We have recently introduced the dynamical Distance Geometry Problem (dynDGP) for dealing with problems in distance space where time is a fundamental component. Here below some animations presented in our recent publications are reported. It is in fact not easy to discuss and evaluate the quality of our results only by showing some key frames of the animations we have obtained. As new articles on the topic will be published in the near future, the new animations will be added to this page.

   The first example that we propose is the classical problem of collision avoidance for a set of moving "particles". These particles may represent the walking motion of persons, or the trajectories of airplanes. This example is limited to the 2-dimensional space.

The first animation on the left-hand side is the original animation that we have represented in terms of distances. In order to define our dynDGP instance, we have introduced new distance constraints encoding our wish to avoid the collisions occurring in the first animation. The other two animations on the right-hand side show two obtained solutions. In both animations, the new distance constraints are satisfied in the solutions, while preserving the original motion as far as this does not go in contrast with these new constraints. The minimal allowed distance is doubled in the last animation on the right side.

   This is a video clip that was initially published for a psychological study in 1944. The main "characters" in the video clip are simple geometrical figures, which are however able to transmit emotions, such as anger, that people perceives by watching the video.

   From this original animation, we have created dynDGP instances where distances are measured between pairs of original characters in the animation, and then manipulated in order to introduce some desired effects by modifying the initial animation as little as possible. The animation is manipulated from frame 100, which is, since all "characters" are present on the scene.

   Here below the original animation after the extraction process (from the video above); it shows that no undesired effects were introduced during the extraction process. The "house" is omitted.

   When the distance constraints are modified so that all characters need to be at least 0.2 units far apart (the environment is a box with sides 1 by 1), we obtain the following animation:

   When the distance constraints are instead modified so that all characters need to always be closer than 0.2 units, we obtain the following animation:

   The first solution shows an animation where the perception of the scene is stronger, because the movements of one character, even without approaching too much (as imposed by our distance constraints), still induce the step-back movement of the others. The second solution shows the three characters in closer interaction (as imposed by our constraints), which gives to the general scene a stronger feeling of stress and danger.

   This animation was artificially generated so that the objects' trajectories are sinusoidal and they collide in some specific frames. The animation is manipulated by adding a set of distance constraints that makes it possible to preserve as much as possible the original animation while all collisions are avoided.
   This animated gif shows four animations running together, for an easier comparison. The left-most animation is the original one. The other animations were obtained by dynDGP and with three different thresholds for the new introduced distance constraints (more details can be found in our publications).