I am trying to write an optimized code that renders a 3D scene using OpenGL onto a sphere and then displays the unwrapped sphere on the screen ie producing a planar map of a purely reflective sphere. In math terms, I would like to produce a projection map where the x axis is the polar angle and y axis is the azimuth.
I am trying to do this by placing the camera at the center of the sphere probe and taking planar shots around so as to approximate spherical quads with planar tiles of the frustum. Then I can use this as texture to apply to a distorted planar patch.
Seems to me this is pretty tedious approach. I wonder if there is way to take this on using shaders or some GPU-smart method.
Thank you
S.
I can give you two solutions.
The first is to make a standard render-to-texture, but with a cubemap attached as the destination buffer. If your hardware is recent enough, it can be done in a single pass. This will deal with all the needed math in HW for you, but data repartition of cubemaps aren't ideal (quite a lot of distortion if the corners). In most cases, it should be enough though.
After this, you render a quad to the screen, and in a shader you map your UV coordinates to xyz vectors using staightforwad spherical mapping. The HW will compute for you which side of the cubemap to take, at which UV.
The second is more or less the same, but with a custom deformation and less HW support : dual paraboloids. Two paraboloids may not be enough, but you are free to slightly modify the equations and make 6 passes. The rendering pass is the same, but this time you're all by yourself to choose the right texture and compute the UVs.
By the time you've bothered to build the model, take the planar shots, apply non-affine transformations and stitch the whole thing together, you've probably gained no performance and considerable complexity. Just project the planar image mathematically and be done with it.
You seem to be asking for OpenGL's sphere mapping. NeHe has a tutorial on sphere mapping that might be useful.
Related
To draw a sphere, one does not need to know anything else but it's position and radius. Thus, rendering a sphere by passing a triangle mesh sounds very inefficient unless you need per-vertex colors or other such features. Despite googling, searching D3D11 documentation and reading Introduction to 3D Programming with DirectX 11, I failed to understand
Is it possible to draw a sphere by passing only the position and radius of it to the GPU?
If not, what is the main principle I have misunderstood?
If yes, how to do it?
My ultimate goal is to pass more parameters later on which will be used by a shader effect.
You will need to implement Geometry Shader. This shader should take Sphere center and radius as input and emit a banch of vertices for rasterization. In general this is called point sprites.
One option would be to use tessellation.
https://en.wikipedia.org/wiki/Tessellation_(computer_graphics)
Most of the mess will be generated on the gpu side.
Note:
In the end you still have more parameters sent to the shaders because the sphere will be split into triangles that will be each rendered individually on the screen.
But the split is done on the gpu side.
While you can create a sphere from a point & vertex on the GPU, it's generally not very efficient. With higher-end GPUs you could use Hardware Tessellation, but even that would be better done a different way.
The better solution is to use instancing and render lots of the same VB/IB of sphere geometry scaled to different positions and sizes.
I am looking for a way to "fill" three-dimensional geometry with color, and quite possibly a texture at some time later on.
Suppose for a moment that you could physically phase your head into a concrete wall, logically you would see only darkness. In OpenGL, however, when you do this the world is naturally hollow and transparent due to culling and because of how the geometry is drawn. I want to simulate the darkness/color/texture within it instead.
I know some games do this by overlaying a texture/color directly over the hud--therefore blinding the player.
Is there another way to do this, though? Suppose the player is standing half in water; they can partially see below the waves. How would you fill it to prevent them from being able to see clearly below what is now half of their screen?
What is this concept even called?
A problem with the texture-in-front-of-the-camera method is a texture is 2D but you want to visualize a slice of a 3D volume. For the first thing you talk about, the head-inside-a-wall idea, I'll point you to "3D/volume texturing". For standing-half-in-water, you're after "volume rendering" with "absorption" (discussed by #user3670102).
3D texturing
The general idea here is you have some function that defines a colour everywhere in a 3D space, not just on a surface (as with regular texture mapping). This is nice because you can put geometry anywhere and colour it in the fragment shader based on the 3D position. Think of taking a slice through the volume and looking at the intersection colour.
For the head-in-a-wall effect you could draw a full screen polygon in front of the player (right on the near clipping plane, although you might want to push this forwards a bit so its not too small) and colour it based on a 3D function. Now it'll look properly solid and move ad the player does and not like you've cheaply stuck a texture over the screen.
The actual function could be defined with a 3D texture but that's very memory intensive. Instead, you could look into either procedural 3D colour (a procedural wood or brick shader is pretty common as an example). Even assuming a 2D texture is "extruded" through the volume will work, or better yet weight 3 textures (one for each axis) based on the angle of the intersection/surface you're drawing on.
Detecting an intersection with the geometry and the near clipping plane is probably the hardest bit here. If I were you I'd look at tricks with the z-buffer and make sure to draw everything as solid non-self-intersecting geometry. A simple idea might be to draw back faces only after drawing everything with front faces. If you can see back faces that part of the near plane must be inside something. For these pixels you could calculate the near clipping plane position in world space and apply a 3D texture. Though I suspect there are faster ways than drawing everything twice.
In reality there would probably be no light getting to what you see and it should be black, but I guess just ignore this and render the colour directly, unlit.
Absorption
This sounds way harder than it actually is. If you have some transparent solid that's all the one colour ("homogeneous") then it removes light the further light has to travel through it. Think of many alpha-transparent surfaces, take the limit and you have an exponential. The light remaining is close to 1/exp(dist) or exp(-dist). Google "Beer's Law". From here,
vec3 Absorbance = WaterColor * WaterDensity * -WaterDepth;
vec3 Transmittance = exp(Absorbance);
A great way to find distances through something is to render the back faces (or seabed/water floor) with additive blending using a shader that draws distance to a floating point texture. Then switch to subtractive blending and render all the front faces (or water surface). You're left with a texture containing distances/depth for the above equation.
Volume Rendering
Combining the two ideas, the material is both a transparent solid but the colour (and maybe density) varies throughout the volume. This starts to get pretty complicated if you have large amounts of data and want it to be fast. A straight forward way to render this is to numerically integrate a ray through the 3D texture (or procedural function, whatever you're using), at the same time applying the absorption function. A basic brute force Euler integration might start a ray for each pixel on the near plane, then march forwards at even distances. Over each step while you march you assume the colour remains constant and apply absorption, keeping track of how much light you have left. A quick google brings up this.
This seems related to looking through what's called "participating media". On the less extreme end, you'd have light fog, or smoky haze. In the middle could be, say, dirty water. And the extreme case would be your head-in-the-wall example.
Doing this in a physically accurate way isn't trivial, because the darkening effect is more pronounced when the thickness of the media is greater.
But you can fake this by making some assumptions and giving the interior geometry (under the water or inside the wall) darker by reduced lighting or using darker colors. If you care about the depth effect, look at OpenGL and fog.
For underwater, you can make the back side of the water a semi-transparent color that causes stuff above it to have a suitable change in color.
If you really want to go nuts with accuracy, look at Kajia's Rendering Equation. That covers everything (including stuff that glows), but generally needs simplification and approximations to be more useful.
I have a program in which I need to apply a 2-dimensional texture (simple image) to a surface generated using the marching-cubes algorithm. I have access to the geometry and can add texture coordinates with relative ease, but the best way to generate the coordinates is eluding me.
Each point in the volume represents a single unit of data, and each unit of data may have different properties. To simplify things, I'm looking at sorting them into "types" and assigning each type a texture (or portion of a single large texture atlas).
My problem is I have no idea how to generate the appropriate coordinates. I can store the location of the type's texture in the type class and use that, but then seams will be horribly stretched (if two neighboring points use different parts of the atlas). If possible, I'd like to blend the textures on seams, but I'm not sure the best manner to do that. Blending is optional, but I need to texture the vertices in some fashion. It's possible, but undesirable, to split the geometry into parts for each type, or to duplicate vertices for texturing purposes.
I'd like to avoid using shaders if possible, but if necessary I can use a vertex and/or fragment shader to do the texture blending. If I do use shaders, what would be the most efficient way of telling it was texture or portion to sample? It seems like passing the type through a parameter would be the simplest way, but possible slow.
My volumes are relatively small, 8-16 points in each dimension (I'm keeping them smaller to speed up generation, but there are many on-screen at a given time). I briefly considered making the isosurface twice the resolution of the volume, so each point has more vertices (8, in theory), which may simplify texturing. It doesn't seem like that would make blending any easier, though.
To build the surfaces, I'm using the Visualization Library for OpenGL and its marching cubes and volume system. I have the geometry generated fine, just need to figure out how to texture it.
Is there a way to do this efficiently, and if so what? If not, does anyone have an idea of a better way to handle texturing a volume?
Edit: Just to note, the texture isn't simply a gradient of colors. It's actually a texture, usually with patterns. Hence the difficulty in mapping it, a gradient would've been trivial.
Edit 2: To help clarify the problem, I'm going to add some examples. They may just confuse things, so consider everything above definite fact and these just as help if they can.
My geometry is in cubes, always (loaded, generated and saved in cubes). If shape influences possible solutions, that's it.
I need to apply textures, consisting of patterns and/or colors (unique ones depending on the point's "type") to the geometry, in a technique similar to the splatting done for terrain (this isn't terrain, however, so I don't know if the same techniques could be used).
Shaders are a quick and easy solution, although I'd like to avoid them if possible, as I mentioned before. Something usable in a fixed-function pipeline is preferable, mostly for the minor increase in compatibility and development time. Since it's only a minor increase, I will go with shaders and multipass rendering if necessary.
Not sure if any other clarification is necessary, but I'll update the question as needed.
On the texture combination part of the question:
Have you looked into 3d textures? As we're talking marching cubes I should probably immediately say that I'm explicitly not talking about volumetric textures. Instead you stack all your 2d textures into a 3d texture. You then encode each texture coordinate to be the 2d position it would be and the texture it would reference as the third coordinate. It works best if your textures are generally of the type where, logically, to transition from one type of pattern to another you have to go through the intermediaries.
An obvious use example is texture mapping to a simple height map — you might have a snow texture on top, a rocky texture below that, a grassy texture below that and a water texture at the bottom. If a vertex that references the water is next to one that references the snow then it is acceptable for the geometry fill to transition through the rock and grass texture.
An alternative is to do it in multiple passes using additive blending. For each texture, draw every face that uses that texture and draw a fade to transparent extending across any faces that switch from one texture to another.
You'll probably want to prep the depth buffer with a complete draw (with the colour masks all set to reject changes to the colour buffer) then switch to a GL_EQUAL depth test and draw again with writing to the depth buffer disabled. Drawing exactly the same geometry through exactly the same transformation should produce exactly the same depth values irrespective of issues of accuracy and precision. Use glPolygonOffset if you have issues.
On the coordinates part:
Popular and easy mappings are cylindrical, box and spherical. Conceptualise that your shape is bounded by a cylinder, box or sphere with a well defined mapping from surface points to texture locations. Then for each vertex in your shape, start at it and follow the normal out until you strike the bounding geometry. Then grab the texture location that would be at that position on the bounding geometry.
I guess there's a potential problem that normals tend not to be brilliant after marching cubes, but I'll wager you know more about that problem than I do.
This is a hard and interesting problem.
The simplest way is to avoid the issue completely by using 3D texture maps, especially if you just want to add some random surface detail to your isosurface geometry. Perlin noise based procedural textures implemented in a shader work very well for this.
The difficult way is to look into various algorithms for conformal texture mapping (also known as conformal surface parametrization), which aim to produce a mapping between 2D texture space and the surface of the 3D geometry which is in some sense optimal (least distorting). This paper has some good pictures. Be aware that the topology of the geometry is very important; it's easy to generate a conformal mapping to map a texture onto a closed surface like a brain, considerably more complex for higher genus objects where it's necessary to introduce cuts/tears/joins.
You might want to try making a UV Map of a mesh in a tool like Blender to see how they do it. If I understand your problem, you have a 3D field which defines a solid volume as well as a (continuous) color. You've created a mesh from the volume, and now you need to UV-map the mesh to a 2D texture with texels extracted from the continuous color space. In a tool you would define "seams" in the 3D mesh which you could cut apart so that the whole mesh could be laid flat to make a UV map. There may be aliasing in your texture at the seams, so when you render the mesh it will also be discontinuous at those seams (ie a triangle strip can't cross over the seam because it's a discontinuity in the texture).
I don't know any formal methods for flattening the mesh, but you could imagine cutting it along the seams and then treating the whole thing as a spring/constraint system that you drop onto a flat surface. I'm all about solving things the hard way. ;-)
Due to the issues with texturing and some of the constraints I have, I've chosen to write a different algorithm to build the geometry and handle texturing directly in that as it produces surfaces. It's somewhat less smooth than the marching cubes, but allows me to apply the texcoords in a way that works for my project (and is a bit faster).
For anyone interested in texturing marching cubes, or just blending textures, Tommy's answer is a very interesting technique and the links timday posted are excellent resources on flattening meshes for texturing. Thanks to both of them for their answers, hopefully they can be of use to others. :)
From what I gathered he used sparse voxel octrees and raycasting. It doesn't seem like he used opengl or direct3d and when I look at the game Voxelstein it appears that miniature cubes are actually being drawn instead of just a bunch of 2d square. Which caught me off guard I'm not sure how he is doing that without opengl or direct3d.
I tried to read through the source code but it was difficult for me to understand what was going on. I would like to implement something similar and would like the algorithm to do so.
I'm interested in how he performed rendering, culling, occlusion, and lighting. Any help is appreciated.
The algorithm is closer to ray-casting than ray-tracing. You can get an explanation from Ken Silverman himself here:
https://web.archive.org/web/20120321063223/http://www.jonof.id.au/forum/index.php?topic=30.0
In short: on a grid, store an rle list of surface voxels for each x,y stack of voxels (if z means 'up'). Assuming 4 degrees of freedom, ray-cast across it for each vertical line on the screen, and maintain a list of visible spans which is clipped as each cube is drawn. For 6 degrees of freedom, do something similar but with scanlines which are tilted in screenspace.
I didn't look at the algorithm itself, but I can tell the following based off the screenshots:
it appears that miniature cubes are actually being drawn instead of just a bunch of 2d square
Yep, that's how ray-tracing works. It doesn't draw 2d squares, it traces rays. If you trace your rays against many miniature cubes, you'll see many miniature cubes. The scene is represented by many miniature cubes (voxels), hence you see them when you look up close. It would be nice to actually smoothen the data somehow (trace against smoothed energy function) to make them look smoother.
I'm interested in how he performed rendering
by ray-tracing
culling
no need for culling when ray-tracing, particularly in a voxel scene. As you move along the ray you check only the voxels that the ray intersects.
occlusion
voxel-voxel occlusion is handled naturally by ray-tracing; it would return the first voxel hit, which is the closest. If you draw sprites you can use a Z-buffer generated by the ray-tracer.
and lighting
It's possible to approximate the local normal by looking at nearby cells and looking which are occupied and which are not. Then performing the lighting calculation. Alternatively each voxel can store the normal along with its color or other material properties.
I am working on an application that detects the most prominent rectangle in an image, then seeks to rotate it so that the bottom left of the rectangle rests at the origin, similar to how IUPR's OSCAR system works. However, once the most prominent rectangle is detected, I am unsure how to take into account the depth component or z-axis, as the rectangle won't always be "head-on". Any examples to further my understanding would be greatly appreciated. Seen below is an example from IUPR's OSCAR system.
alt text http://quito.informatik.uni-kl.de/oscar/oscar.php?serverimage=img_0324.jpg&montage=use
You don't actually need to deal with the 3D information in this case, it's just a mappping function, from one set of coordinates to another.
Look at affine transformations, they're capable of correcting simple skew and perspective effects. You should be able to find code somewhere that will calculate a transform from the 4 points at the corners of your rectangle.
Almost forgot - if "fast" is really important, you could simplify the system to only use simple shear transformations in combination, though that'll have a bad impact on image quality for highly-tilted subjects.
Actually, I think you can get away with something much simpler than Mark's approach.
Once you have the 2D coordinates on the skewed image, re-purpose those coordinates as texture coordinates.
In a renderer, draw a simple rectangle where each corner's vertices are texture mapped to the vertices found on the skewed 2D image (normalized and otherwise transformed to your rendering system's texture coordinate plane).
Now you can rely on hardware (using OpenGL or similar) to do the correction for you, or you can write your own texture mapper:
The aspect ratio will need to be guessed at since we are disposing of the actual 3D info. However, you can get away with just taking the max width and max height of your skewed rectangle.
Perspective Texture Mapping by Chris Hecker