Hello. I am Precipitation24. Thank you for playing “Basic Vocabulary 48”, my silly adult game. In this game, I had many important themes and one of them was “improving my animation.” In order to create animation, I had to learn a lot of techniques or create by myself, and at some time, I thought that I would forget all this knowledge a month after its completion. So please let me write them here as a reminder of this knowledge and so that I could share and discuss them with someone else if I could.

Repetitive Animation

When I was a little child, I saw how dear Walt Disney created animation. He draws each frame from scratch, so there are no repetitive or static parts, giving the illusion of a real living being in motion. I do not even know how exactly he made such a beautiful animation.

When I tried to make an animation, I realized that they should have been a repetitive animation to adopt the game. And I set the period of each animation 12 frames. At this point, I found a big problem: If I imitate Mr. Disney's works and draw an animation by shifting the picture little by little, it would not probably be a 12 frame cycle.

Piston Motion ≠ Triangular Motion

The fact that the animation is periodic means that it deals with piston motion. It is convenient to use piston motion in animation, especially in nsfw animation (for obvious reasons). However, I didn't want to use triangular motion as they are, because I thought they would not appear that often in real physical phenomena. So what functions should we use?

At least, piston motion has a minimum and a maximum value. As a specific example, let's think of a girl riding a horse. In this case, the minimum value is when the girl relaxes her legs and puts all her weight on the horse. To move from this state to the maximum, she would accelerate her hips by gradually applying force from zero speed and subconsciously adjust the amount of force to stop the movement of her hips by the time she reached the top to prevent it from slipping away. There for the movement of her hip is going to be like this: f(t) = -cos(t)+A. Yes, I used a triangular function. However, the problem is about how she would go down. When she lowers her hips, she will probably relax her legs and let herself fall freely. This means that the curve of the fall must be described by a parabola, not a trigonometric function. Then the horse absorbs the impact caused by the free-falling girl's butt and that will bring us back to MIN.

Unfortunately, I can only show one example here, but I would like to move on to the next step, knowing that various physical phenomena are hidden in the behavior of one cycle.

Delay

Let's forget about the girl on the horse and get back to the whole piston movement. This so-called "non-triangular piston movement" is only about the movement near the junction, but we have to be aware that these movements are transferred to the whole body with a delay. An example is as follows

Reference movement: the movement of the person who is applying force to his/her muscles and moving them

Delayed movement: partner's movement

If we look at the individual, we can further break it down as follows

Reference movement: movement near the junction

Delayed movement: breasts, hair

Also, this phase shift can always be constant. For example, if a person is moving according to f(t) as a reference, his/her partner will move according to f(t-α), and his/her partner's hair will move according to f(t-α-β). In particular, since hair and breasts move by inertia, it is easier to animate them by considering them to be the same as vector changing gravity that is delayed in phase.

Completion of Human Skeleton Animation

After these calculations, the animation of the human skeleton was completed. In the next article, I will explain the fleshing and coloring techniques.

Thank you very much for your interest.