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  • Two Virtualization Webinars This Week

    - by chris.kawalek(at)oracle.com
    If you're interested in virtualization, be sure to catch our two free webinars this week. You'll hear directly from Oracle technologists and can ask questions in a live Q&A. Deploying Oracle VM Templates for Oracle E-Business Suite and Oracle PeopleSoft Enterprise Applications Tuesday, Feb 15, 2011 9AM Pacific Time Register Now Is your company trying to manage costs; meet or beat service level agreements and get employees up and running quickly on business-critical applications like Oracle E-Business Suite and Oracle PeopleSoft Enterprise Applications? The fastest way to get the benefits of these applications deployed in your organization is with Oracle VM Templates. Cut application deployment time from weeks to just hours or days. Attend this session for the technical details of how your IT department can deliver rapid software deployment and eliminate installation and configuration costs by providing pre-installed and pre-configured software images. Increasing Desktop Security for the Public Sector with Oracle Desktop Virtualization Thursday, Feb 17, 2011 9AM Pacific Time Register Now Security of data as it moves across desktop devices is a concern for all industries. But organizations such as law enforcement, local, state, and federal government and others have higher security ne! eds than most. A virtual desktop model, where no data is ever stored on the local device, is an ideal architecture for these organizations to deploy. Oracle's comprehensive portfolio of desktop virtualization solutions, from thin client devices, to sever side management and desktop hosting software, provide a complete solution for this ever-increasing problem.

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  • 256 Windows Azure Worker Roles, Windows Kinect and a 90's Text-Based Ray-Tracer

    - by Alan Smith
    For a couple of years I have been demoing a simple render farm hosted in Windows Azure using worker roles and the Azure Storage service. At the start of the presentation I deploy an Azure application that uses 16 worker roles to render a 1,500 frame 3D ray-traced animation. At the end of the presentation, when the animation was complete, I would play the animation delete the Azure deployment. The standing joke with the audience was that it was that it was a “$2 demo”, as the compute charges for running the 16 instances for an hour was $1.92, factor in the bandwidth charges and it’s a couple of dollars. The point of the demo is that it highlights one of the great benefits of cloud computing, you pay for what you use, and if you need massive compute power for a short period of time using Windows Azure can work out very cost effective. The “$2 demo” was great for presenting at user groups and conferences in that it could be deployed to Azure, used to render an animation, and then removed in a one hour session. I have always had the idea of doing something a bit more impressive with the demo, and scaling it from a “$2 demo” to a “$30 demo”. The challenge was to create a visually appealing animation in high definition format and keep the demo time down to one hour.  This article will take a run through how I achieved this. Ray Tracing Ray tracing, a technique for generating high quality photorealistic images, gained popularity in the 90’s with companies like Pixar creating feature length computer animations, and also the emergence of shareware text-based ray tracers that could run on a home PC. In order to render a ray traced image, the ray of light that would pass from the view point must be tracked until it intersects with an object. At the intersection, the color, reflectiveness, transparency, and refractive index of the object are used to calculate if the ray will be reflected or refracted. Each pixel may require thousands of calculations to determine what color it will be in the rendered image. Pin-Board Toys Having very little artistic talent and a basic understanding of maths I decided to focus on an animation that could be modeled fairly easily and would look visually impressive. I’ve always liked the pin-board desktop toys that become popular in the 80’s and when I was working as a 3D animator back in the 90’s I always had the idea of creating a 3D ray-traced animation of a pin-board, but never found the energy to do it. Even if I had a go at it, the render time to produce an animation that would look respectable on a 486 would have been measured in months. PolyRay Back in 1995 I landed my first real job, after spending three years being a beach-ski-climbing-paragliding-bum, and was employed to create 3D ray-traced animations for a CD-ROM that school kids would use to learn physics. I had got into the strange and wonderful world of text-based ray tracing, and was using a shareware ray-tracer called PolyRay. PolyRay takes a text file describing a scene as input and, after a few hours processing on a 486, produced a high quality ray-traced image. The following is an example of a basic PolyRay scene file. background Midnight_Blue   static define matte surface { ambient 0.1 diffuse 0.7 } define matte_white texture { matte { color white } } define matte_black texture { matte { color dark_slate_gray } } define position_cylindrical 3 define lookup_sawtooth 1 define light_wood <0.6, 0.24, 0.1> define median_wood <0.3, 0.12, 0.03> define dark_wood <0.05, 0.01, 0.005>     define wooden texture { noise surface { ambient 0.2  diffuse 0.7  specular white, 0.5 microfacet Reitz 10 position_fn position_cylindrical position_scale 1  lookup_fn lookup_sawtooth octaves 1 turbulence 1 color_map( [0.0, 0.2, light_wood, light_wood] [0.2, 0.3, light_wood, median_wood] [0.3, 0.4, median_wood, light_wood] [0.4, 0.7, light_wood, light_wood] [0.7, 0.8, light_wood, median_wood] [0.8, 0.9, median_wood, light_wood] [0.9, 1.0, light_wood, dark_wood]) } } define glass texture { surface { ambient 0 diffuse 0 specular 0.2 reflection white, 0.1 transmission white, 1, 1.5 }} define shiny surface { ambient 0.1 diffuse 0.6 specular white, 0.6 microfacet Phong 7  } define steely_blue texture { shiny { color black } } define chrome texture { surface { color white ambient 0.0 diffuse 0.2 specular 0.4 microfacet Phong 10 reflection 0.8 } }   viewpoint {     from <4.000, -1.000, 1.000> at <0.000, 0.000, 0.000> up <0, 1, 0> angle 60     resolution 640, 480 aspect 1.6 image_format 0 }       light <-10, 30, 20> light <-10, 30, -20>   object { disc <0, -2, 0>, <0, 1, 0>, 30 wooden }   object { sphere <0.000, 0.000, 0.000>, 1.00 chrome } object { cylinder <0.000, 0.000, 0.000>, <0.000, 0.000, -4.000>, 0.50 chrome }   After setting up the background and defining colors and textures, the viewpoint is specified. The “camera” is located at a point in 3D space, and it looks towards another point. The angle, image resolution, and aspect ratio are specified. Two lights are present in the image at defined coordinates. The three objects in the image are a wooden disc to represent a table top, and a sphere and cylinder that intersect to form a pin that will be used for the pin board toy in the final animation. When the image is rendered, the following image is produced. The pins are modeled with a chrome surface, so they reflect the environment around them. Note that the scale of the pin shaft is not correct, this will be fixed later. Modeling the Pin Board The frame of the pin-board is made up of three boxes, and six cylinders, the front box is modeled using a clear, slightly reflective solid, with the same refractive index of glass. The other shapes are modeled as metal. object { box <-5.5, -1.5, 1>, <5.5, 5.5, 1.2> glass } object { box <-5.5, -1.5, -0.04>, <5.5, 5.5, -0.09> steely_blue } object { box <-5.5, -1.5, -0.52>, <5.5, 5.5, -0.59> steely_blue } object { cylinder <-5.2, -1.2, 1.4>, <-5.2, -1.2, -0.74>, 0.2 steely_blue } object { cylinder <5.2, -1.2, 1.4>, <5.2, -1.2, -0.74>, 0.2 steely_blue } object { cylinder <-5.2, 5.2, 1.4>, <-5.2, 5.2, -0.74>, 0.2 steely_blue } object { cylinder <5.2, 5.2, 1.4>, <5.2, 5.2, -0.74>, 0.2 steely_blue } object { cylinder <0, -1.2, 1.4>, <0, -1.2, -0.74>, 0.2 steely_blue } object { cylinder <0, 5.2, 1.4>, <0, 5.2, -0.74>, 0.2 steely_blue }   In order to create the matrix of pins that make up the pin board I used a basic console application with a few nested loops to create two intersecting matrixes of pins, which models the layout used in the pin boards. The resulting image is shown below. The pin board contains 11,481 pins, with the scene file containing 23,709 lines of code. For the complete animation 2,000 scene files will be created, which is over 47 million lines of code. Each pin in the pin-board will slide out a specific distance when an object is pressed into the back of the board. This is easily modeled by setting the Z coordinate of the pin to a specific value. In order to set all of the pins in the pin-board to the correct position, a bitmap image can be used. The position of the pin can be set based on the color of the pixel at the appropriate position in the image. When the Windows Azure logo is used to set the Z coordinate of the pins, the following image is generated. The challenge now was to make a cool animation. The Azure Logo is fine, but it is static. Using a normal video to animate the pins would not work; the colors in the video would not be the same as the depth of the objects from the camera. In order to simulate the pin board accurately a series of frames from a depth camera could be used. Windows Kinect The Kenect controllers for the X-Box 360 and Windows feature a depth camera. The Kinect SDK for Windows provides a programming interface for Kenect, providing easy access for .NET developers to the Kinect sensors. The Kinect Explorer provided with the Kinect SDK is a great starting point for exploring Kinect from a developers perspective. Both the X-Box 360 Kinect and the Windows Kinect will work with the Kinect SDK, the Windows Kinect is required for commercial applications, but the X-Box Kinect can be used for hobby projects. The Windows Kinect has the advantage of providing a mode to allow depth capture with objects closer to the camera, which makes for a more accurate depth image for setting the pin positions. Creating a Depth Field Animation The depth field animation used to set the positions of the pin in the pin board was created using a modified version of the Kinect Explorer sample application. In order to simulate the pin board accurately, a small section of the depth range from the depth sensor will be used. Any part of the object in front of the depth range will result in a white pixel; anything behind the depth range will be black. Within the depth range the pixels in the image will be set to RGB values from 0,0,0 to 255,255,255. A screen shot of the modified Kinect Explorer application is shown below. The Kinect Explorer sample application was modified to include slider controls that are used to set the depth range that forms the image from the depth stream. This allows the fine tuning of the depth image that is required for simulating the position of the pins in the pin board. The Kinect Explorer was also modified to record a series of images from the depth camera and save them as a sequence JPEG files that will be used to animate the pins in the animation the Start and Stop buttons are used to start and stop the image recording. En example of one of the depth images is shown below. Once a series of 2,000 depth images has been captured, the task of creating the animation can begin. Rendering a Test Frame In order to test the creation of frames and get an approximation of the time required to render each frame a test frame was rendered on-premise using PolyRay. The output of the rendering process is shown below. The test frame contained 23,629 primitive shapes, most of which are the spheres and cylinders that are used for the 11,800 or so pins in the pin board. The 1280x720 image contains 921,600 pixels, but as anti-aliasing was used the number of rays that were calculated was 4,235,777, with 3,478,754,073 object boundaries checked. The test frame of the pin board with the depth field image applied is shown below. The tracing time for the test frame was 4 minutes 27 seconds, which means rendering the2,000 frames in the animation would take over 148 hours, or a little over 6 days. Although this is much faster that an old 486, waiting almost a week to see the results of an animation would make it challenging for animators to create, view, and refine their animations. It would be much better if the animation could be rendered in less than one hour. Windows Azure Worker Roles The cost of creating an on-premise render farm to render animations increases in proportion to the number of servers. The table below shows the cost of servers for creating a render farm, assuming a cost of $500 per server. Number of Servers Cost 1 $500 16 $8,000 256 $128,000   As well as the cost of the servers, there would be additional costs for networking, racks etc. Hosting an environment of 256 servers on-premise would require a server room with cooling, and some pretty hefty power cabling. The Windows Azure compute services provide worker roles, which are ideal for performing processor intensive compute tasks. With the scalability available in Windows Azure a job that takes 256 hours to complete could be perfumed using different numbers of worker roles. The time and cost of using 1, 16 or 256 worker roles is shown below. Number of Worker Roles Render Time Cost 1 256 hours $30.72 16 16 hours $30.72 256 1 hour $30.72   Using worker roles in Windows Azure provides the same cost for the 256 hour job, irrespective of the number of worker roles used. Provided the compute task can be broken down into many small units, and the worker role compute power can be used effectively, it makes sense to scale the application so that the task is completed quickly, making the results available in a timely fashion. The task of rendering 2,000 frames in an animation is one that can easily be broken down into 2,000 individual pieces, which can be performed by a number of worker roles. Creating a Render Farm in Windows Azure The architecture of the render farm is shown in the following diagram. The render farm is a hybrid application with the following components: ·         On-Premise o   Windows Kinect – Used combined with the Kinect Explorer to create a stream of depth images. o   Animation Creator – This application uses the depth images from the Kinect sensor to create scene description files for PolyRay. These files are then uploaded to the jobs blob container, and job messages added to the jobs queue. o   Process Monitor – This application queries the role instance lifecycle table and displays statistics about the render farm environment and render process. o   Image Downloader – This application polls the image queue and downloads the rendered animation files once they are complete. ·         Windows Azure o   Azure Storage – Queues and blobs are used for the scene description files and completed frames. A table is used to store the statistics about the rendering environment.   The architecture of each worker role is shown below.   The worker role is configured to use local storage, which provides file storage on the worker role instance that can be use by the applications to render the image and transform the format of the image. The service definition for the worker role with the local storage configuration highlighted is shown below. <?xml version="1.0" encoding="utf-8"?> <ServiceDefinition name="CloudRay" >   <WorkerRole name="CloudRayWorkerRole" vmsize="Small">     <Imports>     </Imports>     <ConfigurationSettings>       <Setting name="DataConnectionString" />     </ConfigurationSettings>     <LocalResources>       <LocalStorage name="RayFolder" cleanOnRoleRecycle="true" />     </LocalResources>   </WorkerRole> </ServiceDefinition>     The two executable programs, PolyRay.exe and DTA.exe are included in the Azure project, with Copy Always set as the property. PolyRay will take the scene description file and render it to a Truevision TGA file. As the TGA format has not seen much use since the mid 90’s it is converted to a JPG image using Dave's Targa Animator, another shareware application from the 90’s. Each worker roll will use the following process to render the animation frames. 1.       The worker process polls the job queue, if a job is available the scene description file is downloaded from blob storage to local storage. 2.       PolyRay.exe is started in a process with the appropriate command line arguments to render the image as a TGA file. 3.       DTA.exe is started in a process with the appropriate command line arguments convert the TGA file to a JPG file. 4.       The JPG file is uploaded from local storage to the images blob container. 5.       A message is placed on the images queue to indicate a new image is available for download. 6.       The job message is deleted from the job queue. 7.       The role instance lifecycle table is updated with statistics on the number of frames rendered by the worker role instance, and the CPU time used. The code for this is shown below. public override void Run() {     // Set environment variables     string polyRayPath = Path.Combine(Environment.GetEnvironmentVariable("RoleRoot"), PolyRayLocation);     string dtaPath = Path.Combine(Environment.GetEnvironmentVariable("RoleRoot"), DTALocation);       LocalResource rayStorage = RoleEnvironment.GetLocalResource("RayFolder");     string localStorageRootPath = rayStorage.RootPath;       JobQueue jobQueue = new JobQueue("renderjobs");     JobQueue downloadQueue = new JobQueue("renderimagedownloadjobs");     CloudRayBlob sceneBlob = new CloudRayBlob("scenes");     CloudRayBlob imageBlob = new CloudRayBlob("images");     RoleLifecycleDataSource roleLifecycleDataSource = new RoleLifecycleDataSource();       Frames = 0;       while (true)     {         // Get the render job from the queue         CloudQueueMessage jobMsg = jobQueue.Get();           if (jobMsg != null)         {             // Get the file details             string sceneFile = jobMsg.AsString;             string tgaFile = sceneFile.Replace(".pi", ".tga");             string jpgFile = sceneFile.Replace(".pi", ".jpg");               string sceneFilePath = Path.Combine(localStorageRootPath, sceneFile);             string tgaFilePath = Path.Combine(localStorageRootPath, tgaFile);             string jpgFilePath = Path.Combine(localStorageRootPath, jpgFile);               // Copy the scene file to local storage             sceneBlob.DownloadFile(sceneFilePath);               // Run the ray tracer.             string polyrayArguments =                 string.Format("\"{0}\" -o \"{1}\" -a 2", sceneFilePath, tgaFilePath);             Process polyRayProcess = new Process();             polyRayProcess.StartInfo.FileName =                 Path.Combine(Environment.GetEnvironmentVariable("RoleRoot"), polyRayPath);             polyRayProcess.StartInfo.Arguments = polyrayArguments;             polyRayProcess.Start();             polyRayProcess.WaitForExit();               // Convert the image             string dtaArguments =                 string.Format(" {0} /FJ /P{1}", tgaFilePath, Path.GetDirectoryName (jpgFilePath));             Process dtaProcess = new Process();             dtaProcess.StartInfo.FileName =                 Path.Combine(Environment.GetEnvironmentVariable("RoleRoot"), dtaPath);             dtaProcess.StartInfo.Arguments = dtaArguments;             dtaProcess.Start();             dtaProcess.WaitForExit();               // Upload the image to blob storage             imageBlob.UploadFile(jpgFilePath);               // Add a download job.             downloadQueue.Add(jpgFile);               // Delete the render job message             jobQueue.Delete(jobMsg);               Frames++;         }         else         {             Thread.Sleep(1000);         }           // Log the worker role activity.         roleLifecycleDataSource.Alive             ("CloudRayWorker", RoleLifecycleDataSource.RoleLifecycleId, Frames);     } }     Monitoring Worker Role Instance Lifecycle In order to get more accurate statistics about the lifecycle of the worker role instances used to render the animation data was tracked in an Azure storage table. The following class was used to track the worker role lifecycles in Azure storage.   public class RoleLifecycle : TableServiceEntity {     public string ServerName { get; set; }     public string Status { get; set; }     public DateTime StartTime { get; set; }     public DateTime EndTime { get; set; }     public long SecondsRunning { get; set; }     public DateTime LastActiveTime { get; set; }     public int Frames { get; set; }     public string Comment { get; set; }       public RoleLifecycle()     {     }       public RoleLifecycle(string roleName)     {         PartitionKey = roleName;         RowKey = Utils.GetAscendingRowKey();         Status = "Started";         StartTime = DateTime.UtcNow;         LastActiveTime = StartTime;         EndTime = StartTime;         SecondsRunning = 0;         Frames = 0;     } }     A new instance of this class is created and added to the storage table when the role starts. It is then updated each time the worker renders a frame to record the total number of frames rendered and the total processing time. These statistics are used be the monitoring application to determine the effectiveness of use of resources in the render farm. Rendering the Animation The Azure solution was deployed to Windows Azure with the service configuration set to 16 worker role instances. This allows for the application to be tested in the cloud environment, and the performance of the application determined. When I demo the application at conferences and user groups I often start with 16 instances, and then scale up the application to the full 256 instances. The configuration to run 16 instances is shown below. <?xml version="1.0" encoding="utf-8"?> <ServiceConfiguration serviceName="CloudRay" xmlns="http://schemas.microsoft.com/ServiceHosting/2008/10/ServiceConfiguration" osFamily="1" osVersion="*">   <Role name="CloudRayWorkerRole">     <Instances count="16" />     <ConfigurationSettings>       <Setting name="DataConnectionString"         value="DefaultEndpointsProtocol=https;AccountName=cloudraydata;AccountKey=..." />     </ConfigurationSettings>   </Role> </ServiceConfiguration>     About six minutes after deploying the application the first worker roles become active and start to render the first frames of the animation. The CloudRay Monitor application displays an icon for each worker role instance, with a number indicating the number of frames that the worker role has rendered. The statistics on the left show the number of active worker roles and statistics about the render process. The render time is the time since the first worker role became active; the CPU time is the total amount of processing time used by all worker role instances to render the frames.   Five minutes after the first worker role became active the last of the 16 worker roles activated. By this time the first seven worker roles had each rendered one frame of the animation.   With 16 worker roles u and running it can be seen that one hour and 45 minutes CPU time has been used to render 32 frames with a render time of just under 10 minutes.     At this rate it would take over 10 hours to render the 2,000 frames of the full animation. In order to complete the animation in under an hour more processing power will be required. Scaling the render farm from 16 instances to 256 instances is easy using the new management portal. The slider is set to 256 instances, and the configuration saved. We do not need to re-deploy the application, and the 16 instances that are up and running will not be affected. Alternatively, the configuration file for the Azure service could be modified to specify 256 instances.   <?xml version="1.0" encoding="utf-8"?> <ServiceConfiguration serviceName="CloudRay" xmlns="http://schemas.microsoft.com/ServiceHosting/2008/10/ServiceConfiguration" osFamily="1" osVersion="*">   <Role name="CloudRayWorkerRole">     <Instances count="256" />     <ConfigurationSettings>       <Setting name="DataConnectionString"         value="DefaultEndpointsProtocol=https;AccountName=cloudraydata;AccountKey=..." />     </ConfigurationSettings>   </Role> </ServiceConfiguration>     Six minutes after the new configuration has been applied 75 new worker roles have activated and are processing their first frames.   Five minutes later the full configuration of 256 worker roles is up and running. We can see that the average rate of frame rendering has increased from 3 to 12 frames per minute, and that over 17 hours of CPU time has been utilized in 23 minutes. In this test the time to provision 140 worker roles was about 11 minutes, which works out at about one every five seconds.   We are now half way through the rendering, with 1,000 frames complete. This has utilized just under three days of CPU time in a little over 35 minutes.   The animation is now complete, with 2,000 frames rendered in a little over 52 minutes. The CPU time used by the 256 worker roles is 6 days, 7 hours and 22 minutes with an average frame rate of 38 frames per minute. The rendering of the last 1,000 frames took 16 minutes 27 seconds, which works out at a rendering rate of 60 frames per minute. The frame counts in the server instances indicate that the use of a queue to distribute the workload has been very effective in distributing the load across the 256 worker role instances. The first 16 instances that were deployed first have rendered between 11 and 13 frames each, whilst the 240 instances that were added when the application was scaled have rendered between 6 and 9 frames each.   Completed Animation I’ve uploaded the completed animation to YouTube, a low resolution preview is shown below. Pin Board Animation Created using Windows Kinect and 256 Windows Azure Worker Roles   The animation can be viewed in 1280x720 resolution at the following link: http://www.youtube.com/watch?v=n5jy6bvSxWc Effective Use of Resources According to the CloudRay monitor statistics the animation took 6 days, 7 hours and 22 minutes CPU to render, this works out at 152 hours of compute time, rounded up to the nearest hour. As the usage for the worker role instances are billed for the full hour, it may have been possible to render the animation using fewer than 256 worker roles. When deciding the optimal usage of resources, the time required to provision and start the worker roles must also be considered. In the demo I started with 16 worker roles, and then scaled the application to 256 worker roles. It would have been more optimal to start the application with maybe 200 worker roles, and utilized the full hour that I was being billed for. This would, however, have prevented showing the ease of scalability of the application. The new management portal displays the CPU usage across the worker roles in the deployment. The average CPU usage across all instances is 93.27%, with over 99% used when all the instances are up and running. This shows that the worker role resources are being used very effectively. Grid Computing Scenarios Although I am using this scenario for a hobby project, there are many scenarios where a large amount of compute power is required for a short period of time. Windows Azure provides a great platform for developing these types of grid computing applications, and can work out very cost effective. ·         Windows Azure can provide massive compute power, on demand, in a matter of minutes. ·         The use of queues to manage the load balancing of jobs between role instances is a simple and effective solution. ·         Using a cloud-computing platform like Windows Azure allows proof-of-concept scenarios to be tested and evaluated on a very low budget. ·         No charges for inbound data transfer makes the uploading of large data sets to Windows Azure Storage services cost effective. (Transaction charges still apply.) Tips for using Windows Azure for Grid Computing Scenarios I found the implementation of a render farm using Windows Azure a fairly simple scenario to implement. I was impressed by ease of scalability that Azure provides, and by the short time that the application took to scale from 16 to 256 worker role instances. In this case it was around 13 minutes, in other tests it took between 10 and 20 minutes. The following tips may be useful when implementing a grid computing project in Windows Azure. ·         Using an Azure Storage queue to load-balance the units of work across multiple worker roles is simple and very effective. The design I have used in this scenario could easily scale to many thousands of worker role instances. ·         Windows Azure accounts are typically limited to 20 cores. If you need to use more than this, a call to support and a credit card check will be required. ·         Be aware of how the billing model works. You will be charged for worker role instances for the full clock our in which the instance is deployed. Schedule the workload to start just after the clock hour has started. ·         Monitor the utilization of the resources you are provisioning, ensure that you are not paying for worker roles that are idle. ·         If you are deploying third party applications to worker roles, you may well run into licensing issues. Purchasing software licenses on a per-processor basis when using hundreds of processors for a short time period would not be cost effective. ·         Third party software may also require installation onto the worker roles, which can be accomplished using start-up tasks. Bear in mind that adding a startup task and possible re-boot will add to the time required for the worker role instance to start and activate. An alternative may be to use a prepared VM and use VM roles. ·         Consider using the Windows Azure Autoscaling Application Block (WASABi) to autoscale the worker roles in your application. When using a large number of worker roles, the utilization must be carefully monitored, if the scaling algorithms are not optimal it could get very expensive!

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  • Calculating angle a segment forms with a ray

    - by kr1zz
    I am given a point C and a ray r starting there. I know the coordinates (xc, yc) of the point C and the angle theta the ray r forms with the horizontal, theta in (-pi, pi]. I am also given another point P of which I know the coordinates (xp, yp): how do I calculate the angle alpha that the segment CP forms with the ray r, alpha in (-pi, pi]? Some examples follow: I can use the the atan2 function.

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  • Most efficient AABB - Ray intersection algorithm for input/output distance calculation

    - by Tobbey
    Thanks to the following thread : most efficient AABB vs Ray collision algorithms I have seen very fast algorithm for ray/AABB intersection point computation. Unfortunately, most of the recent algorithm are accelerated by omitting the "output" intersection point of the box. In my application, I would interested in getting both the the distance from source ray to input: t0 and source ray to output of bounding box: t1. I have seen for instance Eisemann designed a very fast version regarding plucker, smits, ... , but it does not compare the case when both input/output distance should be computed see: http://www.cg.cs.tu-bs.de/publications/Eisemann07FRA/ Does someone know where I can find more information on algorithm performances for the specific input/output problem ? Thank you in advance

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  • Ray Intersecting Plane Formula in C++/DirectX

    - by user4585
    I'm developing a picking system that will use rays that intersect volumes and I'm having trouble with ray intersection versus a plane. I was able to figure out spheres fairly easily, but planes are giving me trouble. I've tried to understand various sources and get hung up on some of the variables used within their explanations. Here is a snippet of my code: bool Picking() { D3DXVECTOR3 vec; D3DXVECTOR3 vRayDir; D3DXVECTOR3 vRayOrig; D3DXVECTOR3 vROO, vROD; // vect ray obj orig, vec ray obj dir D3DXMATRIX m; D3DXMATRIX mInverse; D3DXMATRIX worldMat; // Obtain project matrix D3DXMATRIX pMatProj = CDirectXRenderer::GetInstance()->Director()->Proj(); // Obtain mouse position D3DXVECTOR3 pos = CGUIManager::GetInstance()->GUIObjectList.front().pos; // Get window width & height float w = CDirectXRenderer::GetInstance()->GetWidth(); float h = CDirectXRenderer::GetInstance()->GetHeight(); // Transform vector from screen to 3D space vec.x = (((2.0f * pos.x) / w) - 1.0f) / pMatProj._11; vec.y = -(((2.0f * pos.y) / h) - 1.0f) / pMatProj._22; vec.z = 1.0f; // Create a view inverse matrix D3DXMatrixInverse(&m, NULL, &CDirectXRenderer::GetInstance()->Director()->View()); // Determine our ray's direction vRayDir.x = vec.x * m._11 + vec.y * m._21 + vec.z * m._31; vRayDir.y = vec.x * m._12 + vec.y * m._22 + vec.z * m._32; vRayDir.z = vec.x * m._13 + vec.y * m._23 + vec.z * m._33; // Determine our ray's origin vRayOrig.x = m._41; vRayOrig.y = m._42; vRayOrig.z = m._43; D3DXMatrixIdentity(&worldMat); //worldMat = aliveActors[0]->GetTrans(); D3DXMatrixInverse(&mInverse, NULL, &worldMat); D3DXVec3TransformCoord(&vROO, &vRayOrig, &mInverse); D3DXVec3TransformNormal(&vROD, &vRayDir, &mInverse); D3DXVec3Normalize(&vROD, &vROD); When using this code I'm able to detect a ray intersection via a sphere, but I have questions when determining an intersection via a plane. First off should I be using my vRayOrig & vRayDir variables for the plane intersection tests or should I be using the new vectors that are created for use in object space? When looking at a site like this for example: http://www.tar.hu/gamealgorithms/ch22lev1sec2.html I'm curious as to what D is in the equation AX + BY + CZ + D = 0 and how does it factor in to determining a plane intersection? Any help will be appreciated, thanks.

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  • How does this snippet of code create a ray direction vector?

    - by Isaac Waller
    In the Minecraft source code, this code is used to create a direction vector for a ray from pitch and yaw:' float f1 = MathHelper.cos(-rotationYaw * 0.01745329F - 3.141593F); float f3 = MathHelper.sin(-rotationYaw * 0.01745329F - 3.141593F); float f5 = -MathHelper.cos(-rotationPitch * 0.01745329F); float f7 = MathHelper.sin(-rotationPitch * 0.01745329F); return Vec3D.createVector(f3 * f5, f7, f1 * f5); I was wondering how it worked, and what is the constant 0.01745329F?

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  • Ray intersection and child camera

    - by lutangar
    I've been playing with three.js for few weeks now and got few inconsistencies on ray casting. Here is a simplified version demonstrating one of the bug I encoutered : http://jsfiddle.net/eMrhb/12/ The camera is added to the sphere mesh for further use of TrackBallControl for example. scene.add(mesh); mesh.add(camera); Clicking a few times on the sphere and opening the console, show us none of the expected intersections between the ray and the mesh. Adding the camera to the scene (http://jsfiddle.net/eMrhb/9/), solves the problem: scene.add(mesh); scene.add(camera); But I could use a much more complex hierarchy between my scene objects and the camera to suit my needs. Is this a limitation? If it is, is there any workarounds I could use?

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  • Trouble using Ray.Intersect method on bounding boxes in a 2D XNA game

    - by getsauce
    I am trying to use a ray and bounding box to determine if a box is between the player and the mouse pointer in 2D space. When I try testing the code, the collision will return true when pointed at the box but it also returns true under other circumstances where it shouldn't. For instance. If I have a player on the left and a box directly to the right, I can put the mouse pointer a few hundred pixels above the box or a few hundred below and it will still return true. Also, I can put my mouse pointer to the left of the player and in a certain area it will still return true. Does anyone have any idea what might cause this? I have left out definitions for some of my members and properties just to make this code sample easier to read. The position property is just a Vector2 for where each object is located. ray = new Ray(new Vector3(player.Position, 0), new Vector3(mouse.Position, 0); box = new BoundingBox(new Vector3(box.Position, 0), new Vector3( new Vector2(box.Position + box.Width, box.Position + box.Height), 0); if (ray.Intersects(box) != null) collision = true; else collision = false;

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  • Ray Tracing Shadows in deferred rendering

    - by Grieverheart
    Recently I have programmed a raytracer for fun and found it beutifully simple how shadows are created compared to a rasterizer. Now, I couldn't help but I think if it would be possible to implement somthing similar for ray tracing of shadows in a deferred renderer. The way I though this could work is after drawing to the gbuffer, in a separate pass and for each pixel to calculate rays to the lights and draw them as lines of unique color together with the geometry (with color 0). The lines will be cut-off if there is occlusion and this fact could be used in a fragment shader to calculate which rays are occluded. I guess there must be something I'm missing, for example I'm not sure how the fragment shader could save the occlusion results for each ray so that they are available for pixel at the ray's origin. Has this method been tried before, is it possible to implement it as I described and if yes what would be the drawbacks in performance of calculating shadows this way?

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  • Ray-Box Intersection during Scene traversal with matrix transforms

    - by Myx
    Hello: There are a few ways that I'm testing my ray-box intersections: Using the ComputeIntersectionBox(...) method, that takes a ray and a box as arguments and computes the closest intersection of the ray and the box. This method works by forming a plane with each of the faces of the box and finding an intersection with each of the planes. Once an intersection is found, a check is made whether or not the point is on the surface of the box by checking that the intersection point is between the corner points. When I look at rays after running this algorithm on two different boxes, I obtain the correct intersections. Using ComputeIntersectionScene(...) method without using the matrix transformations on a scene that has two spheres, a dodecahedron (a triangular mesh), and two boxes. ComputeIntersectionScene(...) recursively traverses all of the nodes of the scene graph and computes the closest intersection with the given ray. This test in particular does not apply any transformations that parent nodes may have that also need to be applied to their children. With this test, I also obtain the correct intersections. Using ComputeIntersectionScene(...) method WITH the matrix transformations. This test works like the one above except that before finding an intersection between the ray and a node in the scene, the ray is transformed into the node's coordinate frame using the inverse of the node's transformation matrix and after the intersection has been computed, this intersection is transformed back into the world coordinates by applying the transformation matrix to the intersection point. When testing with the third method on the same scene file as described in 2, testing with 4 rays (thus one ray intersects the one sphere, one ray the the other sphere, one ray one box, and one ray the other box), only the two spheres get intersected and the two boxes do not get intersections. When I debug looking into my ComputeIntersectionBox(...) method, it actually tells me that the ray intersects every plane on the box but each intersection point does not lie on the box. This seems to be strange behavior, since when using test 2 without transformations, I obtain the correct box intersections (thus, I believe my ray-box intersection to be correct) and when using test 3 WITH transformations, I obtain the correct sphere intersections (thus, I believe my transformed ray should be OK). Any suggestions where I could be going wrong? Thank you in advance.

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  • Is there an easy way to read Blu-ray discs on Windows?

    - by ereOn
    Some time ago, I bought my parents a computer dedicated to media (mostly photographs and movies through DLNA). My father asked me if he could read Blu-ray discs on it, so I bought a Blu-ray reader, but I can't find a software to do the playback. I installed PowerDVD (a free version we got with a Blu-ray disc), but it seems it now requires a (non-free) upgrade. Even if it were free, I hardly see my parents do the upgrade by themselves as they barely understand how computers work. I thought I would find a free software (something like VLC, but for Blu-ray discs), but so far I had no luck. Is there software that would solve my issues? It should run on Windows Vista, shouldn't require an update every monday, or at least a free one.

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  • Sun Ray 3 Plus Unboxing video

    - by [email protected]
    Shot using a prototype Sun Ray 3 Plus weeks before the Oracle acquisition of Sun was completed, this video gives you the sense of how this newly announced Sun Ray 3 Plus is packaged when shipped.   It also shows what the bits of the SR 3 Plus are all about, including the most commonly asked about specs.  While the Production unit is available for ordering NOW, it will obviously have the Oracle logo in addition to the Sun logo.Enjoy the video here:

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  • Bullet Physics - Casting a ray straight down from a rigid body (first person camera)

    - by Hydrocity
    I've implemented a first person camera using Bullet--it's a rigid body with a capsule shape. I've only been using Bullet for a few days and physics engines are new to me. I use btRigidBody::setLinearVelocity() to move it and it collides perfectly with the world. The only problem is the Y-value moves freely, which I temporarily solved by setting the Y-value of the translation vector to zero before the body is moved. This works for all cases except when falling from a height. When the body drops off a tall object, you can still glide around since the translate vector's Y-value is being set to zero, until you stop moving and fall to the ground (the velocity is only set when moving). So to solve this I would like to try casting a ray down from the body to determine the Y-value of the world, and checking the difference between that value and the Y-value of the camera body, and disable or slow down movement if the difference is large enough. I'm a bit stuck on simply casting a ray and determining the Y-value of the world where it struck. I've implemented this callback: struct AllRayResultCallback : public btCollisionWorld::RayResultCallback{ AllRayResultCallback(const btVector3& rayFromWorld, const btVector3& rayToWorld) : m_rayFromWorld(rayFromWorld), m_rayToWorld(rayToWorld), m_closestHitFraction(1.0){} btVector3 m_rayFromWorld; btVector3 m_rayToWorld; btVector3 m_hitNormalWorld; btVector3 m_hitPointWorld; float m_closestHitFraction; virtual btScalar addSingleResult(btCollisionWorld::LocalRayResult& rayResult, bool normalInWorldSpace) { if(rayResult.m_hitFraction < m_closestHitFraction) m_closestHitFraction = rayResult.m_hitFraction; m_collisionObject = rayResult.m_collisionObject; if(normalInWorldSpace){ m_hitNormalWorld = rayResult.m_hitNormalLocal; } else{ m_hitNormalWorld = m_collisionObject->getWorldTransform().getBasis() * rayResult.m_hitNormalLocal; } m_hitPointWorld.setInterpolate3(m_rayFromWorld, m_rayToWorld, m_closestHitFraction); return 1.0f; } }; And in the movement function, I have this code: btVector3 from(pos.x, pos.y + 1000, pos.z); // pos is the camera's rigid body position btVector3 to(pos.x, 0, pos.z); // not sure if 0 is correct for Y AllRayResultCallback callback(from, to); Base::getSingletonPtr()->m_btWorld->rayTest(from, to, callback); So I have the callback.m_hitPointWorld vector, which seems to just show the position of the camera each frame. I've searched Google for examples of casting rays, as well as the Bullet documentation, and it's been hard to just find an example. An example is really all I need. Or perhaps there is some method in Bullet to keep the rigid body on the ground? I'm using Ogre3D as a rendering engine, and casting a ray down is quite straightforward with that, however I want to keep all the ray casting within Bullet for simplicity. Could anyone point me in the right direction? Thanks.

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  • Ray Picking Problems

    - by A Name I Haven't Decided On
    I've read so many answers on here about how to do Ray Picking, that I thought I had the idea of it down. But when I try to implement it in my game, I get garbage. I'm working with LWJGL. Here's the code: public static Ray getPick(int mouseX, int mouseY){ glPushMatrix(); //Setting up the Mouse Clip Vector4f mouseClip = new Vector4f((float)mouseX * 2 / 960f - 1, 1 - (float)mouseY * 2 / 640f ,0 ,1); //Loading Matrices FloatBuffer modMatrix = BufferUtils.createFloatBuffer(16); FloatBuffer projMatrix = BufferUtils.createFloatBuffer(16); glGetFloat(GL_MODELVIEW_MATRIX, modMatrix); glGetFloat(GL_PROJECTION_MATRIX, projMatrix); //Assigning Matrices Matrix4f proj = new Matrix4f(); Matrix4f model = new Matrix4f(); model.load(modMatrix); proj.load(projMatrix); //Multiplying the Projection Matrix by the Model View Matrix Matrix4f tempView = new Matrix4f(); Matrix4f.mul(proj, model, tempView); tempView.invert(); //Getting the Camera Position in World Space. The 4th Column of the Model View Matrix. model.invert(); Point cameraPos = new Point(model.m30, model.m31, model.m32); //Theoretically getting the vector the Picking Ray goes Vector4f rayVector = new Vector4f(); Matrix4f.transform(tempView, mouseClip, rayVector); rayVector.translate((float)-cameraPos.getX(),(float) -cameraPos.getY(),(float) -cameraPos.getZ(), 0f); rayVector.normalise(); glPopMatrix(); //This Basically Spits out a value that changes as the Camera moves. //When the Mouse moves, the values change around 0.001 points from screen edge to edge. System.out.format("Vector: %f %f %f%n", rayVector.x, rayVector.y, rayVector.z); //return new Ray(cameraPos, rayVector); return null; } I don't really know why this isn't working. I was hoping some more experienced eyes might be able to help me out. I can get the camera position like a champ, it's the vector the rays going in that I can't seem to get right. Thanks.

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  • Streaming Media with Sony Blu-ray Disc Player

    - by Ben Griswold
    The best gift under the tree this year? A Sony Blu-ray Disc player: The BDP-N460 allows you to instantly stream thousands of movies, videos and music from the largest selection of leading content providers including Netflix, Amazon Video On Demand, YouTube™, Slacker® Radio and many, many more. Plus, enjoy the ultimate in high-definition entertainment and watch Blu-ray Disc movies in Full HD 1080p quality with HD audio. The BDP-N460 includes built-in software that makes it easy to connect this player to your existing wireless network.  So I did… I paired the disc player with the recommended Linksys Wireless Ethernet Bridge (WET-610N) and I was streaming the last season of Lost episodes in no time. Really cool. Highly recommended.

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  • The Social Business Thought Leaders - Ray Wang

    - by kellsey.ruppel
    It seems both consumers and businesses are at the peak of the social hype. Overwhelmed by social media channels, platforms, and processes both in their private and professional life, many early adopters are starting to feel the social fatigue. Mirroring what happened with email and web sites during the late 1990's - early 2000's, more and more managers are looking to move from ubiquitous social media tactics to the most appropriate business use case and processes. This step becomes even more important considering the year over year contraction in IT budgets and the consequent need to maximize return on every dollar spent in new technologies. Ray Wang, CEO and Principal Analyst at Constellation Research, suggests engagement through collaborative technologies both as a conceptual model and a transformational tool for enterprises to reap business value. Without participation - the reasoning goes - there is no value and good technology alone is not enough to guarantee employee and customer adoption. Enterprise gamification is a new lever to succeed with Social Business by directing a critical mass of participation towards desired outcomes. What kind of outcomes? A recent study from Constellation Research (see 2012 Q1 Gamification Early Adopters Best Practices) highlights how Marketing, Customer Service and HR are leading the pack with gamification in processes such as: Sustaining long term customer loyalty (76.4%) Improving response in campaign to lead (74.5%) Right channeling incidents for resolution in social media (67.3%) Growing the number service and support incidents resolved by the community (63.6%) Improving employee referral rates and effective recruiting (43.6%) Driving on-boarding success with new hires (20%) More than simply adding badges, points and leaderboards to existing processes, enterprise gamification should be holistically embedded into employee and customer experience to stimulate specific behaviors. According to Ray Wang this can be done at three core levels: Measurable actions. The behaviors we want to facilitate consist of granular actions (i.e likes, comments, posts, recommendations, etc) and more complex actions (i.e projects, initiatives, programmes) attributed to individuals, groups and/or external actors  Reputation. The reputation an individual has earned through his actions is a key factor in building motivation among others and it is determined by its identity, social standing status and competitiveness Incentives or the intrinsic and extrinsic rewards that motivate behaviors and drive actions Listen to Ray Wang's video-interview to learn more about the dynamics that are shaping the future of collaboration and how gamification can help organizations attain new levels of engagement.

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  • Sea Ray : le premier Nokia sous Windows Phone présenté en interne par le PDG de Nokia

    Sea Ray : le premier Nokia sous Windows Phone Présenté en interne par le PDG de Nokia Stephen Elop, le PDG de Nokia a promis de livrer les premiers téléphones Nokia Windows Phone à la fin de cette année au lieu de 2012, comme initialement prévu. D'après une vidéo et des images d'une réunion interne qui ont fuité sur internet, le patron du constructeur finlandais aurait même déjà présenté le premier téléphone Nokia Windows Phone baptisé « Sea Ray ». Le nouveau téléphone de Nokia sera équipé d'une camera de 8 mégapixels et embarquera la prochaine mise à jour de Windows Phone Mango. Le design de Sea Ra...

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  • ray collision with rectangle and floating point accuracy

    - by phq
    I'm trying to solve a problem with a ray bouncing on a box. Actually it is a sphere but for simplicity the box dimensions are expanded by the sphere radius when doing the collision test making the sphere a single ray. It is done by projecting the ray onto all faces of the box and pick the one that is closest. However because I'm using floating point variables I fear that the projected point onto the surface might be interpreted as being below in the next iteration, also I will later allow the sphere to move which might make that scenario more likely. Also the bounce coefficient might be as low as zero, making the sphere continue along the surface. So my naive solution is to project not only forwards but backwards to catch those cases. That is where I got into problems shown in the figure: In the first iteration the first black arrow is calculated and we end up at a point on the surface of the box. In the second iteration the "back projection" hits the other surface making the second black arrow bounce on the wrong surface. If there are several boxes close to each other this has further consequences making the sphere fall through them all. So my main question is how to handle possible floating point accuracy when placing the sphere on the box surface so it does not fall through. In writing this question I got the idea to have a threshold to only accept back projections a certain amount much smaller than the box but larger than the possible accuracy limitation, this would only cause the "false" back projection when the sphere hit the box on an edge which would appear naturally. To clarify my original approach, the arrows shown in the image is not only the path the sphere travels but is also representing a single time step in the simulation. In reality the time step is much smaller about 0.05 of the box size. The path traveled is projected onto possible sides to avoid traveling past a thinner object at higher speeds. In normal situations the floating point accuracy is not an issue but there are two situations where I have the concern. When the new position at the end of the time step is located very close to the surface, very unlikely though. When using a bounce factor of 0, here it happens every time the sphere hit a box. To add some loss of accuracy, the motivation for my concern, is that the sphere and box are in different coordinate systems and thus the sphere location is transformed for every test. This last one is why I'm not willing to stand on luck that one floating point value lying on top of the box always will be interpreted the same. I did not know voronoi regions by name, but looking at it I'm not sure how it would be used in a projection scenario that I'm using here.

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  • most efficient AABB vs Ray collision algorithms

    - by Asher Einhorn
    Is there a known 'most efficient' algorithm for AABB vs Ray collision detection? I recently stumbled accross Arvo's AABB vs Sphere collision algorithm, and I am wondering if there is a similarly noteworthy algorithm for this. One must have condition for this algorithm is that I need to have the option of querying the result for the distance from the ray's origin to the point of collision. having said this, if there is another, faster algorithm which does not return distance, then in addition to posting one that does, also posting that algorithm would be very helpful indeed. Please also state what the function's return argument is, and how you use it to return distance or a 'no-collision' case. For example, does it have an out parameter for the distance as well as a bool return value? or does it simply return a float with the distance, vs a value of -1 for no collision? (For those that don't know: AABB = Axis Aligned Bounding Box)

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  • (My) Sun Ray 3i

    - by user13346636
    Last week, some Sun Ray devices were shown at the LASDEC exhibition. Afterward, they were brought back to the Aoyama Center, but not all of them found a place to be stored. So, two days ago, Iwasaki-san, one of the co-workers I've been close to (and who was at the exhibition), put a Sun Ray 3i (all-in-one with 21.5" screen) on my (shared) desk. Yay! I managed to get a Japanese keyboard, and now I can access my card and cardless sessions from Germany, and the performance is just great, as good as when I work from home in Hamburg. That's the way my deskt looks now,almost as messy as my desk in Hamburg: And my back is very grateful.

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  • Windows 8 will only recognize the Blu-Ray drive, if the Windows 8 disc is present at boot time

    - by aceinthehole
    If I have the install disc in the Blu-Ray ROM drive at boot time and subsequently remove the disc and replace it with Blu-Ray media, everything functions as I’d expect. However, if I have no media present, or another disc in the drive at boot time, then Windows 8 does not seem to recognize that the Blu-Ray player is even present in the computer. It is not present in My Computer, the Device Manager does not show the player, and scanning for new hardware yields nothing. It seems that the driver is installed and working as expected, but what is it about having the Windows 8 install disc in the drive or not that would cause this kind of behavior?

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  • How can I play Blu-Ray movies on a PC upgraded to Windows 8?

    - by Rowland Shaw
    How can I play Blu-Ray movies via Windows Media Centre on Windows 8? If I choose the "play dvd" option, I get an error: Cannot Play Disc To play this DVD, you must first install a playback application that supports Blu-ray Disc. [ OK ] However, I have got the HP MediaSmart application installed, which does work (although it's "less than awesome"), so I'm confused why I get this warning?

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  • Writing the correct value in the depth buffer when using ray-casting

    - by hidayat
    I am doing a ray-casting in a 3d texture until I hit a correct value. I am doing the ray-casting in a cube and the cube corners are already in world coordinates so I don't have to multiply the vertices with the modelviewmatrix to get the correct position. Vertex shader world_coordinate_ = gl_Vertex; Fragment shader vec3 direction = (world_coordinate_.xyz - cameraPosition_); direction = normalize(direction); for (float k = 0.0; k < steps; k += 1.0) { .... pos += direction*delta_step; float thisLum = texture3D(texture3_, pos).r; if(thisLum > surface_) ... } Everything works as expected, what I now want is to sample the correct value to the depth buffer. The value that is now written to the depth buffer is the cube coordinate. But I want the value of pos in the 3d texture to be written. So lets say the cube is placed 10 away from origin in -z and the size is 10*10*10. My solution that does not work correctly is this: pos *= 10; pos.z += 10; pos.z *= -1; vec4 depth_vec = gl_ProjectionMatrix * vec4(pos.xyz, 1.0); float depth = ((depth_vec.z / depth_vec.w) + 1.0) * 0.5; gl_FragDepth = depth;

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  • Ray Tracing concers: Efficient Data Structure and Photon Mapping

    - by Grieverheart
    I'm trying to build a simple ray tracer for specific target scenes. An example of such scene can be seen below. I'm concerned as to what accelerating data structure would be most efficient in this case since all objects are touching but on the other hand, the scene is uniform. The objects in my ray tracer are stored as a collection of triangles, thus I also have access to individual triangles. Also, when trying to find the bounding box of the scene, how should infinite planes be handled? Should one instead use the viewing frustum to calculate the bounding box? A few other questions I have are about photon mapping. I've read the original paper by Jensen and many more material. In the compact data structure for the photon they introduce, they store photon power as 4 chars, which from my understanding is 3 chars for color and 1 for flux. But I don't understand how 1 char is enough to store a flux of the order of 1/n, where n is the number of photons (I'm also a bit confused about flux vs power). The other question about photon mapping is, if it would be more efficient in my case to store photons per object (or even per Object's triangle) instead of using a balanced kd-tree. Also, same question about bounding box of the scene but for photon mapping. How should one find a bounding box from the pov of the light when infinite planes are involved?

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