To give you an idea of where I'm coming from, this started as a teaching exercise to get a 12-year-old video game addict into coding. The 2D games, I did in SDL with him and that was fine because I wasn't planning on going into 3D. Yeah, right! So now I'm in at the deep end in OpenGL and mainly trying to figure out exactly what it can and cannot do. I understand the theory (still working on beziers and nurbs if the truth be told) and could code the whole thing by hand in calculated triangular vertices but I'd hate to spend days on that only to be told that there's a built in function/library that does the whole thing faster and easier.
Quadrics seem to be extremely powerful but not terribly flexible. Consider the human head - roughly speaking a 3x4x3 sphere or a torso as a truncated cone that's taller than it is wide than it is thick. Again, a quadric shape with independent x,y and z radii. Since only one radius is provided, am I right in thinking that I would have to generate it around the origin and then apply a scaling matrix to adjust them? Furthermore, if this is so, am I also correct in thinking that saving the results into a vertex array rather than a frame list results in the system neither knowing or caring how they got there?
Transitions: I'm familiar with the basic transitions but, again, consider the torso. It can achieve, maybe, a 45 degree twist from the hips to the shoulders that is distributed linearly across the entire length or even the sideways lean. This is applied around the Y or Z axis respectively but I've obviously missed something about applying transformations that are based on an independent value. (eg rot = dist x (max_rot/max_dist). Again, I could do this by hand (and will probably have to in order to apply the correct physics) but does OpenGL have this functionality built in somewhere?
Any other areas of research I need to put in would be appreciated in the notes.
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I'm writing to ask about homography and perspective projection.
I'm trying to write a piece of code, that will "warp" my image so that its corners align with 4 reference points that are in the 3D space - however, the game engine that I'm running it in, already allows me to get the screen position of them, so I already have their screen-space coordinates of both xi,yi and ui,vi, normalized to values between 0 and 1.
I have to mention that I don't have a degree in mathematics, which seems to be a requirement in the posts I've seen on this topic so far, but I'm hoping there is actually a solution to this problem that one can comprehend. I never had a chance to take classes in Computer Vision.
The reason I came here is that in all the posts I've seen online, the simple explanation that I came across is that each point must be put into a 1x3 matrix and multiplied by a 3x3 homography, which consists of 9 components h1,h2,h3...h9, and this transformation matrix will transform each point to the correct perspective. And that's where I'm hitting a brick wall - how do I calculate the transformation matrix? It feels like it should be a relatively simple algebraic task, but apparently it's not.
At this point I spent days reading on the topic, and the solutions I've come across are either based on matlab (which have a ton of mathematical functions built into them), or include elaborations and discussions that don't really explain much; sometimes they suggest tons of different parameters and simplifications, but rarely explain why and what's their purpose, or they are referencing books and studies that have been since removed from the web, and I found myself more confused than I was in the beginning. Most of the resources I managed to find online are also made in a different context - image stitching and 3d engine development.
I also want to mention that I need to run this code each frame on the CPU, and I'm fairly concerned about the effect of having to run too many matrix transformations and solving a ton of linear algebra equations.
I apologize for not asking about any specific code, but my general question is - can anyone point me in the right direction with this issue?
Limit the problem you deal with.
For example, if you always warp the entire rectangular image, you can treat that the coordinates of the image corners are {(0,0), (1,0), (0,1), (1,1)}.
This can simplify the equation, and you'll be able to solve the equation by yourself.
So you'll be able to implement the answer.
Note : Homograpy is scale invariant. So you can decrease the freedom to 8. (e.g. you can solve the equation under h9=1).
Best advice I can give: read a good book on the subject. For example, "Multiple View Geometry" by Hartley and Zisserman
I'm trying to make a viewport grid like the ones seen in most 3D Modelers where zooming adjusts the grid spacing so lines don't get too dense or too far apart. For example zooming out changes the spacing from 1m to 2m then 5m then 10m and 20m etc. Any help?
Here it's usually not as complicated as you might think it would be initially. For example, you might notice that panning and orbiting the camera has no effect on that grid density, even though the nearest distance from grid plane to viewer could be changing. Likewise, changing FOV has no effect on the chosen grid unit size, even though ideally perhaps it should given how it can significantly skew and narrow the view.
So there's usually just this basic, 1-dimensional kind of notion of zoom distance relative to the look at target (camera pivot), and it involves no fancy math, just adjusting a scalar that affects values passed to glScale or glTranslate, e.g.
As it increases, so does the unit size used for drawing the grid (and possibly snapping to it), and here it's often not some brilliant, mathematical solution but just a linear mapping from that zoom distance to hard-coded unit sizes like 1mm, 2mm, 5mm, 10mm, 20mm, 50mm, 1cm, etc.
These kinds of things usually aren't the result of some algorithmic paper but just a developer/designer sitting down and tweaking things until they look/feel about right. If you're trying to develop a 3D software, I'd recommend never to overlook this basic solution for things related to user interaction because it's easy to become convinced in 3D that everything has to be complicated and have a lot of research and a perfectly-accurate mathematical solution behind it. For the UI parts, you can get away with far more informal solutions.
Sometimes the formal mathematical solutions for these UI visuals/interactions don't work quite as well in practice as these kludged solutions, as you might have noticed in the user interfaces coming from the more academic realm (which are usually much smarter mathematically and algorithmically for these things, but actually less intuitive).
I have made several attempts to fix this and read all I could find here/forum/google. I used a CCD treshold mush lower than my objects move speed and using a CCD radius much smaller than the objects half radius. The only thing this does is make the multisphere get stuck on seams. I also tried to set ERP/ERP2 to 0.9/1.0.
[EDIT] Ok, so after some more reading; CCD will not work if the sphere is already touching the ground and ERP only affeccts objectts with joints if I understand correctly.
The ground is a trimesh made in Blender and using the obtainStaticNodeShape to get the shape. I have tried to scale the mesh to get smaller polygons but even the smallest (for the game acceptable) size does not work, about 32k indices with 11k polys, 500x500 units, the multisphere has a radius of 0.45 units.
[EDIT] the multi-sphere is two spheres on top of each other and they are restricted to angular movement around the Y-axis only, so no rolling.
The sphere gets "sucked" fast through the ground it does not sink slowly. I tried to make the fixedtimestep smaller 1/420 with 64 substeps did not give any better results. This happens most often while ascending or descending a slope. My ground is gently sloped but an incline of 20% seems to be enough for it to fall through a lot but it can happen on level ground too, just not as often.
When I did my first test I used a big stretched out cube as ground and it worked well.
So my problem now is I don't even know why this is happening so I have no idea what to try next? Can anyone please give me a solution or some pointers.
Is there any use in increasing the multi-sphere size (for the game I can not increase more than 25-30%) I have not explicitly set any collision margins but I think this would just make my sphere float over the ground? Is there any profit in changing the ground from a static object to a kinematic?
Would it work to use a raytest from the sphere straight down and push it up if it is lower than the ground? I think not, why would it fall through if it could detect the ground in the first place..?
[EDIT: additional info]
There are quite a few occurrences of similar problems floating around on forums and also here at stack overflow. Most seem to be about very small objects. Small objects (>0.2m) is clearly not a good option for bullet unless you want to increase the number of simulation steps quite a lot. My problems does not seem to fall under this category since my smallest object is 0.9m in diameter?
I have now also done a debug draw to see the normals of the trimesh that I use as ground. I can not find any errors with the normals.
I also tried to increase the collission margins of the speheres but to no avail.
I further tried to use suggested settings:
((btDefaultCollisionConfiguration)world.collisionConfiguration).setPlaneConvexMultipointIterations(3,3); ((btDefaultCollisionConfiguration)world.collisionConfiguration).setConvexConvexMultipointIterations(3, 3);
No difference.
I did however read about big trimeshes not working very well for raycasting, my mesh is big 512x512 units but I am not sure if this could cause my object to fall through the mesh?
I also read that sphere shapes has problems with trimeshes, but again I am not sure if this would be my case? The sphere I am using is locked for rotation on all axes.
I have also tried using a btCapsule but it gave same results.. Would a cylinder work better?
[EDIT]
I have tried using a cylinder instead since sphere and capsule did not work. The cylinder is working a lot better. I have still got it to fall through once though. The clyinder was jerking around a lot before it went through where the sphere/capsule would just go through really fast and easy. Maybe this could be a clue of whats the underlaying problem? A cylinder is not the best for a character shape though..
An other possible reason could be if a triangle in the mesh has too long sides or a large ratio between sides. I found a few of those on a slope where my sphere always falls through. If this is indeed the problem can I do anything about it except manually editing the mesh in Blender?
As you can see there are a lot of these questions and a lot of possible answers and I have no idea which one corresponds to my case, someone with better insight giving some pointers would mean a lot, thanks!
I'm working on a relatively small 2D (top-view) game demo, using OpenGL for my graphics. It's going for a basic stealth-based angle, and as such with all my enemies I'm drawing a sight arc so the player knows where they are looking.
One of my problems so far is that when I draw this sight arc (as a filled polygon) it naturally shows through any walls on the screen since there's nothing stopping it:
http://tinyurl.com/43y4o5z
I'm curious how I might best be able to prevent something like this. I do already have code in place that will let me detect line-intersections with walls and so on (for the enemy sight detection), and I could theoretically use this to detect such a case and draw the polygon accordingly, but this would likely be quite fiddly and/or inefficient, so I figure if there's any built-in OpenGL systems that can do this for me it would probably do it much better.
I've tried looking for questions on topics like clipping/occlusion but I'm not even sure if these are exactly what I should be looking for; my OpenGL skills are limited. It seems that anything using, say, glClipPlanes or glScissor wouldn't be suited to this due to the large amount of individual walls and so on.
Lastly, this is just a demo I'm making in my spare time, so graphics aren't exactly my main worry. If there's a (reasonably) painless way to do this then I'd hope someone can point me in the right direction; if there's no simple way then I can just leave the problem for now or find other workarounds.
This is essentially a shadowing problem. Here's how I'd go about it:
For each point around the edge of your arc, trace a (2D) ray from the enemy towards the point, looking for intersections with the green boxes. If the green boxes are always going to be axis-aligned, the math will be a lot easier (look for Ray-AABB intersection). Rendering the intersection points as a triangle fan will give you your arc.
As you mention that you already have the line-wall intersection code going, then as long as that will tell you the distance from the enemy to the wall, then you'll be able to use it for the sight arc. Don't automatically assume it'll be too slow - we're not running on 486s any more. You can always reduce the number of points around the edge of your arc to speed things up.
OpenGL's built-in occlusion handling is designed for 3D tasks and I can't think of a simple way to rig it to achieve the effect you are after. If it were me, the way I would solve this is to use a fragment shader program, but be forewarned that this definitely does not fall under "a (reasonably) painless way to do this". Briefly, you first render a binary "occlusion map" which is black where there are walls and white otherwise. Then you render the "viewing arc" like you are currently doing with a fragment program that is designed to search from the viewer towards the target location, searching for an occluder (black pixel). If it finds an occluder, then it renders that pixel of the "viewing arc" as 100% transparent. Overall though, while this is a "correct" solution I would definitely say that this is a complex feature and you seem okay without implementing it.
I figure if there's any built-in OpenGL systems that can do this for me it would probably do it much better.
OpenGL is a drawing API, not a geometry processing library.
Actually your intersection test method is the right way to do it. However to speed it up you should use a spatial subdivision structure. In your case you have something that's cries for a Binary Space Partitioning tree. BSP trees have the nice property, that the complexity for finding intersections of a line with walls is in average about O(log n) and worst case is O(n log n), or in other words, BSP tress are very efficient. See the BSP FAQ for details http://www.opengl.org//resources/code/samples/bspfaq/index.html
I have a path made up of a list of 2D points. I want to turn these into a strip of triangles in order to render a textured line with a specified thickness (and other such things). So essentially the list of 2D points need to become a list of vertices specifying the outline of a polygon that if rendered would render the line. The problem is handling the corner joins, miters, caps etc. The resulting polygon needs to be "perfect" in the sense of no overdraw, clean joins, etc. so that it could feasibly be extruded or otherwise toyed with.
Are there any simple resources around that can provide algorithm insight, code or any more information on doing this efficiently?
I absolutely DO NOT want a full fledged 2D vector library (cairo, antigrain, OpenVG, etc.) with curves, arcs, dashes and all the bells and whistles. I've been digging in multiple source trees for OpenVG implementations and other things to find some insight, but it's all terribly convoluted.
I'm definitely willing to code it myself, but there are many degenerate cases (small segments + thick widths + sharp corners) that create all kinds of join issues. Even a little help would save me hours of trying to deal with them all.
EDIT: Here's an example of one of those degenerate cases that causes ugliness if you were simply to go from vertex to vertex. Red is the original path. The orange blocks are rectangles drawn at a specified width aligned and centered on each segment.
Oh well - I've tried to solve that problem myself. I wasted two month on a solution that tried to solve the zero overdraw problem. As you've already found out you can't deal with all degenerated cases and have zero overdraw at the same time.
You can however use a hybrid approach:
Write yourself a routine that checks if the joins can be constructed from simple geometry without problems. To do so you have to check the join-angle, the width of the line and the length of the joined line-segments (line-segments that are shorter than their width are a PITA). With some heuristics you should be able to sort out all the trivial cases.
I don't know how your average line-data looks like, but in my case more than 90% of the wide lines had no degenerated cases.
For all other lines:
You've most probably already found out that if you tolerate overdraw, generating the geometry is a lot easier. Do so, and let a polygon CSG algorithm and a tesselation algorithm do the hard job.
I've evaluated most of the available tesselation packages, and I ended up with the GLU tesselator. It was fast, robust, never crashed (unlike most other algorithms). It was free and the license allowed me to include it in a commercial program. The quality and speed of the tesselation is okay. You will not get delaunay triangulation quality, but since you just need the triangles for rendering that's not a problem.
Since I disliked the tesselator API I lifted the tesselation code from the free SGI OpenGL reference implementation, rewrote the entire front-end and added memory pools to get the number of allocations down. It took two days to do this, but it was well worth it (like factor five performance improvement). The solution ended up in a commercial OpenVG implementation btw :-)
If you're rendering with OpenGL on a PC, you may want to move the tesselation/CSG-job from the CPU to the GPU and use stencil-buffer or z-buffer tricks to remove the overdraw. That's a lot easier and may be even faster than CPU tesselation.
I just found this amazing work:
http://www.codeproject.com/Articles/226569/Drawing-polylines-by-tessellation
It seems to do exactly what you want, and its licence allows to use it even in commercial applications. Plus, the author did a truly great job to detail his method. I'll probably give it a shot at some point to replace my own not-nearly-as-perfect implementation.
A simple method off the top of my head.
Bisect the angle of each 2d Vertex, this will create a nice miter line. Then move along that line, both inward and outward, the amount of your "thickness" (or thickness divided by two?), you now have your inner and outer polygon points. Move to the next point, repeat the same process, building your new polygon points along the way. Then apply a triangualtion to get your render-ready vertexes.
I ended up having to get my hands dirty and write a small ribbonizer to solve a similar problem.
For me the issue was that I wanted fat lines in OpenGL that did not have the kinds of artifacts that I was seeing with OpenGL on the iPhone. After looking at various solutions; bezier curves and the like - I decided it was probably easiest to just make my own. There are a couple of different approaches.
One approach is to find the angle of intersection between two segments and then move along that intersection line a certain distance away from the surface and treat that as a ribbon vertex. I tried that and it did not look intuitive; the ribbon width would vary.
Another approach is to actually compute a normal to the surface of the line segments and use that to compute the ideal ribbon edge for that segment and to do actual intersection tests between ribbon segments. This worked well except that for sharp corners the ribbon line segment intersections were too far away ( if the inter-segment angle approached 180' ).
I worked around the sharp angle issue with two approaches. The Paul Bourke line intersection algorithm ( which I used in an unoptimized way ) suggested detecting if the intersection was inside of the segments. Since both segments are identical I only needed to test one of the segments for intersection. I could then arbitrate how to resolve this; either by fudging a best point between the two ends or by putting on an end cap - both approaches look good - the end cap approach may throw off the polygon front/back facing ordering for opengl.
See http://paulbourke.net/geometry/lineline2d/
See my source code here : https://gist.github.com/1474156
I'm interested in this too, since I want to perfect my mapping application's (Kosmos) drawing of roads. One workaround I used is to draw the polyline twice, once with a thicker line and once with a thinner, with a different color. But this is not really a polygon, it's just a quick way of simulating one. See some samples here: http://wiki.openstreetmap.org/wiki/Kosmos_Rendering_Help#Rendering_Options
I'm not sure if this is what you need.
I think I'd reach for a tessellation algorithm. It's true that in most case where these are used the aim is to reduce the number of vertexes to optimise rendering, but in your case you could parameterise to retain all the detail - and the possibility of optimising may come in useful.
There are numerous tessellation algorithms and code around on the web - I wrapped up a pure C on in a DLL a few years back for use with a Delphi landscape renderer, and they are not an uncommon subject for advanced graphics coding tutorials and the like.
See if Delaunay triangulation can help.
In my case I could afford to overdraw. I just drow circles with radius = width/2 centered on each of the polyline's vertices.
Artifacts are masked this way, and it is very easy to implement, if you can live with "rounded" corners and some overdrawing.
From your image it looks like that you are drawing box around line segments with FILL on and using orange color. Doing so is going to create bad overdraws for sure. So first thing to do would be not render black border and fill color can be opaque.
Why can't you use GL_LINES primitive to do what you intent to do? You can specify width, filtering, smoothness, texture anything. You can render all vertices using glDrawArrays(). I know this is not something you have in mind but as you are focusing on 2D drawing, this might be easier approach. (search for Textured lines etc.)