Connect Centroids / Dynamic Medium

Hello, I have been here about 2 months ago with my Dynamic Foam project and got help from a developer but we ran into some problems connecting centroids to establish a network between the 'foam bubbles'. Here is some extra information for why those centroids need to be connected and form a network along with the problem explained at the end. I. Dynamic Medium II. Fields and Boids III. From Boids to a PBD Network IV. From Curling Motion to Strings V. Position Based Dynamics (PBD) VI. The Problem -- I. Dynamic Medium The goal of this project is to create a kind on a Zero-player game, a bit like Conway's Game of Life, where cells fluctuate based on surrounding cells, and where the goal to generate Knots within a Dynamic Medium. To get a sense of such a dynamic network think of a foam with bubbles (volumes) where a micro-fluid runs through the edges (currents). These currents move from high to low pressure, forming circuits. The intensity of the fluid passing the bubbles can make the bubbles shrink or expand. Some currents will be able to line up and form closed circuits. In 2D these structures are simple loops, in 3D these loops can form strings, and in a next step these strings form again closed-circuits -> knots. -- II. Fields and Boids One way to get a model of bubbles and currents going was by using Boid-particles and Fields, which was tried in Processing. Here are short clips to show the interaction: • http://imgur.com/a/Mp0SG • https://vimeo.com/user37290268 A. In the first clip the Fields (red circles) keep their size while the small particles flow in between and form a circuit. B. In the second version the size of the Fields is influenced by the number of particles within. This gives rise to a dynamic foam with Fields fluctuating. Expand <-> Shrink -- III. From Boids to a PBD Network The problem with using Boids is that they have their limitations whereby the quick expansion of Fields causes the particles to be splattered around, interrupting the steady current. (stable flow vs. splashed around) Keeping the Boid-particles flowing is important, because a flow-circuit gives rise to organisational rules such as flows going against each other block each other, others can go along and strengthen each other, similar to an electronic circuit: So to fix these problems a move to PBD was made and hoping to create a network model (nodes/edges) that replaces the small particles. The flow replaced by edges: Fields expanding and shrinking depending on the amount of flow through the edges: • Having two Fields A.B. and in between from point a. to b. an edge. • This edges (a.b.) can replace all the boids moving in between (A.B.) • Edge (a.b.) can represents 1 or 1 million small particles or more, simplification. • Between Field A. and B. a measurement of tension •-VVVVV-• (A/B) • The more tension between (A.B.) the less flow there can be in (a.b.) • Inverse the more flow there is in (a.b.) the less tension between (A.B.) • The edge (a.b.) runs through the Fields A. and B, cooling or heating up Fields A. and B. • Through edge (a.b.) runs a current the larger this current the bigger the Fields A. and B. become, expansion vs. shrinking, hot vs. cold, condense vs. vaporise. The inspiration for the move to 'Position Based Dynamics' came from a talk by Jos Stam where he explained a method explicit on position and using springs: http://www.birs.ca/events/2014/5-day-workshops/14w5147/videos/watch/201402191414-Stam.html http://www.birs.ca//workshops//2014/14w5147/files/Stam-BIRS-2014.pdf -- IV. From Curling Motion to Strings At the basis of this Dynamic Foam is the idea to get the bubbles moving through the medium based on self regulated currents between the bubbles: The mechanics are like a sliding-puzzle where the parts can move to where there is space (created): Space can be created by letting the bubbles shrink on one side and expand on the other, so they can move into that created space, and as a result we get fluctuations and a rolling-curling-motion: Here is a fun animation that is similar to the idea: https://imgur.com/gallery/xIUGOd9 But for those lemons the input-force is gravity, in my model it are the micro-fluid-currents that effect the size. If the fluid is colder than the bubble than it will condensate and the field will expand; when it is warmer the field will vaporise and shrink. The dynamic curing motion from above, could also turn around and close-loop into knots: In 3D the wind up curls would be like these folk dansers waving strings: http://www.youtube.com/watch?v=uvE5yt83WPU (at 1:44) These strings can turn into knots etc. etc. -- V. Position Based Dynamics (PBD) For a look at the current situation you can check this short clip, where a small network is in place based on centroids, and where the volumes can fluctuate: http://imgur.com/QSG71hW Here is are the project files on GitHub if you would like to have a closer look: • https://github.com/VirtualOrganics/PBD_DynamicFoam_Files • https://github.com/InteractiveComputerGraphics/PositionBasedDynamics (The PDB software) -- VI. The Problem We took the PBD software from GitHub and modified the Demo example called 'GenericConstraintsDemos'. All constraints are taken out except the distance constraint , and the simulation is limited to work on a 2D plane with the intention of extending to 3D eventually. Check out the graph: As you can see in the example, there are nine circles. The simulation allows for any number of circles. The green dots represent the centers of the circles; the red dots represent the centroids of the three adjacent/connected circles; the black dots represent some (outer) intersections between circles; and the blue lines connect either centroids with other centroids, or centroids to intersections in a particular pattern. In the simulation, the radii of the circles can change and, since a distance constraint is applied, the varying sizes of the circles causes the locations (and existence) of the dots and lines to change. The code at this point is able to identify/calculate the locations of the black dots and the red dots, but he had trouble coming up with an algorithm that correctly connects the red and black dots. The diagram above shows the correct connections, but coming up with an algorithm to do this automatically and as the simulation runs stalled our progress. So I'm now looking for a developer who can take it to the next level. It doesn't necessarily need to be in PBD an other Physics Engine (Bullet?) might do the job, one where on top of the physics-interactions a network-formula can balance out the weights and regulate the system. All suggestions and questions are more than welcome! Best, m.