Sign in to follow this  

OpenGL camera transformation

Recommended Posts

I'm trying to make a simple 3d renderer, without dx or ogl. I have all objects in world space as standard, and I use right = +x, up = +y, forward = +z, which is left-handed I believe. With the camera at (0,0,0) and facing the positive z-axis, all objects are rendered how they should. However, the camera should ideally be able to move around and rotate. I can handle the code for moving, but I can't figure out how to transform the points accordingly. The camera simply has two 3d vectors, one for the eyepoint, and the other for the lookAt point. The up vector is by default (0,1,0). I have functions for getting the view, side, and up vectors based on the eye and lookAt. However since I can't get the transformations to work, I can't be sure they are right. My current process is to subtract each point by the camera's eyepoint, setting it at the origin. The part I can't get is properly rotating the view vector to point along the positive z-axis. I've looked online extensively, and everything I find either tells me how to use directx or opengl's functions, or it didn't work for me. I have implementations of 3d vectors, 4d vectors, 3x3 matrices, 4x4 matrices, tons of stuff tried and failed. Alternatively, not a problem per se, but a question. Currently, my implementation of projection is just to divide the x and y coords by the z coord, something I remember hearing a while ago. It works, and moving the camera around (the eyepoint... it still has to look straight ahead) seems realistic. However, it tends to stretch things along the z-axis, ie. things look longer than they really are. I have seen many projection transformations in my searches for view transformations, and although I didn't try any of them, I still wonder: is my implementation acceptable and/or what is the best way to do projection?

Share this post

Link to post
Share on other sites
In most rendering APIs, the concept of a camera is more of a convenience than an integral part of the renderer. Basically, you have a chain of transformations -- model-to-world, world-to-view, view-to-clip, and something like clip-to-screen, and the renderer just deals in terms of these transformations. Luckily, the camera fits into this scheme very easily -- it generates the world-to-view transformation.

To generate the world-to-view transformation, you take the position and orientation of the camera in world space and compute a transformation (view-to-world) from that, and finally invert that to get the world-to-view transformation.

That's the basics. I left out a lot of details.

Share this post

Link to post
Share on other sites
How to Compute the View Matrix from the Camera's Look-At and Eye Positions, and an Up Vector

The view matrix is simply the inverse of the camera's orientation/position matrix.

To generate the camera's orientation/position matrix, combine the local x, y, and z axes, and eye position. You compute the local axes like this:
    z = normalize( lookAt - eye );
x = normalize( cross( up, z ) );
y = cross( z, x );
The x, y, and z vectors go into the first, second, and third columns (if you are using column vectors) of the matrix. The eye position goes into the 4th column (if you are using column vectors). If you are using row vectors, then they go into the rows of the matrix. Now you have your camera's orientation/position matrix, which conveniently happens to be the view-to-world matrix. To make a world-to-view matrix, you simply invert it.

Now, rather than doing a general 4x4 matrix inversion, you can take advantage of some of the properties of the matrix in order to invert it quickly. First, let's simplify the notation. The matrix can be represented like this:
    R  T
0 1
where R is the upper-left 3x3 part of the 4x4 matrix, T is the upper-right 3x1 part of the 4x4 matix, 0 is the 1x3 row of zeros on the bottom, and 1 is the 1 in the lower-right corner. Note that R and T conveniently correspond to the rotation and translation portions of the matrix. If you are using row vectors, then the matrices here are shown transposed. That doesn't affect the math, it just affects the notation.

The inverse of this 2x2 matrix is:
    R-1 T'
0 1
where T' = -R-1T. In addition, since R is orthonormal (or orthogonal, or whatever the correct terminology is), R-1 = RT. The result is:
    RT T'
0 1
where T' = -RTT, and so no inversion is actually necessary. This is your world-to-view matrix.

One more possible optimization... T' = -RTT can also be computed like this:
    T'X = -(RX dot T)
T'Y = -(RY dot T)
T'Z = -(RZ dot T)
where RX, RY, and RZ are the first, second, and third columns (or rows) of R -- the x, y, and z axes you computed at the beginning!

Note: It doesn't matter how the camera's orientation/position matrix is computed. The matrix inversion presented above will work for any transformation matrix that involves only rotation and translation.

Share this post

Link to post
Share on other sites
Thanks a lot for the detailed reply! I will implement this and hopefully it works fine.

I don't know a ton about transformation matrices, but I think that the top 3x3, or R, is just a rotation matrix, and T is a translation matrix, just combined into the 4x4 matrix that way. Could I simply perform the translation of -T, then multiply R * [point] to rotate the point? The inverse of a 3x3 matrix isn't hard to calculate, although your optimizations make a 4x4's easy also.

Share this post

Link to post
Share on other sites
Original post by deej21
Could I simply perform the translation of -T, then multiply R * [point] to rotate the point?

Not R, RT. Transforming a point by the view matrix looks like this:
    | v' |  =  | RT  -RTT |  | v |
| 1 | = | 0  1  | | 1 |
which simplifies to v' = RTv - RTT, or v' = RT(v - T).

Original post by deej21
The inverse of a 3x3 matrix isn't hard to calculate, although your optimizations make a 4x4's easy also.

Don't forget that the inverse of a rotation matrix is simply its transpose.

Share this post

Link to post
Share on other sites
Sweet, that worked out great. Thanks a lot, johnbolton.
Just a note, it also worked just using the 3x3 matrix. I just subtracted the eyepoint, then multiplied by the transposed rotation matrix. This eliminates the need to calculate T'

Share this post

Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this  

  • Announcements

  • Forum Statistics

    • Total Topics
    • Total Posts
  • Similar Content

    • By test opty
      Hi all,
      I'm starting OpenGL using a tut on the Web. But at this point I would like to know the primitives needed for creating a window using OpenGL. So on Windows and using MS VS 2017, what is the simplest code required to render a window with the title of "First Rectangle", please?
    • By DejayHextrix
      Hi, New here. 
      I need some help. My fiance and I like to play this mobile game online that goes by real time. Her and I are always working but when we have free time we like to play this game. We don't always got time throughout the day to Queue Buildings, troops, Upgrades....etc.... 
      I was told to look into DLL Injection and OpenGL/DirectX Hooking. Is this true? Is this what I need to learn? 
      How do I read the Android files, or modify the files, or get the in-game tags/variables for the game I want? 
      Any assistance on this would be most appreciated. I been everywhere and seems no one knows or is to lazy to help me out. It would be nice to have assistance for once. I don't know what I need to learn. 
      So links of topics I need to learn within the comment section would be SOOOOO.....Helpful. Anything to just get me started. 
      Dejay Hextrix 
    • By mellinoe
      Hi all,
      First time poster here, although I've been reading posts here for quite a while. This place has been invaluable for learning graphics programming -- thanks for a great resource!
      Right now, I'm working on a graphics abstraction layer for .NET which supports D3D11, Vulkan, and OpenGL at the moment. I have implemented most of my planned features already, and things are working well. Some remaining features that I am planning are Compute Shaders, and some flavor of read-write shader resources. At the moment, my shaders can just get simple read-only access to a uniform (or constant) buffer, a texture, or a sampler. Unfortunately, I'm having a tough time grasping the distinctions between all of the different kinds of read-write resources that are available. In D3D alone, there seem to be 5 or 6 different kinds of resources with similar but different characteristics. On top of that, I get the impression that some of them are more or less "obsoleted" by the newer kinds, and don't have much of a place in modern code. There seem to be a few pivots:
      The data source/destination (buffer or texture) Read-write or read-only Structured or unstructured (?) Ordered vs unordered (?) These are just my observations based on a lot of MSDN and OpenGL doc reading. For my library, I'm not interested in exposing every possibility to the user -- just trying to find a good "middle-ground" that can be represented cleanly across API's which is good enough for common scenarios.
      Can anyone give a sort of "overview" of the different options, and perhaps compare/contrast the concepts between Direct3D, OpenGL, and Vulkan? I'd also be very interested in hearing how other folks have abstracted these concepts in their libraries.
    • By aejt
      I recently started getting into graphics programming (2nd try, first try was many years ago) and I'm working on a 3d rendering engine which I hope to be able to make a 3D game with sooner or later. I have plenty of C++ experience, but not a lot when it comes to graphics, and while it's definitely going much better this time, I'm having trouble figuring out how assets are usually handled by engines.
      I'm not having trouble with handling the GPU resources, but more so with how the resources should be defined and used in the system (materials, models, etc).
      This is my plan now, I've implemented most of it except for the XML parts and factories and those are the ones I'm not sure of at all:
      I have these classes:
      For GPU resources:
      Geometry: holds and manages everything needed to render a geometry: VAO, VBO, EBO. Texture: holds and manages a texture which is loaded into the GPU. Shader: holds and manages a shader which is loaded into the GPU. For assets relying on GPU resources:
      Material: holds a shader resource, multiple texture resources, as well as uniform settings. Mesh: holds a geometry and a material. Model: holds multiple meshes, possibly in a tree structure to more easily support skinning later on? For handling GPU resources:
      ResourceCache<T>: T can be any resource loaded into the GPU. It owns these resources and only hands out handles to them on request (currently string identifiers are used when requesting handles, but all resources are stored in a vector and each handle only contains resource's index in that vector) Resource<T>: The handles given out from ResourceCache. The handles are reference counted and to get the underlying resource you simply deference like with pointers (*handle).  
      And my plan is to define everything into these XML documents to abstract away files:
      Resources.xml for ref-counted GPU resources (geometry, shaders, textures) Resources are assigned names/ids and resource files, and possibly some attributes (what vertex attributes does this geometry have? what vertex attributes does this shader expect? what uniforms does this shader use? and so on) Are reference counted using ResourceCache<T> Assets.xml for assets using the GPU resources (materials, meshes, models) Assets are not reference counted, but they hold handles to ref-counted resources. References the resources defined in Resources.xml by names/ids. The XMLs are loaded into some structure in memory which is then used for loading the resources/assets using factory classes:
      Factory classes for resources:
      For example, a texture factory could contain the texture definitions from the XML containing data about textures in the game, as well as a cache containing all loaded textures. This means it has mappings from each name/id to a file and when asked to load a texture with a name/id, it can look up its path and use a "BinaryLoader" to either load the file and create the resource directly, or asynchronously load the file's data into a queue which then can be read from later to create the resources synchronously in the GL context. These factories only return handles.
      Factory classes for assets:
      Much like for resources, these classes contain the definitions for the assets they can load. For example, with the definition the MaterialFactory will know which shader, textures and possibly uniform a certain material has, and with the help of TextureFactory and ShaderFactory, it can retrieve handles to the resources it needs (Shader + Textures), setup itself from XML data (uniform values), and return a created instance of requested material. These factories return actual instances, not handles (but the instances contain handles).
      Is this a good or commonly used approach? Is this going to bite me in the ass later on? Are there other more preferable approaches? Is this outside of the scope of a 3d renderer and should be on the engine side? I'd love to receive and kind of advice or suggestions!
    • By nedondev
      I 'm learning how to create game by using opengl with c/c++ coding, so here is my fist game. In video description also have game contain in Dropbox. May be I will make it better in future.
  • Popular Now