Given a 3D object in Computer graphics, whose surface is represented as a 3D triangular mesh (mesh of 3D triangle objects), I need to find the maximum continual Convex patches on the surface of the given 3D object.
I am using OpenGl to render the graphics within a C++ program. What kind of methods or algorithms should I use to find the convex patches.
I have to apply different colors to the different convex patches on the object to signify the selection.
Say I have a sphere then the whole sphere is one maximal convex patch. Any portion of the sphere surface will be a convex patch, by maximal I mean the maximum continuous convex patch that can be found. Well in the rendering, depending on the viewing angles, the maximal convex patches visible to the viewer will have to colored.
Start from any triangle. Traverse it's edge's and check that the angle between the two triangles is less than 180deg. If it is add it to the current selection and continue expanding.
The check is actually really simple if you use vector geometry. Say A - B is the common edge with C on the selected side and D on the other. Then just check if dot(cross((A-B), (D-B)), cross((A-B), (C-B)) < 0.
Unfortunately OpenGL doesn't help with object algorithms. It only handles converting triangles to pixels.
I need to do it using OpenGL
Then you're out of luck. OpenGL only draws points, lines and triangles. OpenGL is not a 3D modelling library, OpenGL is not a scene graph, OpenGL is not a graphics engine.
It does not do all purpose geometry processing (it may be possible to use a combination of geometry/tesselation shaders, transform feedback and compute shaders to do it, but it would be very cumbersome to implement).
Related
I've been searching for vector graphics and flash for quite some time but I haven't really found what I was looking for. Can anyone tell me exactly what area of mathematics is required for building vector images in 3D space? Is this just vector math? I saw some C++ libraries for it but I wasn't sure if it was the sort of vectors meant to for smaller file size like flash images are. Thanks in advance.
If you're wanting to do something from scratch (there are plenty of open-source libraries out there if you don't), keep in mind that "vector graphics" (this is different than the idea of a 3D space vector) themselves are typically based on parametric curves like Bezier curves, which are essentially 3rd degree polynomials for each x, y, and/or z point parameterized from a value t that goes from 0 to 1. Now projecting the texture-map image you create with those curves (i.e., the so-called "vector graphics" image) onto triangle polygon via uv coordinates would involve some interpolation, which is fairly straight forward linear algebra, as you would utilize the barycentric coordinate of the 3D point on the surface of the triangle polygon in order to calculate the uv point you want to look-up from the texture.
So essentially the steps are:
Create the parametric-curve based image (i.e, the "vector graphic") and make a texture map out of it
That texture map will have uv coordinates
When you rasterize the 3D triangle polygon, you will get a barycentric coordinate on the surface of the triangle from the actual 3D points of the triangle polygon. Those points of the polygon should also have UV coordinates assigned to them.
Use the barycentric coordinates to calculate the uv coordinate on the texture map.
When you get that color from the texture map, then shade the triangle (i.e, calculate lighting, etc. if that's what you're doing, or just save that color of the pixel if there is no lighting).
Please note I haven't gotten into antialiasing, that's a completely different beast. Best thing if you don't know what you're doing there is to simply brute-force antialias through super-sampling (i.e., render a really big image and then average pixels to shrink it back to the desired size).
If you've taken multivariable calculus, the concepts behind parametric curves and surfaces should be familiar, and a basic understanding of linear algebra would be necessary in order to work with barycentric coordinates and linear interpolation from 3D vectors.
I need to visualize 3D point clouds using C++, I started learning OpenGL but so far all I find is drawing shapes using vertices
What if I want the 3D scene to be built using pixels, does OpenGL support this ? if not what alternatives I have ?
Two approaches:
Render geometry using GL_POINTS mode. You'll end up with a
literal display of a point cloud (i.e. bigger and smaller dots, no
vertices, no solid faces). This is very simple to implement.
Process your data so that you'll have solid geometry (i.e. triangles) representing the original shape. There is a couple of algorithms which try to generate a mesh from a 3D bitmap. Most notable are Marching Cubes and Marching Tetrahedrons. These are commonly used i.e. in medicine (to create a 3D mesh of an organ after it's scanned by MRI or something). You'll find plenty of resources for them on Google.
I think what you are looking for is Point Sprites. There are some examples of Point Sprites and particle clouds on http://www.codesampler.com/oglsrc/oglsrc_6.htm (although I haven't tried these examples myself).
Is there a way to extract a point cloud from a rendered 3D Scene (using OPENGL)?
in Detail:
The input should be a rendered 3D Scene.
The output should be e.g a three dimensional array with vertices(x,y,z).
Mission possible or impossible?
Render your scene using an orthographic view so that all of it fits on screen at once.
Use a g-buffer (search for this term or "fat pixel" or "deferred rendering") to capture
(X,Y,Z, R, G, B, A) at each sample point in the framebuffer.
Read back your framebuffer and put the (X,Y,Z,R,G,B,A) tuple at each sample point in a
linear array.
You now have a point cloud sampled from your conventional geometry using OpenGL. Apart from the readback from the GPU to the host, this will be very fast.
Going further with this:
Use depth peeling (search for this term) to generate samples on surfaces that are not
nearest to the camera.
Repeat the rendering from several viewpoints (or equivalently for several rotations
of the scene) to be sure of capturing fragments from a the nooks and crannies of the
scene and append the points generated from each pass into one big linear array.
I think you should take your input data and manually multiply it by your transformation and modelview matrices. No need to use OpenGL for that, just some vector/matrices math.
If I understand correctly, you want to deconstruct a final rendering (2D) of a 3D scene. In general, there is no capability built-in to OpenGL that does this.
There are however many papers describing approaches to analyzing a 2D image to generate a 3D representation. This is for example what the Microsoft Kinect does to some extent. Look at the papers presented at previous editions of SIGGRAPH for a starting point. Many implementations probably make use of the GPU (OpenGL, DirectX, CUDA, etc.) to do their magic, but that's about it. For example, edge-detection filters to identify the visible edges of objects and histogram functions can run on the GPU.
Depending on your application domain, you might be in for something near impossible or there might be a shortcut you can use to identify shapes and vertices.
edit
I think you might have a misunderstanding of how OpenGL rendering works. The application produces and sends to OpenGL the vertices of triangles forming polygons and 3d objects. OpenGL then rasterizes (i.e. converts to pixels) these objects to form a 2d rendering of the 3d scene from a particular point of view with a particular field of view. When you say you want to retrieve a "point cloud" of the vertices, it's hard to understand what you want since you are responsible for producing these vertices in the first place!
Hi
How can I extrude cut (like solidworks) a 3D model?
Is there an easy way or I have to do some complex calculation?
What you want to do is part of a discipline called Constructive Solid Geometry (CSG) and it's about one of the trickiest subjects of 3D graphics and processing. There are several approaches how to tackle the problem:
If you're just interested in rendering CSG in a raytracer things get actually quite easy: At every ray/surface intersection you increment/decrement a counter. CSG combinations can also be transformed into surface count. By compariring ray intersection counter and CSG surface count you can apply the CSG operations on the traced ray
If you're interested on doing CSG on triangulated models, the most common approach is to build BSP trees from the geometry and apply the CSG operations on the BSP. Then from the resulting BSP you recreate the mesh. This is how it's implemented in mesh based modellers (take a look at Blender's source code, which does exactly this)
CSG on analytical surfaces is extremely difficult. There are no closed solutions for the intersection of curves or curved surfaces. The best approach is to numerically find a number of sampling points in the intersection and fit a curve along the intersection. This can get numerically unstable.
Tesselation Phase Processing (this is what I implemented (or even invented maybe) for my 3D engine): When rendering curves or curved patches on 3D hardware, one usually must tesselate them into triangular meshes before. In this tesselation phase you can test if the edges of a newly created triangle intersect with curves/curved surfaces; use a few iterations in a Newton zero crossing solver to find the point of intersection of both curves/surfaces and store this as a sampling point at the edge for both patches involved (so that the tesselation of the other surface will share its vertices' positions with the first surface). After the first tesselation stage use a relaxation method (basically apply a Laplacian) on the vertices, while constraining them to the surface (remember that your surfaces are mathematical exact and it's very easy to fiddle with the variables of the surface, but use the resulting positions as metric). It works very well as long as not intersections with ordinary triangulated meshes are to be considered (each triangle of the mesh had to be turned into a surface patch, slowing down the method)
You tagged this OpenGL, so to get this straight: OpenGL can't help you there, as OpenGL is just drawing triangles, not processing complex geometry.
Citing OpenGl faq:
What is OpenGL?
OpenGL stands for Open Graphics
Library. It is an API for doing 3D
graphics.
In more specific terms, it is an API
that is used to "draw triangles on
your scene". In this age of GPUs, it
is about talking to the GPU so that it
does the job of drawing. It does not
deal with file formats. It does not
open bmp, png and any image format. It
does not open 3d object formats like
obj, max, maya. It does not do
animation. It does not handle
keyboard, mouse and any input devices.
It does not create a window, and so
on.
All that stuff should be handled by an
external library (GLUT is one example
that is used for creating and
destroying a window and handling mouse
and keyboard).
GL has gone through a number of
versions.
So the answer is no. Things like extrude cut are complex operations. You have to implement it by your own, ore use third party libraries.
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.