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90 degree field of view without distortion in THREE.PerspectiveCamera
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Is this an FOV issue with my perspective camera? In my scene, spheres look like eggs/oval shaped rather than spheres when they reach the edges of the screen. Anyone know why this happens?
It sounds like you've encountered one of the unfortunate realities of 3D.
In any 3-dimensional scene, the view from a given point is most naturally thought of as a sphere. When we render a scene, we're rendering a piece of that sphere, but we need to somehow convert that piece of a sphere into a flat rectangle, since our computer screens are flat, not round.
So, in order to render a 3D scene as a rectangle, the software needs to use a projection. For 3D rendering, the most common projection is probably a rectilinear projection, also called a gnomonic projection. (On Wikipedia, see "Rectilinear lens" for a discussion of rectilinear projections in photography, and "Gnomonic projection" for a discussion of rectilinear projections in mapmaking.)
The biggest advantage of a rectilinear projection is that straight lines in the scene appear as straight lines in the rendering. A big disadvantage is that objects far from the center are distorted: small circles get turned into large ovals.
This phenomenon is an unalterable mathematical fact that no software will ever be able to overcome. However, there are things you may be able to do to mitigate the situation. One option is to use a narrower field of view. Another option is to use a different projection; the answers here have a few suggestions for how to do that: Three.js - Fisheye effect
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I've been trying to render silhouettes on CAD models with webgl. The closest i got to the desired result was with fwidth and a dot between the normal and the eye vector. I found it difficult to control the width though.
I saw another web based viewer and it's capable of doing something like this:
I started digging through the shaders, and the most i could figure out is that this is analytical - an actual line entity is drawn and that the width is achieved by rendering a quad instead of default webgl lines. There is a bunch of logic in the shader and my best guess is that the vertex positions are simply updated on every render.
This is a procedural model, so i guess that for cones and cylinders, two lines can always be allocated, silhouette points computed, and the lines updated.
If that is the case, would it be a good idea to try and do something like this in the shader (maybe it's already happening and i didn't understand it). I can see a cylinder being written to attributes or uniforms and the points computed.
Is there an approach like this already documented somewhere?
edit 8/15/17
I have not found any papers or documented techniques about this. But it got a couple of votes.
Given that i do have information about cylinders and cones, my idea is to sample the normal of that parametric surface from the vertex, push the surface out by some factor that would cover some amount of pixels in screen space, stencil it, and draw a thick line thus clipping it with the actual shape of the surface.
The traditional shader-based method is Gooch shading. The original paper is here:
http://artis.imag.fr/~Cyril.Soler/DEA/NonPhotoRealisticRendering/Papers/p447-gooch.pdf
The old fashing OpenGL technique from Jeff Lander
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.
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
Assume I have a camera defined by its position and direction, and a box defined by its center and extents (three orthogonal vectors from the box center to face centers). Face is visible when its outer surface is facing the camera and invisible when its inner surface is facing it.
It seems obvious that depending on box position and orientation there may be 1-3 faces of the box visible. Is there some clever way how to determine which faces are visible? An obvious solution would be to compute 6 dot-products of the face normal against the face-camera vector for each face. Is there a better way?
Note: perspective projection will be used, but I do not think it matters, the property of "facing camera" seems independent to a projecting.
I believe the method you described is the normal way to do this. It's a very fast calculation so you shouldn't be worried too much about speed. This is the same method they use to reduce the number of calculations for ray-triangle intersection algorithms. If the front of the face isn't visible, the method doesn't continue calculations for that face. See this paper for a c++ implementation of this algorithm. It's in the first half of the calculations. http://jgt.akpeters.com/papers/MollerTrumbore97/code.html
The only cleverness is that if a face of the cube is visible, the opposing face definitely isn't. At least in a regular perspective projection.
Note that the opposite might not be true: if a face is invisible, the opposing face might be invisible too. This is because the type of projection does matter. Imagine the cube being really up close to the camera, which is looking straight at one face. Then rotate the cube slightly, and while with a parallel projection, another face would immediately become visible, in a perspective projection this doesn't happen.
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.