Develop Reference

How to shrink polygon by a defined amount in centimetres using co-ordinates

I am trying to shrink a polygon by a specific amount where all edges in the new polygon are of equal distance to the old one. To explain better I have a picture here.
If the picture doesnt work I have a link here.
https://imgur.com/a/A27mVHs
This is a rough drawing.
I have a point array in ([x,y])
[[390,435], [388,430], [391,425], [425,428], [410,435]]
I am trying to shrink it so the new array
[[x1,y1], [x2,y2] ... [x5,y5]]
ensures that the distance between the new area and the original one is 2 at all sides of the area.
How can I do this by only manipulating the co-ordinates. I know I need some kind of scalar vector but I'm unsure how to do this. I am trying to implement this in javascript

In the general case this is indeed an arduous problem. But for a convex polygon, it is pretty easy.
At every angle, draw the bissector and find the point at distance of the vertex equal to d / sin α/2 where α is the measure of the angle.

Have you done some research because there is lots of topics in internet about that subject, the short answer is this is not easy because there is lots of edge cases (look this topic for exemple).
A good term if you want to look more and find nice libs to do this task for your is Polygon offsetting
Others good links :
An algorithm for inflating/deflating (offsetting, buffering) polygons
ClipperOffset
A Survey of Polygon Offseting Strategies
Javascript Clipper

Classify lon/lat coordinate into geojson polygon using Javascript

I have a geojson object defining Neighborhoods in Los Angeles using lon/lat polygons. In my web application, the client has to process a live stream of spatial events, basically a list of lon/lat coordinates. How can I classify these coordinates into neighborhoods using Javascript on the client (in the browser)?
I am willing to assume neighborhoods are exclusive. So once a coordinate as been classified as neighborhood X, there is no need to further test it for other neighborhoods.

There's a great set of answers here on how to solve the general problem of determining whether a point is contained by a polygon. The two options there that sound the most interesting in your case:
As #Bubbles mentioned, do a bounding box check first. This is very fast, and I believe should work fine with either projected or unprotected coordinates. If you have SVG paths for the neighborhoods, you can use the native .getBBox() method to quickly get the bounding box.
the next thing I'd try for complex polygons, especially if you can use D3 v3, is rendering to an off-screen canvas and checking pixel color. D3 v3 offers a geo path helper that can produce canvas paths as well as SVG paths, and I suspect if you can pre-render the neighborhoods this could be very fast indeed.
Update: I thought this was an interesting problem, so I came up with a generalized raster-based plugin here: http://bl.ocks.org/4246925
This works with D3 and a canvas element to do raster-based geocoding. Once the features are drawn to the canvas, the actual geocoding is O(1), so it should be very fast - a quick in-browser test could geocode 1000 points in ~0.5 sec. If you were using this in practice, you'd need to deal with edge-cases better than I do here.
If you're not working in a browser, you may still be able to do this with node-canvas.

I've seen a few libraries out there that do this, but most of them are canvas libraries that may rely on approximations more than you'd want, and might be hard to adapt to a project which has no direct need to rely on them for intersections.
The only other half-decent option I can think of is implementing ray casting in javascript. This algorithm isn't technically perfect since it's for Euclidean geometry and lat/long coordinates are not (as they denote points on a curved surface), but for areas as small as a neighbourhood in a city I doubt this will matter.
Here's a google maps extension that essentially does this algorithm. You'd have to adapt it a bit, but the principles are quite similar. The big thing is you'd have to preprocess your coordinates into paths of just two coordinates, but that should be doable.*
This is by no means cheap - for every point you have to classify, you must test every line segment in the neighborhood polygons. If you expect a user to be reusing the same coordinates over and over between sessions, I'd be tempted to store their neighborhood as part of it's data. Otherwise, if you are testing against many, many neighborhoods, there are a few simple timesavers you can implement. For example, you can preprocess every neighborhoods extreme coordinates (get their northmost, eastmost, southmost, and westmost points), and use these to define a rectangle that inscribes the town. Then, you can first check the points for candidate neighborhoods by checking if it lies inside the rectangle, then run the full ray casting algorithm.
*If you decide to go this route and have any trouble adapting this code, I'd be happy to help

Javascript & Canvas: Endless random animation of slightly morphing circle?

I'm completely new to canvas and animating objects with it. I did a little bit of research (e.g. I found RaphaelJS) however I couldn't find any general answer or tutorial on how to create a "morphing" circle.
The image I posted here is what I would like to do:
I'd like to create one circle that is endlessly animated via a randomizer and is slightly morphing its contours.
I know this might be not a "real" question for this forum, however I just wonder if anyone could provide a few tipps or tricks on how to do something like that.
By "how to do something like that" I'm speaking actually about the technique on how to morph a circle. Do I have to "mathematically" create a circle with dozens of anchor-points along the edge that are influenced by a randomized function?
I would really appreciate some starting help with this.
Thank you in advance.

A circle can be reasonably well approximated by 4 cubic curves (one for each quarter and the control points on the tangents - google for the correct length of the control segments or calculate them yourself - see here. You could then randomly animate the control points within a small radius to get a wobbling effect.

Do I have to "mathematically" create a circle with dozens of anchor-points along the edge that are influenced by a randomized function?
Yes, you do, although it should not be necessary to create "dozens".
You may find the .bezierCurveTo() and .quadraticCurveTo() functions useful to provide smooth interpolated curves between control points.

When you can use a raster image then for every point you can displace it along the x-axis with a sin function. You can run the same function along the y-axis but instead to simply displace the pixel you can double it. This should give you a morphing circle but it also works with other shapes.

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.

how to "sort" polygons 3d?

I am still working on my "javascript 3d engine" (link inside stackoverflow).
at First, all my polygons were faces of cubes, so sorting them by average Z was working fine.
but now I've "evolved" and I want to draw my polygons (which may contain more than 4 vertices)
in the right order, namely, those who are close to the camera will be drawn last.
basically,
I know how to rotate them and "perspective"-ize them into 2D,
but don't know how to draw them in the right order.
just to clarify:
//my 3d shape = array of polygons
//polygon = array of vertices
//vertex = point with x,y,z
//rotation is around (0,0,0) and my view point is (0,0,something) I guess.
can anyone help?
p.s: some "catch phrases" I came up with, looking for the solution: z-buffering, ray casting (?!), plane equations, view vector, and so on - guess I need a simple to understand answer so that's why I asked this one. thanks.
p.s2: i don't mind too much about overlapping or intersecting polygons... so maybe the painter's algorthm indeed might be good. but: what is it exactly? how do I decide the distance of a polygon?? a polygon has many points.

The approach of sorting polygons and then drawing them bottom-to-top is called the "Painter's algorithm". Unfortunately the sorting step is in general an unsolvable problem, because it's possible for 3 polygons to overlap each other:
Thus there is not necessarily any polygon that is "on top". Alternate approaches such as using a Z buffer or BSP tree (which involves splitting polygons) don't suffer from this problem.

how do I decide the distance of a polygon?? a polygon has many points.
Painter's algorithm is the simplest to implement, but it works only in very simple cases because it assumes that there is only a single "distance" or z-value for each polygon (which you could approximate to be the average of z-values of all points in the polygon). Of course, this will produce wrong results if two polygons intersect each other.
In reality, there isn't a single distance value for a polygon -- each point on the surface of a polygon can be at a different distance from the viewer, so each point has its own "distance" or depth.
You already mentioned Z-buffering, and that is one way of doing this. I don't think you can implement this efficiently on a HTML canvas, but here's the general idea:
You need to maintain an additional canvas, the "z-buffer", where each pixel's colour represents the z-depth of the corresponding pixel on the main canvas.
To draw a polygon, you go through each point on its surface and draw only those points which are closer to the viewer than any previous objects, as indicated by the z-buffer.

I think you will have some ideas by investigating BSP tree ( binary spaces partition tree ), even if the algo will require to split some of your polygon in two.
Some example could be find here http://www.devmaster.net/articles/bsp-trees/ or by google for BSP tree. Posting some code as a reply is, in my opinion, not serious since is a complex topic.