly functional, reasonably clean, and very flexible.

I hope this was all useful to someone. As I mentioned earlier, if you’re interested in getting the full source to the animation system and editor, contact me at ian@aimlessdevelopment.com. I’ll happily provide the code to anyone who asks for it! If you have comments, questions, or I just didn’t explain something thoroughly enough, please email me or leave a comment!

Posted in Game Development, Game Systems, John Smith.

Tagged with , .


11 Responses


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  1. Waker says

    Awesome explanation!

    Learned a lot. Regards from the Open M team. :)

  2. Ian Morrison says

    Glad to be of service! :)

  3. mmankt says

    i found js vids on yt a long time ago and i loved them. i’m now developing my own skeletal animation system and you’re a great example to follow. i’m trying to use my experience as an animator to create the best behavior possible. i’m looking forward to more posts m8!

  4. crazyspacemonkey says

    Awesome!
    Really helped me design the class structure for my own skeletal animation system.
    Thanks a lot

  5. Jayjay says

    Learned a lot – thanks for sharing!

  6. TacDrol says

    Thank you.

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Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 35

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 107

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 109

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 111

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/functions.php on line 112

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: strtotime(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 113

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138

Warning: date(): It is not safe to rely on the system's timezone settings. You are *required* to use the date.timezone setting or the date_default_timezone_set() function. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. We selected the timezone 'UTC' for now, but please set date.timezone to select your timezone. in /home/aimles6/public_html/wp-includes/link-template.php on line 138
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