Does anyone have any good implementation strategies or resources for putting together a b-rep modeling system?
OpenCascade is an apparently good library for b-rep modeling (used by FreeCad and PythonOCC are both very cool) but the library is huge, complicated and may not be a good starting point to learn about b-rep modeling 'engines'.
I've done quite a bit of research paper reading, and while the fundamental math is useful for understanding why everything works, its left me with some implementation questions.
The halfedge data-structure seems to be the preferred way to store information about a body in b-rep implementations.
So a handful of questions in no particular order:
Using the halfedge data-structure how is rendering typically implemented? Triangulation based on the solid's boundaries?
How are circular faces/curved surfaces typically implemented? For instance a cylinder in one basic introduction to b-rep's I read, was internally stored as a prism. IE an extruded triangle and meta-data was stored about the cap faces denoting that they were indeed circular.
How are boolean operations typically implemented? I've read about generating BSP-Tree's along the intersection curves then combining those tree's to generate the new geometry. Are there other ways to implement boolean operations and what sort of pro's/con's do they have?
Thanks!
If you'd like to provide a code example don't worry about the language -- the questions are more about algorithmic/data-structure implementation details
I'm working on a B-Rep modeler in C# (I'm in a very early stage: it's an huge project) so I ask myself the same questions as you. Here is my answers:
Triangulation: I've not done this step, but the strategy I'm thinking about is as follow: project the face boundaries in parameter space to obtain 2D polygons (with holes), triangulate that with the ear clipping algorithm and then reproject triangle vertices in 3D space. For curved surfaces, I need to split the polygons with a grid in order to follow the surface;
For a cylinder, there is 3 edges : two circulars and one line segment. I have classes for each type of curves (Segment3d, Circle3d...) and each half-edge hold an instance of one of theses classes. Each face hold an instance of a surface object (plane, cylinder, sphere...);
There is an interesting project here based on BSP-Tree, but it uses CSG method, not B-rep. I'm still researching how to do this, but I don't think I will need a BSP tree. The difficulty is in computing intersections and topology.
The best books I've found on this subject:
3D CAD - Principles and Applications (old but still relevant)
Geometric Modeling: The mathematics of shapes (more recent than the previous one, but less clear)
Related
PCL's github directs these questions here so I don't really know where else to ask this.
I'm trying to implement pose estimation given a mesh and a generated point cloud. Using PCL, I know you can do pose estimation with two point clouds from the tutorial. In my case I have an accurate faceted model of my target object. Does there exist a PCL pose estimator that can consume faceted truth models? I would like to avoid using mesh_sampling or mesh2pcd as a work around.
Googling does not bring any results relevant to my search with the following 54 terms
point cloud library pose estimation with
mesh
triangles
facets
truth data
model truth data
model
mesh truth data
vertexes
vertices
point cloud library point set registration with
(above)
point cloud library registration with
(above)
point cloud library 6DOF with
(above)
point cloud library pose with
(above)
point cloud library orientation with
(above)
Maybe I don't know the right words to search?
but it appears like it might be possible, because functors like this
pcl::SampleConsensusPrerejective<PointNT,PointNT,FeatureT>
and this
pcl::Registration< PointSource, PointTarget, Scalar >
take what seem to be pretty generic template arguments, only requiring PCL base functionality. But placing pcl::mesh did not compile (though it doesn't appear to be the only "mesh" type in PCL), since mesh doesn't seem to inherit off of base. The documentation does not talk about what is or is not possible with template types. Additionally I have found zero documentation that states this is impossible or indicates that only point clouds are allowed.
Can I use the model directly with out point cloud conversion, and if not why?
PCL is a library for point cloud processing. While some mesh support is available (pcl::PolygonMesh), practically all the implemented algorithms are based on point cloud data.
However keep in mind that a mesh is just a point cloud + additional triangulation information (faces) - so this means that any point cloud algorithm can be applied on a mesh. You just need to generate a point cloud from your mesh's vertices, and ignore the faces - no need for mesh sampling.
I am looking for ideas for algorithms and data structures for representing volumetric objects. I am working on a sculpting system, like sculptrix or mudbox, and want to find a good implementation strategy.
I currently have a very nice dynamic halfedge mesh system to collapse/subdivide faces. It works very well and is incredibly fast, but since it is a surface algorithm, it is not easy to robustly change topology.
So I want to go back to the drawingboard and implement a proper volumetric system. My first idea was some kind of octtree representation for the volume and marching cubes to polygonise it.
However, I have a few problems with this. First, marching cubes often produces small or thin triangles, something that is highly undesirable (reason why later). Second, I want to polygonise the volume only in the area of editing, and at different levels of detail. For example, I may want a low res sphere, but with a few tiny high res bumps. I can easily get that kind of subdivision behaviour with my current surface based sustem, but I can't envision how I could do it robustly with marching cubes.
Another problem is that the actual trianglular mesh is further subdivided on the gpu for smooth surfaces, so I need neighbourhood information too. Again, I already have this with the current half-edge system, but with a volume polygonisation system, I imagine it taking a lot of extra processing to find the extra connectivity information. This is the reason thin triangles are bad.
So I have a lot of constraints, and I am asking this community for ideas or pertinent papers to read. I was thinking about surfacenets to avoid the small/thin triangle problem. Also, I have a feeling kd-trees may be better for storing multiresolution volumes since they seem more flexible then octtrees.
Anyway, any ideas/suggestions very welcome.
I'd like to get an idea what kind of math is typically necessary for 3D game engine programming? Any specific math (such as vector geometry) or calculation algorithms (such as fast fourier transforms), or is this all abstracted away with DirectX/OpenGL so that highly complex math isn't really necessary any more?
Linear Algebra! Lots of lots of Linear Algebra!
Here are just classes and example situations where you need them
Vector - position, velocity, normals
Matrix - transformations
Quaternion - rotations (great for bone animations)
Ray - projectile collision detection
Plane - projectile collision detection
Frustum - render culling
Sphere - render culling, fast collision test
Axis-Align Bounding Box - culling, collision tests, spacial partitioning
Oriented Bounding Box - collision tests
Convex Hull - collision, spacial partitioning
etc.
You should start with Vector and Matrix as they will be used everywhere in the engine (graphics, physics, AI, etc.)
Matrices, trig, geometry mostly and a bit of linear algebra
Take a look here http://www.essentialmath.com/
For the most part linear algebra and computational geometry; Quaternions are used extensively and numerical analysis is necessary if you are working on a physics engine.
How much you'd use the stuff on a daily basis depends on what you are doing. If you are a graphics programmer, and therefore building the 3D graphics engine itself, then you would likely be implementing or maintaining implementations of class libraries and functions that actually do the math, so it would be relatively important to know the gory details. If you are using the library as client or working on another part of the game engine (AI, audio, UI, camera, etc.) then you will need to understand the math conceptually but you can certainly get away with not knowing how to implement a matrix inverse on a whiteboard off the top of your head.
Graphics APIs do not eliminate the need for someone to know this math; they are limited to drawing, so all the scene management and world simulation needs to be implemented outside the graphics API. Of course, there are middleware options there too but many studios roll their own systems.
There are a fair number of resources targeted at this market. For example, on Amazon there are books like 3D Math Primer For Graphics and Game Development, and there's probably a lot of stuff online too.
Complex math comes in to play, but most important is an understanding of the concepts behind such math and often not the math itself. So long as you understand how it all comes together, there are often helper methods for many of the calculations you will need. Of course that depends largely on the development platform you are using as well.
I am creating a game where I want to determine the intersection of a single line. For example if I create a circle on the screen I want to determine when I have closed the circle and figure out the points that exist within the area.
Edit: Ok to clarify I am attempting to create a lasso in a game and I am attempting to figure out how I can tell if the lasso's loop is closed. Is there any nice algorithm for doing this? I heard that there is one but I have not found any references searching on my own.
Edit: Adding more detail
I am working with an array of points. These points happen to wrap around and close. I am trying to figure out a good way of testing for this.
Thanks for the help.
Thoughts?
Your question has been addressed many times in the game development literature. It falls under the broad category of "collision detection." If you are interested in understanding the underlying algorithms, the field of computational geometry is what you want.
Bounding rectangle collision detection in Java
Collision detection on Stack Overflow
Circle collision detection in C#
Collision detection algorithms
Detailed explanation of collision detection algorithms
Game development books will also describe collision detection algorithms. One book of this sort is Game Physics by Eberly.
Whats the best way to detect collisions in a 2d game sprites? I am currently working in allegro and G++
There are a plethora of ways to detect collision detection. The methods you use will be slightly altered if depending on if your using a 2d or 3d environment. Also remember when instituting a collision detection system, to take into account any physics you may want to implement in the game (needed for most descent 3d games) in order to enhance the reality of it.
The short version is to use bounding boxes. Or in other words, make each entity in the world a box, then check if each of the axises of the box are colliding with other entities.
With large amounts of entities to test for collisions you may want to check into an octree. You would simple divide the world into sectors, then only check for collision between objects in the same sectors.
For more resources, you can go to sourceforge and search for the Bullet dynamics engine which is an open source collision detection and physics engine, or you could check out http://www.gamedev.net which has plenty of resources on copious game development topics.
Any decent 2D graphics library will either provide its own collision detection functions for everything from aligned sprites to polygons to pixels, or have one or more good third party libraries to perform those functions. Your choice of engine/library/framework should dictate your collision detection choices, as they are likely far more optimized than what you could produce alone.
For Allegro there is Collegro. For SDL there is SDL_Collide.h or SDL-Collide. You can use I_COLLIDE with OpenGL. DarkBASIC has a built in collision system, and DarkPhysics for very accurate interactions including collisions.
Use a library, I recommend Box2D
This question is pretty general. There are many ways to go about collision detection in a 2d game. It would help to know what you are trying to do.
As a starting point though, there are pretty simple methods that allow for detection between circles, rectangles, etc. I'm not a huge fan of gamedev.net, but there are some good resources there about this type of detection. One such article is here. It covers some basic material that might help you get started.
Basic 2d games can use rectangles or circles to "enclose" an object on the screen. Detection of when rectangles overlap or when circles overlap is fairly straightfoward math. If you need something more complicated (such as convex artibrary polys), then the solution is more complicated. Again, gamedev.net might be of some help here.
But really to answer your question, we need to know what you are trying to do? What type of game? What type of objects are you trying to collide? Are you trying to collide with screen boundaries, etc.
Checking for collision between two balls in 2D is easy. You can google it but basically you check if the length of the two balls radius combined is larger or equal to the distance between the center of the two balls.
Then you can find the collision point by taking the unit vector between the center of the balls and multiply it with one of the balls radius.
Implementation of a collision detection system is a complicated matter, but you want to consider three points.
World of objects. Space Partitioning.
If you do a collision check against every 2d sprite in your world against everything else, you'll have a slow slow program! You need to prioritize. You need to partition the space. You can use an orthogonal grid system and slice your world up into a 2d grid. Or you could use a BSP tree, using lines as the seperator function.
Broad phase collision detection
This uses bounding volumes such as cylinders or elipses (whichever approximates the shape of your sprites the best) to determine whether or not objects are worth comparing in more detail. The math for this is easy. Learn your 2d matrix transformations. And for 2d intersection, you can even use high powered video cards to do a lot of the work!
Narrow phase collision detection
Now that you've determined that two or more objects are worth comparing, you step into your fine tuned section. The goal of this phase is to determine the collision result. Penetration depth, volume encompassed, etc... And this information will be fed into whatever physics engine you got planned. In 3d this is the realm of GJK distance algs and other neato algorithms that we all love so much!
You can implement all of this generically and specify the broad and narrow resolutions polymorphically, or provide a hook if you're working in a lower level language.
Collisions between what? It depends whether you use sprites, concave polygons, convex polygons, rectangles, squares, circles, points...