For instance:
An approach to compute efficiently the first intersection between a viewing ray and a set of three objects: one sphere, one cone and one cylinder (other 3D primitives).
What you're looking for is a spatial partitioning scheme. There are a lot of options for dealing with this, and lots of research spent in this area as well. A good read would be Christer Ericsson's Real-Time Collision Detection.
One easy approach covered in that book would be to define a grid, assign all objects to all cells it intersects, and walk along the grid cells intersecting the line, front to back, intersecting with each object associated with that grid cell. Keep in mind that an object might be associated with more grid-cells, so the intersection point computed might actually not be in the current cell, but actually later on.
The next question would be how you define that grid. Unfortunately, there's no one good answer, and you need to consider what approach might fit your scenario best.
Other partitioning schemes of interest are different tree structures, such as kd-, Oct- and BSP-trees. You could even consider using trees combined with a grid.
EDIT
As pointed out, if your set is actually these three objects, you're definately better of just intersecting each one, and just pick the earliest one. If you're looking for ray-sphere, ray-cylinder, etc, intersection tests, these are not really hard and a quick google should supply all the math you might possibly need. :)
"computationally efficient" depends on how large the set is.
For a trivial set of three, just test each of them in turn, it's really not worth trying to optimise.
For larger sets, look at data structures which divide space (e.g. KD-Trees). Whole chapters (and indeed whole books) are dedicated to this problem. My favourite reference book is An Introduction to Ray Tracing (ed. Andrew. S. Glassner)
Alternatively, if I've misread your question and you're actually asking for algorithms for ray-object intersections for specific types of object, see the same book!
Well, it depends on what you're really trying to do. If you'd like to produce a solution that is correct for almost every pixel in a simple scene, an extremely quick method is to pre-calculate "what's in front" for each pixel by pre-rendering all of the objects with a unique identifying color into a background item buffer using scan conversion (aka the z-buffer). This is sometimes referred to as an item buffer.
Using that pre-computation, you then know what will be visible for almost all rays that you'll be shooting into the scene. As a result, your ray-environment intersection problem is greatly simplified: each ray hits one specific object.
When I was doing this many years ago, I was producing real-time raytraced images of admittedly simple scenes. I haven't revisited that code in quite a while but I suspect that with modern compilers and graphics hardware, performance would be orders of magnitude better than I was seeing then.
PS: I first read about the item buffer idea when I was doing my literature search in the early 90s. I originally found it mentioned in (I believe) an ACM paper from the late 70s. Sadly, I don't have the source reference available but, in short, it's a very old idea and one that works really well on scan conversion hardware.
I assume you have a ray d = (dx,dy,dz), starting at o = (ox,oy,oz) and you are finding the parameter t such that the point of intersection p = o+d*t. (Like this page, which describes ray-plane intersection using P2-P1 for d, P1 for o and u for t)
The first question I would ask is "Do these objects intersect"?
If not then you can cheat a little and check for ray collisions in order. Since you have three objects that may or may not move per frame it pays to pre-calculate their distance from the camera (e.g. from their centre points). Test against each object in turn, by distance from the camera, from smallest to largest. Although the empty space is the most expensive part of the render now, this is more effective than just testing against all three and taking a minimum value. If your image is high res then this is especially efficient since you amortise the cost across the number of pixels.
Otherwise, test against all three and take a minimum value...
In other situations you may want to make a hybrid of the two methods. If you can test two of the objects in order then do so (e.g. a sphere and a cube moving down a cylindrical tunnel), but test the third and take a minimum value to find the final object.
Related
I'm taking an introductory graphics course, and while I intuitively understand that converting a click or touch into object coordinates will make the math much cleaner, reduce the chances for human error, and potentially make debugging easier, none of these are actually a very good explanation, conceptually, of why object coordinate spaces are used in selection tests, as opposed to simply using world coordinates for the test - rather, they're just observations of what tends to happen when object coordinates are used. So I ask: why?
A selection test involves comparing the click coordinates, which you get in window coordinates, against lots and lots of object features, which are represented in object coordinates.
You need to transform them into the same coordinate system in order to do the checks, so you can EITHER transform the one simple click point OR you can transform all the various object features.
Transforming one point or line is just a lot easier that transforming a whole bunch of object features of various types.
There are cases where the location of a specific object or point may not be known within a world coordinate system, but is known relative to some other coordinate system.
To summarize an example from my course text, consider the idea of two different towns, one using a grid system for its layout, and the other using what I can only describe as the New England we-made-cow-trails-into-roads method. A government employee is tasked with creating a layout of the area which includes them, and in doing so has to convert the two coordinate systems into a third, which encompasses the other two.
Sometimes, using a world atlas just isn't practical to get across the street, and so something much more local (and relevant) is used instead, as it provides much more detail over a much smaller area.
The text also explains that it may be more than simply impractical to use a given coordinate system - it may yield results that are improbable or just plain wrong. This is evidenced in the evolution of the geocentric and heliocentric models of the universe - the distance of the stars from us was calculated with very different results using the two models.
Thinking of my own example, the best that comes to mind would be something like your own internal organs - from the outside, you don't know for sure exactly the shape, size, and structure of each of them, but your own body does. In order to be able to access that information, you need to look inside the body (ideally in a way that doesn't kill you). It's not something that is plainly observable from outside.
What's the best way to determine if a point is within a certain distance of a GEOJSON polygon? Should one use TurfJS buffer method (https://github.com/Turfjs/turf-buffer#turf-buffer)? Can one perform queries on the buffered polygon?
It's clear to me one could us the TurfJS' inside method (https://github.com/Turfjs/turf-inside) to determine whether a point is within a polygon. I'm just curious what the best approach would be for finding whether or not a point is inside of a buffered polygon.
For example:
I have a number of neighborhoods provided as a GEOJSON polygon files. I also have a set of locations/addresses for employees (already geocoded to lat/long coordinates). What would be the best way to see whether or not my employees live within 10 miles of a given neighborhood polygon?
Thanks!
Yes, you can use buffer in conjunction with inside to find points within 10 miles of something else, eg, expanding on the existing examples,
var pt = point(14.616599, -90.548630)
var unit = 'miles'
var buffered = buffer(pt, 10, unit)
var ptTest = point(-1, 52)
var bIn = inside (ptIn, buffer)
which should obviously be false.
In general, though, buffering is somewhat expensive, so you would not necessarily want to do this every time you run the query. There are a couple of things you can do to speed things up:
1). Pre-buffer your search areas
2). Use some kind of R-tree type index, which will first check bounding box intersection, and avoid lots of unecessary point in polygon operations. turfjs, which I hadn't heard of until seeing your post, uses jsts under the hood for a number of operations, including buffering. This library has an implemention of R-tree indexes that you could potentially use. Here is a fun example of this being done.
In general, in situations where you have a spatial (R-tree type) index in place, such as a spatially enabled database like Postgis on top of Postgres, you would use an operator like ST_Dwithin (geom1, geom2, distance) in a where clause to find all points within some distance of another geometry, and this would be very efficient as many candidates would be rejected for failing an initial bounding box test.
Really, it depends on the size of your data and frequency of queries. There is nothing, in principle, wrong with doing contains queries on a buffer. I hope I haven't created more questions than answers.
I'm using GeoScript to do that sort of calculations in JavaScript. It has a distance method in the geom.Geometry class which can return the minimum distance between two geometries. You could use that, or take a look at the source on GitHub to see how they do it if you want to roll your own solution.
I understand the concept of LOD but I am trying to find out the negative side of it and I see no reference to that from Googling around. The only pro I keep coming across is that it improves performance by omitting details when an object is far and displaying better graphics when the object is near.
Seriously that is the only pro and zero con? Please advice. Tnks.
There are several kinds of LOD based on camera distance. Geometric, animation, texture, and shading variations are the most common (there are also LOD changes that can occur based on image size and, for gaming, hardware capabilities and/or frame rate considerations).
At far distances, models can change tessellation or be replaced by simpler models. Animated details (say, fingers) may simplify or disappear. Textures may move to simpler textures, bump maps vanish, spec/diffuse maps combines, etc. And shaders may also swap-put to reduce the number of texture inputs or calculation (though this is less common and may be less profitable, since when objects are far away they already fill fewer pixels -- but it's important for screen-filling entities like, say, a mountain).
The upsides are that your game/app will have to render less data, and in some cases, the LOD down-rezzed model may actually look better when far away than the more-complex model (usually because the more detailed model will exhibit aliasing when far away, but the simpler one can be tuned for that distance). This frees-up resources for the nearer models that you probably care about, and lets you render overall larger scenes -- you might only be able to render three spaceships at a time at full-res, but hundreds if you use LODs.
The downsides are pretty obvious: you need to support asset swapping, which can mean both the real-time selection of different assets and switching them but also the management (at times of having both models in your memory pipeline (one to discard, one to load)); and those models don't come from the air, someone needs to create them. Finally, and this is really tricky for PC apps, less so for more stable platforms like console gaming: HOW DO YOU MEASURE the rendering benefit? What's the best point to flip from version A of a model to B, and B to C, etc? Often LODs are made based on some pretty hand-wavy specifications from an engineer or even a producer or an art director, based on hunches. Good measurement is important.
LOD has a variety of frameworks. What you are describing fits a distance-based framework.
One possible con is that you will have inaccuracies when you choose an arbitrary point within the object for every distance calculation. This will cause popping effects at times since the viewpoint can change depending on orientation.
The problem I am facing is following.
I have a number of 3D head scans, some of them are taken correctly (like attached example) but in many it is easy to see that the scanned person had his head not exactly aligned with the machine's front and thus one side of the texture (and depth map) seems to be "wider" (the exact reason is that one side was taken more from behind, it can be easily seen if you look at the ears).
Fortunately when I go from the cylindrical coordinates to carthesian ones and render the face with XNA, the face is symmetrical.
Now the thing is that I would like the texture and depth maps of all my heads by as nice and symmetrical as the correct one (because later i want to align them and perform PCA).
The idea I have at the moment is that I could interpolate the surfaces between all of the vertices and from those interpolations take new vertices that are equally distanced from each other.
This solutions seems a lot of work and maybe its an overkill.
Maybe there is some other way (like geting that interpolation data from DirectX/XNA that has to calculate it at some point anyway).
I will be most thankful for helpful answers.
The correct example:
http://i55.tinypic.com/332mio2.jpg
Incorrect example:
http://i54.tinypic.com/309ujvt.jpg
It's probably possible to salvage (some of) the bad scans to some degree using some coordinate transformations, but you would have to guess the "incorrectness" of the alignment and it's probably impossible to do automatically.
But, unless the original subject is dead (or otherwise unavailable); it's probably a lot easier to redo the scans.
Making another scan is very likely to be quicker, and you won't loose quality as transforming the bad scans probably will. The nose on the incorrect sample seems to be shadowing the side of the nose, and no fancy algorithm can ever fix the missing data.
In Panda3D, I've been learning a bit about the built-in physics engine and its collision detection features.
I'm trying to understand the DSSolid collision object, which is mentioned in a table on the Collision Solids manual page without explanation. It is tersely described in the API reference as "A collision volume or object made up of the intersection of two spheres (potentially a lens) and two half-spaces (planes)."
I basically understand that geometric description, but what is the purpose of such a shape??
Interestingly, this DSSolid is the one collision solid, other than a sphere, that can be either a "from" or an "into" solid.
This suggests to me that the shape is considered to be either more commonly needed than other shapes (such as a plane or a tube or an inverse sphere), or is cheaper to test. Neither of those reasons rings true to me... a DS would be more expensive than an inverse sphere to test for collisions against, and it seems to me, less useful. So I'm wondering, what is the use case for a DSSolid?
I'm curious too how the planes are typically arranged in relation to the two spheres... but that would probably become clear given the use case for this solid.
(And what does DS stand for? Double sphere?)
This question has been answered on the Panda3D forums :
Actually, I think this solid doesn't have much general use, and should probably be removed from the codebase. It was implemented once as part of an experiment by one of the Disney engineers whose initials happened to be D.S., and it was never developed further. The student who wrote up the collision page in the manual came across this solid and wrote what he knew about it, which wasn't much.