So I am looking for some general advice. For my final project in my Computational Physics class. I have to complete the following problem.
(4.16 from Computation Physics 2nd Edition By Giordano and Nakanishi)
-Carry out a true three-body simulation in which the motions of Earth, Jupiter, and the Sun are all calculated. Since all three bodies are now in motion, it is useful to take the center of mass of the three-body system as the origin, rather than the position of Sun. We also suggest that you give Sun and initial velocity which makes the total momentum of the system exactly zero(so that the center of mass will remain fixed). Study the motion of Earth with different initial conditions. Also, try increasing the mass of Jupiter to 10, 100, and 1000 times its true mass.
My question: Is it possible to write the code for the problem above, and then import that code(or the result) into Adobe After Effects to model the three-body simulation? My teacher has expressed that if i am able to do so, he would be inclined to give me extra credit, which i desperately need.
It is possible to do some scripting in After Effects, but the language is Javascript (or rather, ExtendScript), not Matlab. I would do everything in a javascript: first calculate your solution (3 streams of position data), and use these to keyframe the corresponding layers in After Effects. You will have to learn a bit of the After Effects object model, but in that case you wont need much: the Layer object and how to keyframe its position property. You should go to the Adobe After Effects scripting forum https://forums.adobe.com/community/aftereffects_general_discussion/ae_scripting/ for some script examples.
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I am making a game in Unity that involves creatures whose animations are determined by physics. For example, to move a limb of a creature, I can apply forces to the rigidbody it's associated with. I know how to apply forces programmatically through a script to create movements, but I'd like to create more complex and organic movements and thought that I might be able to use a neural network to do this.
I'd like each of the creatures to have a distinct way of moving in the world. I'd like to first puppeteer the creatures manually using my hand (with a Leap Motion controller), and have a neural network generate new movements based on the training I did with my hand.
More concretely, my manual puppeteering setup will apply forces to the rigidbodies of the creature as I move my hand. So if I lift my finger up, the system would apply a series of upward forces to the limb that is mapped to my finger. As I am puppeteering the creature, the NN receives Vector3 forces for each of the rigidbodies. In a way this is the same task as generating a new text based on a corpus of texts, but in this case my input is forces rather than strings.
Based on that training set, is it possible for the NN to generate movements for the characters (forces to be applied to the limbs) to mimic the movements I did with my hand?
I don't have that much experience with neural networks, but am eager to learn, specifically for this project. It would be great to know about similar projects that were done in Unity, or relevant libraries I could use that would simplify the implementation. Also, please let me know if there is anything I can clarify!
Not really an answer but would not fit for comments
I'm not sure the strategy you want to apply to train your model is the right one.
I would go for reinforcement learning methods (you can check this question for more infos about it) using, for example, the distance traveled by the center of mass of the creature on the x-axis as a fitness. If this leads to weird behaviours (like this well known robot) you could, for example, think of strategies like penalizing your individuals given the distance traveled on y and z axis (still by the CoM) to try having guys that keep there CoM on the same plane.
Without knowing exactly what you want to achieve this is hard to give you more advices. Although, if you are not looking only for neural network based techniques, there is this really great paper you might want to have a look at (here is the video of their results).
I'm currently in the process of coding a procedural terrain generator for a game. For that purpose, I divide my world into chunks of equal size and generate them one by one as the player strolls along. So far, nothing special.
Now, I specifically don't want the world to be persistent, i.e. if a chunk gets unloaded (maybe because the player moved too far away) and later loaded again, it should not be the same as before.
From my understanding, implicit approaches like treating 3D Simplex Noise as a density function input for Marching Cubes don't suit my problem. That is because I would need to reseed the generator to obtain different return values for the same point in space, leading to discontinuities along chunk borders.
I also looked into Midpoint Displacement / Diamond-Square. By seeding each chunk's heightmap with values from the borders of adjacent chunks and randomizing the chunk corners that don't have any other chunks nearby, I was able to generate a tileable terrain that exhibits the desired behavior. Still, the results look rather dull. Specifically, since this method relies on heightmaps, it lacks overhangs and the like. Moreover, even with the corner randomization, terrain features tend to be confined to small areas, i.e. there are no multiple-chunk hills or similar landmarks.
Now I was wondering if there are other approaches to this that I haven't heard of/thought about yet. Any help is highly appreciated! :)
Cheers!
Post process!
After you do the heightmaps, run back through adding features.
This is how Minecraft does it to get the various caverns and cliff overhangs.
I'm hoping to prototype some very basic physics/statics simulations for "voxel-based" games like Minecraft and Dwarf Fortress, so that the game can detect when a player has constructed a structure that should not be able to stand up on its own.. Obviously this is a very fuzzy definition -- whether a structure is impossible depends upon multitude of material and environmental properties -- but the general idea is to motivate players to build structures that resemble the buildings we see in the real world. I'll describe what I mean in a bit more detail below, but I generally want to know if anyone could suggest either an potential approach to the problem or a resource that I could use.
Here's some examples of buildings that could be impossible if the material was not strong enough.
Here's some example situations. My understanding of this subject is not great but bear with me.
If this structure were to be made of concrete with dimensions of, say, 4m by 200m, it would probably not be able to stand up. Because the center of mass is not over its connection to the ground, I think it would either tip over or crack at the base.
The center of gravity of this arch lies between the columns holding it up, but if it was very big and made of a weak, heavy material, it would crumble under its own weight.
This tower has its center of gravity right over its base, but if it is sufficiently tall then it only takes a bit of force for the wind to topple it over.
Now, I expect that a full-scale real-time simulation of these physics isn't really possible... but there's a lot of ways that I could simplify the simulation. For example:
Tests for physics-defying structures could be infrequently and randomly performed, so a bad building doesn't crumble right as soon as it is built, but as much as a few minutes later.
Minecraft and Dwarf Fortress hardly perform rigid- or soft-body physics. For this reason, any piece of a building that is deemed to be physically impossible can simple "pop" into rubble instead of spawning a bunch of accurate physics props.
Have you considered taking an existing 3d environment physics engine and "rounding off" orientations of objects? In the case of your first object (the L-shaped thing), you could run a simulation of a continuous, non-voxelized object of similar shape behind the scenes and then monitor that object for orientation changes. In a simple case, if the object's representation of the continuous hits the ground, the object in the voxelized gameplay world could move its blocks to the ground.
I don't think there is a feasible way to do this. Minecraft has no notion of physical structure. So you will have to look at each block individually to determine if it should fall (there are other considerations but this is minimum). You would therefore need a way to distinguish between ground and "not ground". This is modeling problem first and foremost, not a programming problem (not even simulation design). I think this question is out of scope for SO.
For instance consider the following model, that may give you an indication of the complexities involved:
each block above height = 0 experiences a "down pull" = P, P may be any of the following:
0 if the box is supported by another box
m*g (where m is its mass which depends on material density * voxel volume) otherwise if it is free
F represents some "friction" or "glue" between vertical faces of boxes, it counteracts P.
This friction should have a threshold beyond which it "breaks" and the block then has a net pull downwards.
if m*g < sum F, box stays where it is. Otherwise, box falls.
F depends on the pairs of materials in contact
for n=2, so you can form a line of blocks between two towers
F is what causes the net pull of a box to be larger than m*g. For instance if you have two blocks a-b-c with c being on d, then a pulls on b, so b should be "heavier" than m*g where it contacts c. If this net is > F, then the pair a-b should fall.
You might be able to simulate the above and get interesting results, but you will find it really challenging to handle the case where there are two towsers with a line of blocks between them: the towers are coupled together by line of blocks, there is no longer a "tip" to the line of blocks. At this stage you might as well get out your physics books to create a system of boxes and springs and come up with equations that you might be able to solve numerically, but in a full 3D system you will have a 3D mesh of springs to navigate iteratively to converge to force values on each box and determine which ones move.
A professor of mine suggested that I look at this paper.
Additionally, I found the keyword for what it is I'm looking for. "Structural Analysis." I bought a textbook and I have a long road ahead of me.
I want to ask about jelly physics ( http://www.youtube.com/watch?v=I74rJFB_W1k ), where I can find some good place to start making things like that ? I want to make simulation of cars crash and I want use this jelly physics, but I can't find a lot about them. I don't want use existing physics engine, I want write my own :)
Something like what you see in the video you linked to could be accomplished with a mass-spring system. However, as you vary the number of masses and springs, keeping your spring constants the same, you will get wildly varying results. In short, mass-spring systems are not good approximations of a continuum of matter.
Typically, these sorts of animations are created using what is called the Finite Element Method (FEM). The FEM does converge to a continuum, which is nice. And although it does require a bit more know-how than a mass-spring system, it really isn't too bad. The basic idea, derived from the study of continuum mechanics, can be put this way:
Break the volume of your object up into many small pieces (elements), usually tetrahedra. Let's call the entire collection of these elements the mesh. You'll actually want to make two copies of this mesh. Label one the "rest" mesh, and the other the "world" mesh. I'll tell you why next.
For each tetrahedron in your world mesh, measure how deformed it is relative to its corresponding rest tetrahedron. The measure of how deformed it is is called "strain". This is typically accomplished by first measuring what is known as the deformation gradient (often denoted F). There are several good papers that describe how to do this. Once you have F, one very typical way to define the strain (e) is:
e = 1/2(F^T * F) - I. This is known as Green's strain. It is invariant to rotations, which makes it very convenient.
Using the properties of the material you are trying to simulate (gelatin, rubber, steel, etc.), and using the strain you measured in the step above, derive the "stress" of each tetrahdron.
For each tetrahedron, visit each node (vertex, corner, point (these all mean the same thing)) and average the area-weighted normal vectors (in the rest shape) of the three triangular faces that share that node. Multiply the tetrahedron's stress by that averaged vector, and there's the elastic force acting on that node due to the stress of that tetrahedron. Of course, each node could potentially belong to multiple tetrahedra, so you'll want to be able to sum up these forces.
Integrate! There are easy ways to do this, and hard ways. Either way, you'll want to loop over every node in your world mesh and divide its forces by its mass to determine its acceleration. The easy way to proceed from here is to:
Multiply its acceleration by some small time value dt. This gives you a change in velocity, dv.
Add dv to the node's current velocity to get a new total velocity.
Multiply that velocity by dt to get a change in position, dx.
Add dx to the node's current position to get a new position.
This approach is known as explicit forward Euler integration. You will have to use very small values of dt to get it to work without blowing up, but it is so easy to implement that it works well as a starting point.
Repeat steps 2 through 5 for as long as you want.
I've left out a lot of details and fancy extras, but hopefully you can infer a lot of what I've left out. Here is a link to some instructions I used the first time I did this. The webpage contains some useful pseudocode, as well as links to some relevant material.
http://sealab.cs.utah.edu/Courses/CS6967-F08/Project-2/
The following link is also very useful:
http://sealab.cs.utah.edu/Courses/CS6967-F08/FE-notes.pdf
This is a really fun topic, and I wish you the best of luck! If you get stuck, just drop me a comment.
That rolling jelly cube video was made with Blender, which uses the Bullet physics engine for soft body simulation. The bullet documentation in general is very sparse and for soft body dynamics almost nonexistent. You're best bet would be to read the source code.
Then write your own version ;)
Here is a page with some pretty good tutorials on it. The one you are looking for is probably in the (inverse) Kinematics and Mass & Spring Models sections.
Hint: A jelly can be seen as a 3 dimensional cloth ;-)
Also, try having a look at the search results for spring pressure soft body model - they might get you going in the right direction :-)
See this guy's page Maciej Matyka, topic of soft body
Unfortunately 2d only but might be something to start with is JellyPhysics and JellyCar
I think it would be fun to model a top view of a train following a track, traversing switches and so on, using a physics library like Box2D. What joints and motors would I need to make this work?
I'm curious about how to implement the forces needed to make the car follow a spline track so it can bump into other train cars, pedestrians, DeLoreans etc. Just saying "the car is now at spline(t)" for each time step would create excessive forces in the physics engine. If I understand correctly, you have to stick the car onto the track with one force, constrain its angle to tend towards parallel with the track with another (or stick the front and back of the car to the track with two forces), and create another force to propel the train forward. I'm looking for some details on how to accomplish these things.
I believe it would be easier without "real" physics, like the ball movement of games such as Luxor or Tumble Bugs. Meaning: let the train follow a spline which is defined by the tracks.
Using phyiscs is probably overkill to make a train follow a track and could lead to all kinds of undesired side-effects, including jerky motion, train derailing, train getting stuck on junctions, etc.
You could still join the individual wagons together using physic joints, however. Just make sure that only the locomotive gets acceleration forces, the rest of the train just follows or is pushed but stays on the spline.
Why are you worried about keeping it "on the tracks"? Where is it going to go? Gravity should keep it down, object intersection should keep it up, and so the only directions you need to worry about are forward and backwards. That's where a motor comes in, and you're done. The rest is decorations.
In response to edit of problem:
Siderails. And have the train long enough / rigid enough compared to its width that you can navigate crossings (make them closer to right angles to minimize the crossing problems.
A top-down view (i.e. seeing the train from the sky) doesn't really require a 2d physics engine - if I understand you correctly. In fact, it seems like it wouldn't really help with the problem (if you want a train simulation), but then maybe you just wanna try it out for fun. :)
However, what about putting something like a slider joint on the train and the cars, and a motor on the locomotive. The slider joint might need some special implementation; you probably want to run the train along a spline and not a segment of straight lines, right?
Some sort of ball joint would connect the cars together.
The implementation is not so toughand I was able to prototype something in a few hours that does the basic job. It will require a lot of work to make it run smoothly, but it's essentially just "siderails."
Being top-down you obviously first must turn off gravity in Box2D. Second, build a train. Treat train wheels like car wheels and it'll suddenly get a lot more simple. For tracks you have a few choices:
Create your own game object (not in the box2D world) that is a simple line the train will then "follow" (you can use motors on train wheels to "steer" towards the line). Then just overlay the line with some nice wide "rail" graphics and you have a nicely faked system. Tell the wheels to turn off if it strays too far from the line and presto, you have a derailment.
Create actual physical rails - outside rails (like siderails) that the trains "wheels" will bump into. They will have to have gentle curves in this instance, which could be very difficult given the limited resources you have (simulating a nice slow curve out of boxes in Box2D is rough on the processor)
Then just let your train go!