This is because OpenGL abstracts away device dependent units, making it more convenient to target multiple devices and to focus on game logic. Sometimes you may need to convert between coordinate systems for which libGDX offers various methods. It is crucial to understand in which coordinate system you are working.

Otherwise it can be easy to get confused and to make assumptions which aren't correct. On this page the various coordinate systems are listed. It is highly recommended to first get familiar with the Cartesian coordinate systemwhich is the most widely used coordinate system.

Starts at the upper left pixel of the application portion of the physical screen and has the size of the application portion of the physical screens width and height in pixels. Each coordinate is an index in the 2D array of this grid, representing a physical pixel on the screen. Therefore these coordinates are always represented as integers, they can't be fractional. If you're familiar with canvas graphics or basic image editors, then you are probably already familiar with these coordinates.

Whenever working with mouse or touch coordinates, you'll be using this coordinate system. You typically want to convert these coordinates as soon as possible to a more convenient coordinate system. This is OpenGL's counterpart to touch coordinates; that is: it is used to specify index a pixel of the portion of the physical screen. It is also used as indexer for an image in memory. Likewise, these are integers, they can't be fractional. The only difference between touch and screen coordinates is that touch coordinates are y-down, while screen coordinates are y-up.

Converting between them is therefore quite easy:. You typically use these coordinates to specify which portion of the screen to render onto. For example when calling glViewportglScissor or manipulating a pixmap see next. In the majority of use-cases you don't need this coordinate system a lot, if any, and it should be isolated from your game logic and its coordinate system.

The camera. Pixmap coordinates are an exception. Pixmaps are commonly used to upload texture data. For example when loading a PNG image file to a texture, it is first decoded uncompressed to a Pixmap, which is the raw pixel data of the image, then it is copied to the GPU for use as texture.

The texture can then be used to render to the screen. It is also possible to modify or create a pixmap by code, e.

Powerapps components examplesThe "problem" with this is that OpenGL expects the texture data to be in image coordinates, which is y-up. However, most image formats store the image data comparable to touch coordinates, which is y-down.

LibGDX does not translate the image data between the two which would involve copying the image line by lineinstead it simply copies the data as is. This practically causes a Texture loaded from Pixmap to be up-side-down. To compensate for this up-side-down texture, SpriteBatch flips the texture UV coordinates see below on the y axis when rendering. Likewise, fbx-conv has the option to flip texture coordinates on the y axis as well.

However, when you use a texture which isn't loaded from a pixmap, for example a Framebuffer, then this might cause that texture to appear up-side-down. The above coordinate systems have one big issue in common: they are device specific. To solve that, OpenGL allows you to use a device independent coordinate system which is automatically mapped to screen coordinates when rendering. But other than that, you should never have to use this coordinate system in a practical use-case.

It is sometimes used in tutorials and such, though, to show the basics. It might be worth to note that the normalization does not respect the aspect ratio. That is: the scale in the X direction does not have to match the scale in the Y direction.

It is up to the application to decide how to deal with various aspect ratios see world units, below.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Instead it seems to be in percents, for example.

Is this how it is, or am I doing something wrong? OpenGL works in the following way: You start of a local coordinate system of arbitrary units. This coordinate system is transformed to so called eye space coordinates by the model-view matrix it is called model-view matrix, because it combines model and view transformations. So if you leave your transformation matrices modelview and projection identity, then indeed the coordinate ranges [-1,1] will map to the Viewport.

However by choosing appropriate transformation and projection you can map from Model Space units to Viewport units arbitrarily. It's not really a percentage: it's related to the size and aspect ratio of your current viewport.

I could write a whole story about it, but I'd suggest you take a look at NeHe's tutorials on OpenGL, starting with lesson 1 about setting up the window. Very thorough, and highly recommended. Essentially, a projection matrix is matrix that projects a vertex on a 2D space. There are two projection matrices: perspective and orthographic. The current projection matrix determine the effective vertex screen position.

Since you do not set the projection matrix, you are using the default one, which is the orthographic, with horizontal and vertical range To control the projection matrix, see gluOrtho2D function. There you can find all information required. Learn more. Ask Question. Asked 8 years, 6 months ago. Active 2 years ago. Viewed 8k times. Adam Ashwal Adam Ashwal 1, 1 1 gold badge 16 16 silver badges 35 35 bronze badges.

Maybe the answers to this question will provide you some insight into OpenGL's transformation pipeline. Active Oldest Votes.

**Modern OpenGL 3.0+ [GETTING STARTED] Tutorial 5 - Projections and Coordinate Systems**

DarkCygnus 4, 3 3 gold badges 28 28 silver badges 48 48 bronze badges. Are they thrown away? Isn't it division first, clipping after htat? Luca Luca Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.A lot of conventions as to how we do things are arbitrary.

Miss world 2018 winnerFor example, driving on the left side of the road is not inherently better or worse than driving on the right side. The same is true of computer graphics. For example, coordinate systems can be right-handed or left-handed ; if you imagine placing your eye at the 0, 0, 0 point and looking in turn in the direction of the positive-X, positive-Y and positive-Z axes, if your gaze describes a clockwise rotation, then the coordinate system is right-handed, while anticlockwise means it is left-handed.

One way to remember which is which is to hold your thumb, index finger and middle finger out at right angles to each other, calling the thumb direction positive-X, index finger pointing at positive-Y, and middle finger at positive-Z; if you do this with your right hand, then the coordinate system is naturally right-handed; while your left hand defines a left-handed coordinate system.

It is quite common in computer graphics to be working in a number of different coordinate systems. For example, a model of a car is defined in terms of its own model coordinate system. To place the car in a scene, perhaps moving along a road, involves transforming those model coordinates to the world coordinates of the scene.

### Tag: Cartesian coordinate system

And just to add to the fun, the car model itself may have multiple coordinate systems. For example, each wheel may be defined in its own child coordinate system, in which it rotates relative to its parent, namely the body of the car. So the transformation pipeline, as far as eye coordinates, looks like this where the steps in square brackets are transformations, the ones that are not represent coordinate values :.

I said above that it is recommended to use right-handed coordinate systems. This is true up to the eye-coordinates stage. It is normal for the projection transformation to then flip the Z-values around to make the coordinate system left -handed, so that Z-values are now increasing away from the viewer, instead of towards them. This is so that the Z-values can be converted and stored in the depth buffer, with increasing values representing increasing depth. The standard range for eye coordinates is for an interval of [ All you have to do is make sure that the combination of all the model and viewing transformations brings the part of the scene you want to see down within that [ The final viewport transformation remaps these in units of actual pixels, corresponding to the actual size of your viewing area.

The normal kind of transformations applied to computer graphics and the only kind supported by OpenGL is called a linear transformation. This is because straight lines before the transformation end up still straight after being transformed. Such a transformation can be handily represented by a matrix. Unlike multiplication of conventional scalar numbers, the order of the transformations matters: a scaling followed by a translation repositioning is not the same if the translation is done first, since the scaling then happens around a different centre point.

You will quite commonly see a 3-dimensional position vector written, not as xyzbut as xyzw. Why is this? Otherwise translation would have to be separated out as an addition step:. It is normal to set w to 1. And here we have another case where you need to pick a convention and stick to it. Transforming a vector V by a transformation M to a vector V' can be written as a premultiplication of column vectors :. It is recommended that you stick to the premultiplication convention, as this is more consistent with how OpenGL operates.

For example, in the pre-OpenGL From OpenGL Wiki. Jump to: navigationsearch. Category : Mathematics. Navigation menu Personal tools Create account Log in. Namespaces Page Discussion. Views Read View source View history. This page was last edited on 3 Augustat I have been using opengl for a while and have been used to knowing that opengl uses a right hand coordinate system, I have recently started looking at vulkan too and found out there were some differences in the coordinate systems between the two rendering methods.

Because of this I decided to do a deep dive in to what happens from the defining of a point to it being draw on the screen and while doing this I have seen some confusion in my previous understanding. Why is opengl defined as a right handed coordinate system when it looks to be left handed? The coordinate system of the underlying data is irrelevant to opengl because the first it really gets to see it is post projection calculations which is not defined in opengl itself and post projection is clip space.

Conventionally, object space and eye space are right-handed. Conventionally, NDC is left-handed, but the projection transformations generated by e. Even whether NDC is left- or right-handed is subjective. Classifying a coordinate system as left-handed or right-handed requires imposing a physical interpretation on the axes. But OpenGL is just performing calculations; interpretation is up to the programmer.

In NDC which is clip space after projective divisionthe clip volume is the signed unit cube, as the calculations are simpler that way. The depth buffer holds unsigned normalised values, so those need to be transformed the actual transformation is controlled by glDepthRange.

Your definition of the behavior of Z assumes a default glDepthRange. And even then, you can reverse the effective meaning of depth by changing the glDepthFunc. Compatibility OpenGL effectively defined its model space and other spaces as right-handed, but clip-space has always been what it is. The difference now is that in Core OpenGL, you have to be aware of it.

A primitive which is partially within clip space is clipped to the clip space boundaries, so that all of its vertices are within clip space. Because the depth buffer has historically been a normalized, unsigned integer, and therefore only stores values on the range [0, 1].

## Coordinate Systems

Thanks for both of your answers, I was struggling when doing the projection matrix maths to understand where the handedness came in to many conversations I have read on the web and you have both answered it by effectively saying that the handedness is arbitrary and purely defined by how the system is configured with regards to depth.

With a like for like depth configuration vulkan and direct x will have a different handedness due to the y NDC coordinates being different in terms of where the positive direction is. Also thanks for clarifying what the final step is for when converting NDC to window coordinates with respect to depth. Questions about opengl coordinate system OpenGL. OpenGL: Basic Coding. Hi I have been using opengl for a while and have been used to knowing that opengl uses a right hand coordinate system, I have recently started looking at vulkan too and found out there were some differences in the coordinate systems between the two rendering methods.

This brings me to my two questions when I have done my mvp transformation I have transformed my vertex in to clip space. From the information I can find the coordinate system of clip space opengl is y up positive, X right positive, z in to screen positive. This seems to be a left handed coordinate system not a right handed coordinate system.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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While i am new to opengl and rarly ask for help i think a need some clarification regarding Z-axis, depth-test and GLM:ortho. Been strugling with this for a week or two and everything have from the start been "reversed". Okej, so everything should add up, small Z is in front and big in the back, but no. Everything is the opposite. So while i read the linked thread i discovered that glm::ortho SHOULD convert right-hand-coordinates because apperently thats what everybody is using in examples to left-hand-coordinates.

Sound greats, so why does it not work? If i use glm::orthoLH everything adds up and works perfect, since it converts all my coordinates to left-hand. So why does glm::ortho not do this for me? Apperently there is a settings for this when you compile the GLM-library. OpenGL is not right-handed, nor left-handed. Each and every of these coordinate systems can have it's own conventions, including its own handedness. Legacy OpenGL with the fixed function pipeline and the integrated matrix stack had some coordinate conventions in mind but it did not completely enforce that you use these conventions either.

The flipping of the handedness was done in the projection matrix. No some other convention of legacy GL was that the near and far clip plane position was always defined as distances into the viewing directionso glOrtho As you see, "small" z -5 is in the back, and "big" z -2 is in the front, like it should be in a right-handed coordinate system.

Classe 2 d ungarettiIt will establish a right-handed view space by flipping z in the proejction matrix and assuming all the later spaces NDC and window space are configured as left-handed. This will have the result of establishing a left-handed view space as long as the NDC and Window space is set up as left-handed, too.

Those are all just conventions. YOu have to just decide them in one way or the other, and no one is better than the other per-say.

THis stuff only becomes interesting and annoying if you have different parts or pieces which uses different conventions, where you have to be very carefult to correcly convert the data at the right places.

Learn more. Ask Question. Asked 2 years, 4 months ago. Active 2 years, 4 months ago. Viewed times. Please correct me if this doesnt make any sense. Rabbid76 Active Oldest Votes. If you look at the mapping I jst wrote, it should explain this quesion: Okej, so everything should add up, small Z is in front and big in the back, but no.

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Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Because the OpenGL screen coordinate space is [-1,1], I'm a little confused as to how it should be interfaced with a generic, Cartesian 2D world coordinate system.

Let's say the viewport in my world is [,] to [, ], where [0, 0] is the world's origin. Do I only need to translate and scale down to coordinates between -1 and 1? Or is there some other form of transformation that needs to be performed? How do you calculate where to draw objects on screen that have defined positions in your own coordinate system? I would appreciate an explanation with and without glOrtho so we can use the Z axis as well for perspective effects.

What you're referring to are normalized device coordinates NDCswhere all three coordinates are in the range [-1, 1]. The different coordinate systems and their names are explained herein the section "9. What are the different coordinate spaces? Secondly, to avoid confusion, in OpenGL the term "viewport" refers to the part of the window that you're rendering to, and it's in window coordinates.

You asked how to "calculate where to draw objects on screen". What you need to do is define a transformation a 4x4 matrix that maps from one coordinate system into another. Your 2D world is given in world coordinates, so you need to define a matrix that transforms world coordinates into NDCs, i.

In your shaders you then simply multiply your vertices with this projection matrix, and you get NDCs. As for the perspective projection, it's not clear what you want to do, but you should experiment with the perspective and lookat functions in glm.

To be clear, you define vertices in whatever coordinate system you want which is called the world coordinate systemand simply draw these vertices. Your vertex shader's job is to apply the transformation you defined. Also note that you specified a square, and typically that's not what you want. Monitors and most windows are not square, so if you map that square onto a typical viewport, you would get a distorted view of your world.

You need to factor in the aspect ratio width:height of the viewport. I've tried to explain that here. Nowadays, programmers are expected and encouraged to manage both the model-view and the projection matrices themselves, since you need them in your shaders. I highly recommend glmit's header-only thus very easy to integrate, and has nice syntax that mirrors GLSL. Use glOrtho on the projection matrix and then draw normally. For your example, Im guessing you want glOrtho 0,0,-1, 1 which would give you a viewport units in width and units in height.

Place your scene in whatever coordinate system you want. Just set up the view and projection correct in glm. Actually, you should not need any graphics pipeline implementation details - so there could be a bad design decision in your game engine. Learn more. Asked 6 years, 11 months ago. Active 3 years, 4 months ago. Viewed 25k times. I'm currently working on implementing an OpenGL powered renderer into a 2D game engine.

Active Oldest Votes. Andreas Haferburg Andreas Haferburg 4, 1 1 gold badge 22 22 silver badges 48 48 bronze badges.As far as OpenGL is concerned, there is no camera. More specifically, the camera is always located at the eye space coordinate 0.

This is commonly referred to as the viewing transformation. In practice this is mathematically equivalent to a camera transformation but more efficient because model transformations and camera transformations are concatenated to a single matrix. For example to position a light source in world space it most be positioned while the viewing transformation and only the viewing transformation is applied to the MODELVIEW matrix.

OpenGL doesn't provide an interface to do this using a camera model. However, the GLU library provides the gluLookAt function, which takes an eye position, a position to look at, and an up vector, all in object space coordinates.

Meddlemonkey extension installationThis function computes the inverse camera transform according to its parameters and multiplies it onto the current matrix stack. Think of the projection matrix as describing the attributes of your camera, such as field of view, focal length, fish eye lens, etc.

Think of the ModelView matrix as where you stand with the camera and the direction you point it. The game dev FAQ has good information on these two matrices. Read Steve Baker's article on projection abuse. This article is highly recommended and well-written. It's helped several new OpenGL programmers. A simple method for zooming is to use a uniform scale on the ModelView matrix. However, this often results in clipping by the zNear and zFar clipping planes if the model is scaled too large.

For example, your program might maintain a zoom factor based on user input, which is a floating-point number. When set to a value of 1. Larger values result in greater zooming or a more restricted field of view, while smaller values cause the opposite to occur.

Code to create this effect might look like:. Instead of gluPerspectiveyour application might use glFrustum. This gets tricky, because the left, right, bottom, and top parameters, along with the zNear plane distance, also affect the field of view. Assuming you desire to keep a constant zNear plane distance a reasonable assumptionglFrustum code might look like this:. The "camera" or viewpoint is at 0. When you turn this into a vector [0 0 0 1] and multiply it by the inverse of the ModelView matrix, the resulting vector is the object-space location of the camera.

You'll need to compute the inverse with your own code. For example, to orbit an object placed somewhere on the Y axis, while continuously looking at the origin, you might do this:.

If you insist on physically orbiting the camera position, you'll need to transform the current camera position vector before using it in your viewing transformations. In either event, I recommend you investigate gluLookAt if you aren't using this routine already. First, compute a bounding sphere for all objects in your scene.

This should provide you with two bits of information: the center of the sphere let c. Next, choose a value for the zNear clipping plane. General guidelines are to choose something larger than, but close to 1. So, let's say you set. This approach should center your objects in the middle of the window and stretch them to fit i. If your window isn't square, compute left, right, bottom, and top, as above, and put in the following logic before the call to glOrtho :.

The above code should position the objects in your scene appropriately. If you intend to manipulate i. Assuming you are using gluPerspective on the Projection matrix stack with zNear and zFar as the third and fourth parameters, you need to set gluLookAt on the ModelView matrix stack, and pass parameters so your geometry falls between zNear and zFar.

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