Suppose I have a 3D model:
The model is given in the form of vertices, faces (all triangles) and normal vectors. The model may have holes and/or transparent parts.
For an arbitrarily placed light source at infinity, I have to determine:
[required] which triangles are (partially) shadowed by other triangles
Then, for the partially shadowed triangles:
[bonus] what fraction of the area of the triangle is shadowed
[superbonus] come up with a new mesh that describe the shape of the shadows exactly
My final application has to run on headless machines, that is, they have no GPU. Therefore, all the standard things from OpenGL, OpenCL, etc. might not be the best choice.
What is the most efficient algorithm to determine these things, considering this limitation?
Do you have single mesh or more meshes ?
Meaning if the shadow is projected on single 'ground' surface or on more like room walls or even near objects. According to this info the solutions are very different
for flat ground/wall surfaces
is usually the best way a projected render to this surface
camera direction is opposite to light normal and screen is the render to surface. Surface is not usually perpendicular to light so you need to use projection to compensate... You need 1 render pass for each target surface so it is not suitable if shadow is projected onto near mesh (just for ground/walls)
for more complicated scenes
You need to use more advanced approach. There are quite a number of them and each has its advantages and disadvantages. I would use Voxel map but if you are limited by space than some stencil/vector approach will be better. Of course all of these techniques are quite expensive and without GPU I would not even try to implement them.
This is how Voxel map looks like:
if you want just self shadowing then voxel map size can be only some boundig box around your mesh and in that case you do not incorporate whole mesh volume instead just projection of each pixel into light direction (ignore first voxel...) to avoid shadow on lighted surface
Related
I am setting up a particle system in threejs by adapting the buffer geometry drawcalls example in threejs. I want to create a series of points, but I want them to be round.
The documentation for threejs points says it accepts geometry or buffer geometry, but I also noticed there is a circleBufferGeometry. Can I use this?
Or is there another way to make the points round besides using sprites? I'm not sure, but it seems like loading an image for each particle would cause a lot of unnecessary overhead.
So, in short, is there a more performant or simple way to make a particle system of round particles (spheres or discs) in threejs without sprites?
If you want to draw each "point"/"particle" as a geometric circle, you can use THREE.InstancedBufferGeometry or take a look at this
The geometry of a Points object defines where the points exist in 3D space. It does not define the shape of the points. Points are also drawn as quads, so they're always going to be a square, though they don't have to appear that way.
Your first option is to (as you pointed out) load a texture for each point. I don't really see how this would introduce "a lot" of overhead, because the texture would only be loaded once, and would be applied to all points. But, I'm sure you have your reasons.
Your other option is to create your own shader to draw the point as a circle. This method takes the point as a square, and discards any fragments (multiple fragments make up a pixel) outside the circle.
I am curious about the limits of three.js. The following question is asked mainly as a challenge, not because I actually need the specific knowledge/code right away.
Say you have a game/simulation world model around a sphere geometry representing a planet, like the worlds of the game Populous. The resolution of polygons and textures is sufficient to look smooth when the globe fills the view of an ordinary camera. There are animated macroscopic objects on the surface.
The challenge is to project everything from the model to a global map projection on the screen in real time. The choice of projection is yours, but it must be seamless/continuous, and it must be possible for the user to rotate it, placing any point on the planet surface in the center of the screen. (It is not an option to maintain an alternative model of the world only for visualization.)
There are no limits on the number of cameras etc. allowed, but the performance must be expected to be "realtime", say two-figured FPS or more.
I don't expect ayn proof in the form of a running application (although that would be cool), but some explanation as to how it could be done.
My own initial idea is to place a lot of cameras, in fact one for every pixel in the map projection, around the globe, within a Group object that is attached to some kind of orbit controls (with rotation only), but I expect the number of object culling operations to become a huge performance issue. I am sure there must exist more elegant (and faster) solutions. :-)
why not just use a spherical camera-model (think a 360° camera) and virtually put it in the center of the sphere? So this camera would (if it were physically possible) be wrapped all around the sphere, looking toward the center from all directions.
This camera could be implemented in shaders (instead of the regular projection-matrix) and would produce an equirectangular image of the planet-surface (or in fact any other projection you want, like spherical mercator-projection).
As far as I can tell the vertex-shader can implement any projection you want and it doesn't need to represent a camera that is physically possible. It just needs to produce consistent clip-space coordinates for all vertices. Fragment-Shaders for lighting would still need to operate on the original coordinates, normals etc. but that should be achievable. So the vertex-shader would just need compute (x,y,z) => (phi,theta,r) and go on with that.
Occlusion-culling would need to be disabled, but iirc three.js doesn't do that anyway.
I need additional theory on view frustum culling to better understand how to implement it. I understand that ray casting is involved in order to figure out what objects are in front, thus figuring out which objects not to render.
I am concerned about CPU usage. From what I understand, I should be casting out rays by my camera's width * height, and maybe increase the amount of rays depending how far the camera sees. Additionally, I would have to multiply that by the amount of object in the scene to verify which is closest to the ray.
Is my understanding of this concept accurate? How exactly could I do this more efficiently?
edit:
The goal is to achieve some type of voxel engine where the world can be sub-divided-up using an oct-tree. It could consist of hundreds of thousands of cubes.
I don't think view frustum culling involves ray casting usually.
Normally you'd just z-transform all your geometry and then clip any polygons whose vertices fall outside of the viewport, or whose z value is greater or less than the near/far clipping planes.
Ray casting would be a lot more expensive, as you are essentially testing each pixel in the viewport to see if there's a polygon behind it, which is potentially NUMBER_OF_PIXELS * NUMBER_OF_POLYGONS math operations, instead of just NUMBER_OF_POLYGONS.
EDIT:
Oh, I see: You're trying to create a voxel-space world like Minecraft. That's a bit different.
The trick there is to make use of the fact that you know the world is a grid to avoid doing calculations for geometry that is occluded by cubes that are closer to the camera.
I'm still not sure that ray casting is the best approach for this - I suspect you want something like an oct-tree structure that lets you discard large groups of blocks quickly, but I'll let somebody with more experience of building such things weigh in ;-)
EDIT 2:
Looks like somebody else on StackOverflow had the same problem (and they used octrees): Culling techniques for rendering lots of cubes
So in general, when we think of Single View Reconstruction we think of working with planes, simple textures and so on... Generally, simple objects from nature's point of view. But what about such thing as wet beach stones? I wonder if there are any algorithms that could help with reconstructing 3d from single picture of stones?
Shape from shading would be my first angle of attack.
Smooth wet rocks, such as those in the first image, may exhibit predictable specular properties allowing one to estimate the surface normal based only on the brightness value and the relative angle between the camera and the light source (the sun).
If you are able to segment individual rocks, like those in the second photo, you could probably estimate the parameters of the ground plane by making some assumptions about all the rocks in the scene being similar in size and lying on said ground plane.
I need the fastest sphere mapping algorithm. Something like Bresenham's line drawing one.
Something like the implementation that I saw in Star Control 2 (rotating planets).
Are there any already invented and/or implemented techniques for this?
I really don't want to reinvent the bicycle. Please, help...
Description of the problem.
I have a place on the 2D surface where the sphere has to appear. Sphere (let it be an Earth) has to be textured with fine map and has to have an ability to scale and rotate freely. I want to implement it with a map or some simple transformation function of coordinates: each pixel on the 2D image of the sphere is defined as a number of pixels from the cylindrical map of the sphere. This gives me an ability to implement the antialiasing of the resulting image. Also I think about using mipmaps to implement mapping if one pixel on resulting picture is corresponding to more than one pixel on the original map (for example, close to poles of the sphere). Deeply inside I feel that this can be implemented with some trivial math. But all these thoughts are just my thoughts.
This question is a little bit related to this one: Textured spheres without strong distortion, but there were no answers available on my question.
UPD: I suppose that I have no hardware support. I want to have an cross-platform solution.
The standard way to do this kind of mapping is a cube map: the sphere is projected onto the 6 sides of a cube. Modern graphics cards support this kind of texture at the hardware level, including full texture filtering; I believe mipmapping is also supported.
An alternative method (which is not explicitly supported by hardware, but which can be implemented with reasonable performance by procedural shaders) is parabolic mapping, which projects the sphere onto two opposing parabolas (each of which is mapped to a circle in the middle of a square texture). The parabolic projection is not a projective transformation, so you'll need to handle the math "by hand".
In both cases, the distortion is strictly limited. Due to the hardware support, I recommend the cube map.
There is a nice new way to do this: HEALPix.
Advantages over any other mapping:
The bitmap can be divided into equal parts (very little distortion)
Very simple, recursive geometry of the sphere with arbitrary precision.
Example image.
Did you take a look at Jim Blinn's articles "How to draw a sphere" ? I do not have access to the full articles, but it looks like what you need.
I'm a big fan of StarconII, but unfortunately I don't remember the details of what the planet drawing looked like...
The first option is triangulating the sphere and drawing it with standard 3D polygons. This has definite weaknesses as far as versimilitude is concerned, but it uses the available hardware acceleration and can be made to look reasonably good.
If you want to roll your own, you can rasterize it yourself. Foley, van Dam et al's Computer Graphics -- Principles and Practice has a chapter on Bresenham-style algorithms; you want the section on "Scan Converting Ellipses".
For the point cloud idea I suggested in earlier comments: you could avoid runtime parameterization questions by preselecting and storing the (x,y,z) coordinates of surface points instead of a 2D map. I was thinking of partially randomizing the point locations on the sphere, so that they wouldn't cause structured aliasing when transformed (forwards, backwards, whatever 8^) onto the screen. On the downside, you'd have to deal with the "fill" factor -- summing up the colors as you draw them, and dividing by the number of points. Er, also, you'd have the problem of what to do if there are no points; e.g., if you want to zoom in with extreme magnification, you'll need to do something like look for the nearest point in that case.