JavaScript Canvas Complex Shape Collision - javascript

I am trying to make a very simple game with the HTML canvas and JavaScript. I have found many tutorials and questions about detecting collisions of basic shapes on a canvas (such as rectangles and circles). But I am wondering is it possible to detect if a complex shape (a shape that is made up of many basic shapes) is colliding with another shape, or even if two complex shapes are colliding. If so, how could this be done? Thanks in advance!

A general algorithm will not provide a better solution than one based specifically on the knowledge of each shape type.
Generally, for complex (i.e. compound) shapes, you would generally try as step #1 and "exit early" test. For optimization reasons, you generally try eliminate false-positives as early in the process as possible.
As simple step #1 is to test for collisions on the "bounding boxes" of each compound shape. If the bounding boxes are NOT overlapping then you can quit early and assume no collision because the compound shapes could not be colliding (see https://gamedevelopment.tutsplus.com/tutorials/collision-detection-using-the-separating-axis-theorem--gamedev-169)
If the bounding-box test cannot eliminate early, you will need to test each sub-shape in turn with algorithms most suitable to the shape (circle-circle, circle-rect etc.) leaving the most "expensive" tests to last - like polygon-polygon.
You might want to also look at this question How do I determine if two convex polygons intersect?

Related

GC friendly convex clipping (union and difference) algorithm

I'm looking for algorithm that will cut my convex polygon based on another convex polygon. It is gonna be for destructible terrain (diff) and for creating terrain (union) in 2D map in game.
Algorithm has to be Garbage Collector friendly and the only boolean operations that are neccessary are Union & Difference.
I've done some research and there are some github projects, but all of them produce some garbage more or less.
https://github.com/tmpvar/2d-polygon-boolean
https://github.com/w8r/GreinerHormann
I guess the best solution would be to learn one of these and re-make it my way. But maybe you've heard about some that suits my needs?
Thanks.
This problem involves two subproblems
find the intersection points between the two outlines
join the vertices that mus be joined.
For 1. you can exploit convexity: see both polygons as two monotone chains. When you travel the chains of the twopolygons simultaneously, say by increasing x, the intersections are detected when the ordinates cross each other between two abscissas.
For 2. notice that the union or difference are made of portions of the outlines alternating between one polygon and the other, at every interesection point.
Note that in the case of the difference, there can be several disconnected pieces.
I guess that you can implement this without any allocation/deallocation at all (but for the output polygon).

How to animate HTML5 shapes using a spine curve

I've made a program that creates parametric shapes (spheres, toruses, and cylinders) and performs matrix transformations on them to animate them in specific ways (e.g. translate(), rotate(), scale()). I now want to animate the shapes using splines which will serve to allow the shapes to move along smoother paths than with the transformations alone. I'm not exactly sure how to approach this with html5 and javascript, but based on my work up to this point, I would think that the approach would involve first calculating all of the points that lie along the spline curve (for x,y, and z), storing each point in a data structure, and then iterating over the data structure passing in each point to the translate() method.
I've looked at some resources on B-Splines and NURB's but sites like these generally seem either very theoretical and hard to translate to code, or they use specific api's in languages that I'm not using. What would be the best implementation (code wise) of this sort of spline animation in html5 and javascript?

Position resizable circles near each other

I am working on this browser-based experiment where i am given N specific circles (let's say they have a unique picture in them) and need to position them together, leaving as little space between them as possible. It doesn't have to be arranged in a circle, but they should be "clustered" together.
The circle sizes are customizable and a user will be able to change the sizes by dragging a javascript slider, changing some circles' sizes (for example, in 10% of the slider the circle 4 will have radius of 20px, circle 2 10px, circle 5 stays the same, etc...). As you may have already guessed, i will try to "transition" the resizing-repositioning smoothly when the slider is being moved.
The approach i have tried tried so far: instead of manually trying to position them i've tried to use a physics engine-
The idea:
place some kind of gravitational pull in the center of the screen
use a physics engine to take care of the balls collision
during the "drag the time" slider event i would just set different
ball sizes and let the engine take care of the rest
For this task i have used "box2Dweb". i placed a gravitational pull to the center of the screen, however, it took a really long time until the balls were placed in the center and they floated around. Then i put a small static piece of ball in the center so they would hit it and then stop. It looked like this:
The results were a bit better, but the circles still moved for some time before they went static. Even after playing around with variables like the ball friction and different gravitational pulls, the whole thing just floated around and felt very "wobbly", while i wanted the balls move only when i drag the time slider (when they change sizes). Plus, box2d doesn't allow to change the sizes of the objects and i would have to hack my way for a workaround.
So, the box2d approach made me realize that maybe to leave a physics engine to handle this isn't the best solution for the problem. Or maybe i have to include some other force i haven't thought of. I have found this similar question to mine on StackOverflow. However, the very important difference is that it just generates some n unspecific circles "at once" and doesn't allow for additional specific ball size and position manipulation.
I am really stuck now, does anyone have any ideas how to approach this problem?
update: it's been almost a year now and i totally forgot about this thread. what i did in the end is to stick to the physics model and reset forces/stop in almost idle conditions. the result can be seen here http://stateofwealth.net/
the triangles you see are inside those circles. the remaining lines are connected via "delaunay triangulation algorithm"
I recall seeing a d3.js demo that is very similar to what you're describing. It's written by Mike Bostock himself: http://bl.ocks.org/mbostock/1747543
It uses quadtrees for fast collision detection and uses a force based graph, which are both d3.js utilities.
In the tick function, you should be able to add a .attr("r", function(d) { return d.radius; }) which will update the radius each tick for when you change the nodes data. Just for starters you can set it to return random and the circles should jitter around like crazy.
(Not a comment because it wouldn't fit)
I'm impressed that you've brought in Box2D to help with the heavy-lifting, but it's true that unfortunately it is probably not well-suited to your requirements, as Box2D is at its best when you are after simulating rigid objects and their collision dynamics.
I think if you really consider what it is that you need, it isn't quite so much a rigid body dynamics problem at all. You actually want none of the complexity of box2d as all of your geometry consists of spheres (which I assure you are vastly simpler to model than arbitrary convex polygons, which is what IMO Box2D's complexity arises from), and like you mention, Box2D's inability to smoothly change the geometric parameters isn't helping as it will bog down the browser with unnecessary geometry allocations and deallocations and fail to apply any sort of smooth animation.
What you are probably looking for is an algorithm or method to evolve the positions of a set of coordinates (each with a radius that is also potentially changing) so that they stay separated by their radii and also minimize their distance to the center position. If this has to be smooth, you can't just apply the minimal solution every time, as you may get "warping" as the optimal configuration might shift dramatically at particular points along your slider's movement. Suffice it to say there is a lot of tweaking for you to do, but not really anything scarier than what one must contend with inside of Box2D.
How important is it that your circles do not overlap? I think you should just do a simple iterative "solver" that first tries to bring the circles toward their target (center of screen?), and then tries to separate them based on radii.
I believe if you try to come up with a simplified mathematical model for the motion that you want, it will be better than trying to get Box2D to do it. Box2D is magical, but it's only good at what it's good at.
At least for me, seems like the easiest solution is to first set up the circles in a cluster. So first set the largest circle in the center, put the second circle next to the first one. For the third one you can just put it next to the first circle, and then move it along the edge until it hits the second circle.
All the other circles can follow the same method: place it next to an arbitrary circle, and move it along the edge until it is touching, but not intersecting, another circle. Note that this won't make it the most efficient clustering, but it works. After that, when you expand, say, circle 1, you'd move all the adjacent circles outward, and shift them around to re-cluster.

how to efficiently draw many interactive curves in JavaScript?

I need the ability to efficiently draw a large number of interactive curves (possibly Bezier) in a web app. Imagine a graph-like structure with many draggable elements that are connected with smooth curves. Hence, the curves must adjust in shape and length as single elements are moved.
What graphic method will be best to assure efficiency and interactivity for a large number curves?
SVG? Canvas? something else?
(And once we know which method is best, is there a good library that would make it easier to implement?)
You might take a look at JSXGraph. I haven't personally used it, but know some who has with nice results. It looks like it will use 'SVG, VML or canvas'.

generate b2Body for a letter

I want to code a little Game, dealing with fonts and letters. I want to make them move arround in 2d space and i am using box2dweb as physics engine, what is actually doing a very great job. At the moment all I am struggling with, is the problem of building the b2Body for a Letter. Box2d can only handle primitive, convex shapes and to build an more complex hitbox I have to combine some of them. In the image I tried to figure out what i would like to reach, an algorithm, that takes an svg-path of a letter and generates a series of b2shapes which represent the hitbox.
All in all i have no Idea where i could find some Information about this, if there is a library that is capable of doing this. Even if this Library is not available in Javascript, i could do the job on Server.
I know that there is paper.js and raphalel, some clever vector libraries, but i have not found any hint how to solve this yet.
I would be happy for any kind of help, links to ressources, or the correct name of the problem in mathematical sense.
Greetings and thanks in advance...
Philipp
I just want to leave the result of investigation here, maybe someone will help it. The initial idea is based on »ear cutting«, »ear culling«, or »ear cropping«. A demo here will describe this. But the algorithm, which produces less, but box2d suitable polygons is shown in a demo here. The idea is to merge as much triangles as possible, as long as they are convex and this case, do not have more than eight edges. A triangle is suitable to be added to a polygon, if one can find two points in the triangle and two adjective points in the polygon, with the same x and y coordinates.

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