I'm a bit confused about the differences between these matrices. I don't know if I understood how them work.
The ModelView matrix is the combination of the Model and the View Matrix where the View matrix is the one that specifies features like location and orientation of my camera while the Model matrix is the one that specifies the position's frame of the primitives that I'm going to draw.
The projection matrix specifies other features of the camera like clip space , projection method and field of view.
Is that right ?
Thanks
It's a little confusing. The View Matrix moves the entire world to be relative the the camera. A Camera matrix (the inverse of the view matrix) puts the camera in the world.
There are multiple ways to make a view matrix. While it's common to use a "lookAt" function that directly generates a view matrix. It's actually more common to put your camera in the world just like any other object. You'd have a scene hierarchy and put everything in the world, rocks, trees, houses, cars, people, camera. You then compute the world matrix for the camera which is the "camera matrix" you then take the inverse of that and you get a "view matrix". This is how pretty much all 3d engines work, Unity, Unreal, Maya, 3DSMax, etc.
The projection matrix decides things like field of view (a wide angle lens or a telephoto lens). It also helps define the aspect so that you can render to a rectangular area and it helps defined what distances in front of the camera are visible.
Here's an article on projection matrices. Here's another on camera and view matrices
Related
for a personal project, I've created a simple 3D engine in python using as little libraries as possible. I did what I wanted - I am able to render simple polygons, and have a movable camera. However, there is a problem:
I implemented a simple flat shader, but in order for it to work, I need to know the camera location (the camera is my light source). However, the problem is that I have no way of knowing the camera's location in the world space. At any point, I am able to display my view matrix, but I am unsure about how to extract the camera's location from it, especially after I rotate the camera. Here is a screenshot of my engine with the view matrix. The camera has not been rotated yet and it is very simple to extract its location (0, 1, 4).
However, upon moving the camera to a point between the X and Z axes and pointing it upwards (and staying at the same height), the view matrix changes to this:
It is obvious now that the last column cannot be taken directly to determine the camera location (it should be something like (4,1,4) on the last picture).
I have tried a lot of math, but I can't figure out the way to determine the camera x,y,z location from the view matrix. I will appreciate any and all help in solving this, as it seems to be a simple problem, yet whose solution eludes me. Thank you.
EDIT:
I was advised to transform a vertex (0,0,0,1) by my view matrix. This, however, does not work. See the example (the vertex obviously is not located at the printed coordinates):
Just take the transform of the vector (0,0,0,1) with the modelview matrix: Which is simply the rightmost column of the modelview matrix.
EDIT: #ampersander: I wonder why you're trying to work with the camera location in the first place, if you assume the source of illumination to be located at the camera's position. In that case, just be aware, that in OpenGL there is no such thing as a camera, and in fact, what the "view" transform does, is move everything in the world around so that where you assume your camera to be ends up at the coordinate origin (0,0,0).
Or in other words: After the modelview transform, the transformed vertex position is in fact the vector from the camera to the vertex, in view space. Which means that for your assumed illumination calculation the direction toward the light source, is the negative vertex position. Take that, normalize it to unit length and stick it into the illumination term.
I have been wondering how I can combine two methods of rendering in a way that the rasterized on-screen shape serves as a canvas for ray-march based rendering in fragment shader.
Take these beautiful examples: https://www.shadertoy.com/view/XsjXRm or https://www.shadertoy.com/view/MtXSzS
The visible part of them can be roughly represented as sphere. Now what I'd like to do is to put say two spheres into some place in the world and run the regular rasterization pass. The rasterization will yield which pixels are occupied by the models and for those pixels I'd like to actually run the shadertoy ray-marching algorithms to get the desired look (my two spheres look like shadertoy "spheres" in the examples above).
Is this something doable?
P.S. I know rasterization and matrix/spaces transformation quite well, but I have very vague understanding of how ray-marching works. Pardon my ignorance.
This is definitely possible.
The idea is to use the same camera for ray tracing and for rasterization.
You can get the camera's position from the camera matrix in the fragment shader and you can get the camera's direction by subtracting the fragments position from the camera's position and normalizing it.
This way the rays are only cast from the camera to the visible fragments.
I am trying to solve a question related to transformation of coordinates in 3-D space but not sure how to approach it.
Lets a vertex point named P is drawn at the origin with a 4x4 transformation matrix. It's then views through a camera that's positioned with a model view matrix and then through a simple projective transform matrix.
How do I calculate the new screen coordinates of P' (x,y,z)?
Before explain of pipeline, you need to know is how pipeline do process to draw on screen.
Everything between process is just matrix multiplication with vector
Model - World - Camera - Projection(or Nomalized Coordinate) - Screen
First step, we call it 'Model Space' because of (0,0,0) is based in model.
And we need to move model space to world space because of we are gonna place model to world so
we need to do transform will be (translate, rotation, scale)TRS * Model(Vector4) because definition of world transform will be different
After do it, model place in world.
Thrid, need to render on camrea space because what we see is through the camera. in world, camera also has position, viewport size and
rotation.. It needs to project from the camera. see
General Formula for Perspective Projection Matrix
After this job done, you will get nomalized coordinate which is Techinically 0-1 coordinates.
Finaly, Screen space. suppose that we are gonna make vido game for mobile. mobile has a lot of screen resolution. so how to get it done?
Simple, scale and translate to get result in screen space coordinate. Because of origin and screen size is different.
So what you are tring to do is 'step 4'.
If you want to get screen position P1 from world, formula will be "Screen Matrix * projection matrix * Camera matrix * P1"
If you want to get position from camera space it would be "Screen Matrix * projection matrix * P1".
There are useful links to understand matrix and calculation so see above links.
https://answers.unity.com/questions/1359718/what-do-the-values-in-the-matrix4x4-for-cameraproj.html
https://www.google.com/search?q=unity+camera+to+screen+matrix&newwindow=1&rlz=1C5CHFA_enKR857KR857&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjk5qfQ18DlAhUXfnAKHabECRUQ_AUIEigB&biw=1905&bih=744#imgrc=Y8AkoYg3wS4PeM:
I'm currently working on a project that uses shadowtextures to render shadows.
It was pretty easy for spotlights, since only 1 texture in the direction of the spotlight is needed, but its a little more difficult since it needs either 6 textures in all directions or 1 texture that somehow renders all the obects around the pointlight.
And thats where my problem is. How can I generate a Projection matrix that somehow renders all the object in a 360 angle around the pointlight?
Basicly how do create a fisheye (or any other 360 degree camera) vertex shader?
How can I generate a Projection matrix that somehow renders all the object in a 360 angle around the pointlight?
You can't. A 4x4 projection matrix in homogenous space cannot represent any operation which would result in bending the edges of polygons. A straight line stays a straight line.
Basicly how do create a fisheye (or any other 360 degree camera) vertex shader?
You can't do that either, at least not in the general case. And this is not a limit of the projection matrix in use, but a general limit of the rasterizer. You could of course put the formula for fisheye distortion into the vertex shader. But the rasterizer will still rasterize each triangle with straight edges, you just distort the position of the corner points of each triangle. This means that it will only be correct for tiny triangles covering a single pixel. For larger triangles, you completely screw up the image. If you have stuff like T-joints, this even results in holes or overlaps in objects which actually should be perfectly closed.
It was pretty easy for spotlights, since only 1 texture in the direction of the spotlight is needed, but its a little more difficult since it needs either 6 textures in all directions or 1 texture that somehow renders all the obects around the pointlight.
The correct solution for this would be using a single cube map texture, with provides 6 faces. In a perfect cube, each face can then be rendered by a standard symmetric perspective projection with a field of view of 90 degrees both horizontally and vertically.
In modern OpenGL, you can use layered rendering. In that case, you attach each of the 6 faces of the cube map as a single layer to an FBO, and you can use the geometry shader to amplify your geomerty 6 times, and transform it according to the 6 different projection matrices, so that you still only need one render pass for the complete shadow map.
There are some other vendor-specific extensions which might be used to further optimize the cube map rendering, like Nvidia's NV_viewport_swizzle (available on Maxwell and newer GPUs), but I only mention this for completness.
After modifying my main camera's projection matrix, the ScreenPointToRay method that use ray casting begin to fail, so the method which detect touched object use raycast fail too. Is there any way to use ScreenPointToRay method with a custom camera projection matrix?
If you made a custom camera projection matrix, then you probably know where is the user pointing to, how about casting a ray yourself and not using the helper?
If you have a problem with translation of the cursor to world position, there is a good approximation - take four angles on approxiamtely the edges of your camera's viewpoint (top of the viewport horizontal center, left of the viewport vertical center etc.) and interpolate between them.