I am really new to optical system engineering and I am trying to do some very basic ray tracing through biconvex and biconcave lenses to understand how all of it works. I know there are tools such as OpticStudio etc, but I just want to code something up really simple to get my hands dirty with it.
Here is the issue I am running into. Consider a biconvex lens that has left surface and right surface with radii 1.628cm and 27.57cm respectively (-27.57 if we are following conventions). The thickness of the lens at the center is 0.357cm.
I am trying to draw this lenses on a plot using MATLAB. Since, these are spherical surfaces, I am basically drawing this lens as the intersection of two circles.
The question I have is, does the radii of the two surfaces and the thickness automatically constrain the height of the lens? Reason I ask this is that I am getting a maximum lens height of ~1.2cm.
Is this really how tall a lens with these parameters can be? Am I missing something really fundamental?
Related
I have been wondering how I can combine two methods of rendering in a way that the rasterized on-screen shape serves as a canvas for ray-march based rendering in fragment shader.
Take these beautiful examples: https://www.shadertoy.com/view/XsjXRm or https://www.shadertoy.com/view/MtXSzS
The visible part of them can be roughly represented as sphere. Now what I'd like to do is to put say two spheres into some place in the world and run the regular rasterization pass. The rasterization will yield which pixels are occupied by the models and for those pixels I'd like to actually run the shadertoy ray-marching algorithms to get the desired look (my two spheres look like shadertoy "spheres" in the examples above).
Is this something doable?
P.S. I know rasterization and matrix/spaces transformation quite well, but I have very vague understanding of how ray-marching works. Pardon my ignorance.
This is definitely possible.
The idea is to use the same camera for ray tracing and for rasterization.
You can get the camera's position from the camera matrix in the fragment shader and you can get the camera's direction by subtracting the fragments position from the camera's position and normalizing it.
This way the rays are only cast from the camera to the visible fragments.
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've got a fairly simple implementation of normal map lighting working for 2D sprites in webgl (GLSL shaders) which I was able to adapt & optimize from an example. It uses just one directional light and works fine for my purposes. Sprites are rendered flat (2D), only the light direction and normals are 3D vectors. Vertex rotation only happens around the z axis, so it's fairly easy-peasy.
I was hoping to add a bump (height) map to cast shadows. There are 3D bump map shadow casting examples and papers available online, but they're more complex than I need and the math goes over my head; I haven't found an example or explanation of how one might do a simple 2D case.
My first inclination is as follows: for the current pixel in the fragment shader, trace back along the direction of the light and check the altitude of the neighbouring bump map pixel. If it's higher than the light direction vector at that point, then that pixel is in the shade. However since "tall" pixels on the bump map may cast shadow across > 1 pixel distance, I'd have to keep testing pixel by pixel in that direction until I find one tall enough to cast a shadow (or reach the edge of the texture, or reach some arbitrary limit.)
This doesn't sound very optimal, especially for larger textures. I've read that if statements in shaders aren't so fast. Is there a faster/better method?
What you are looking for is called parallax (occlusion) mapping.
It's a technique that does exactly what you described, and it can be understood as on-bumpmap ray tracing in tangent space.
Here are some articles:
nVidia - Per-Pixel displacement (w/ sphere tracing)
nVidia - Cone Tracing for PM
AMD - POM
The ways to optimize search are similar to ordinary raytracing and include: sphere tracing, cone tracing, binary search and similar, instead of constant stepping function.
P. S. If you know the name of some rendering technique, it's generally good idea to Google it adding 'nVidia', 'crytek' or 'gpu' in front of the name, it will show you much more relevant results.
Hope this helps.
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.