I have a situation that I'm not realy sure how I can handle. I have an openGl object of about 20k vertices, and I need to offer the user the possibility to select any one of these vertices (let's say with a smallest margin of error possible). Now here is what I want to do in order to do this:
Next to the 3D canvas of the object, I also offer the user 3 'slices' done by the planes x=0; y=0 and z=0. Say for the simplest example for a sphere these would be 3 circles, correponding to 'cutting' out one of the dimensions. Now let's take the z=0 one for the purpose of the example. When the user clicks on a point say (x_circle, y_circle) i would like to get the actual point in the 3d representation where he clicked. The z would be 0 of course but I can't figure out a way to get the x and y. I can easily translate that (x_circle, y_circle) -> (x_screen, y_screen) which would have the same result as a click on the canvas at those coordinates, but I need to find a way to translate that into the (x, y, 0) coordinate in 3D view.
The same thing would need to be done with x=0, y=0 but I think if I can understand/implement a way for z=0 I can just apply more or less the same solution with an added rotation over something. If anyone can help with any examples/code or even math behind this it would help a lot because at the moment I'm not really sure how to proceed.
When the user clicks, you can render the vertices using GL.POINTS (with a certain size, if you like) to an off-screen buffer using a shader that renders each vertex' index into RGBA. Then you read back the pixel on the mouse position and see what index it is.
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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'm making a 3D monster maker. I recently added a feature to flip parts along the x and y axes, this works perfectly fine on its own, however, I also have a feature that allows users to combine parts (sets flags, doesn't combine mesh), this means that simply flipping the individual objects won't flip the "shape" of the combined object. I have had two ideas of how to do this which didn't work and I'll list them below. I have access to the origin of the objects and the centre of mass of all instances that are combined - the 0, 0, 0 point on a theoretical number plane
In these examples we're flipping across the y axis, the axis plane is X = width, Y = height, Z = depth
Attempt #1 - Simply flipping the individual object's X scale, getting the X distance from the centreMass and taking that from the centreMass for position, this works when the direction of the object is (0, 0, 1) and the right (1, 0, 0) or (-1, 0, 0), in any other direction X isn't the exact "left/right" of the object. Here's a video to clarify: https://youtu.be/QXdEF4ScP10
code:
modelInstance[i].scale.x *= -1;
modelInstance[i].basePosition.set(centre.x - modelInstance[i].distFromCentre.x, modelInstance[I].basePosition.y, modelInstance[I].basePosition.z);
modelInstance[i].transform.set(modelInstance[i].basePosition, modelInstance[i].baseRotation, modelInstance[i].scale);
Attempt #2 - Rotate the objects Y180° around the centreMass and then flip their z value. As far as I understand, this is a solution, but I don't think I can do this. The way to rotate an object around a point AFAIK involves transforming the matrix to the point, rotating it, and then translating it back which I can't use. Due to the ability to rotate, join, flip, and scale objects I keep the rotation, position, and scale completely separate because issues with scaling/rotating and movement occur. I have a Vector3 for the position, a matrix for the rotation, and a Vector3 for the scale, whenever I change any of these I use object.transform.set(position, matrix.getRotation(), scale); So when I attempt to do this method (translating rotation matrix to point etc) the objects individually flip but remain in the same place, translating the objects transform matrix has weird results and doesn't work. Video of both variations: https://youtu.be/5xzTAHA1vCU
code:
modelInstance[i].scale.z *= -1;
modelInstance[i].baseRotationMatrix.translate(modelInstance[i].distFromCentre).rotate(Vector3.Y, 180).translate( modelInstance[i].distFromCentre.scl(-1));
modelInstance[i].transform.set(modelInstance[i].basePosition, modelInstance[i].baseRotation, modelInstance[i].scale);
Ok, since no one else has helped I'll give you some code that you can either use directly or use to help you alter your code so that it is done in a similar way.
First of all, I tend to just deal with matrices and pass them to shaders as projection matrices, ie. I don't really know what modelInstance[i] is, is it an actor (I never use them), or some other libgdx class? Whatever it is, if you do use this code to generate your matrices, you should be able to overwrite your modelInstance[i] matrix at the end of it. If not, maybe it'll give you pointers on how to alter your code.
First, rotate or flip your object with out any translation. Don't translate or scale first, because when you rotate you'll also rotate the translation you've performed. I use this function to generate a rotation matrix, it rotates around the y axis first, which I think is way better then other rotation orders. Alternatively you could create an identity matrix and use the libgdx rotation functions on it to create a similar matrix.
public static void setYxzRotationMatrix(double xRotation, double yRotation, double zRotation, Matrix4 matrix)
{
// yxz - y rotation performed first
float c1=(float)Math.cos(yRotation);
float c2=(float)Math.cos(xRotation);
float c3=(float)Math.cos(zRotation);
float s1=(float)Math.sin(yRotation);
float s2=(float)Math.sin(xRotation);
float s3=(float)Math.sin(zRotation);
matrix.val[0]= -c1*c3 - s1*s2*s3; matrix.val[1]=c2*s3; matrix.val[2]=c1*s2*s3-c3*s1; matrix.val[3]=0;
matrix.val[4]= -c3*s1*s2 + c1*s3; matrix.val[5]=c2*c3; matrix.val[6]=c1*c3*s2+s1*s3; matrix.val[7]=0;
matrix.val[8]= -c2*s1; matrix.val[9]=-s2; matrix.val[10]=c1*c2; matrix.val[11]=0;
matrix.val[12]=0; matrix.val[13]=0; matrix.val[14]=0; matrix.val[15]=1.0f;
}
I use the above function to rotate my object to the correct orientation, I then translate it to the correct location, then multiply it by the cameras matrix and scale as the final operation. This will definitely work if you can do it that way, but I just pass my final matrix to the shader. I'm not sure how you use your matrices. If you want to flip the model using the scale, you should try it immediately after the rotation matrix has been created. I'd recommend getting it working without flipping with scale first, so you can test both matrix.scl() and matrix.scale() as the final step. Off hand, I'm not sure which scale function you'll need.
Matrix4 matrix1;
setYxzRotationMatrix(xRotationInRadians, yRotationInRadians, zRotationInRadians,matrix1);
//matrix1 will rotate your model to the correct orientation, around the origin.
//here is where you may wish to use matrix1.scl(-1,1,1) or matrix1.scale(-1,1,1).
//get anchor position here if required - see notes later
//now translate to the correct location, I alter the matrix directly so I know exactly
what is going on. I think matrix1.trn(x, y, z) would do the same.
matrix1.val[12]=x;
matrix1.val[13]=y;
matrix1.val[14]=z;
//Combine with your camera, this may be part of your stage or scene, but I don't use
//these, so can't help.
Matrix4 matrix2;
//set matrix2 to an identity matrix, multiply it by the cameras projection matrix, then
//finally with your rotation/flip/transform matrix1 you've created.
matrix2.idt().mul(yourCamera.combined).mul(matrix1);
matrix2.scale(-1,1,1); //flipping like this will work, but may screw up any anchor
//position if you calculated one earlier.
//matrix2 is the final projection matrix for your model. ie. you just pass that matrix
to a shader and it should be used to multiply with each vertex position vector to create
the fragment positions.
Hopefully you'll be able to adapt the above to your needs. I suggest trying one operation at a time and making sure your next operation doesn't screw up what you've already done.
The above code assumes you know where you want to translate the model to, that is you know where the center is going to be. If you have an anchor point, lets say -3 units in the x direction, you need to find out where that anchor point has been moved to after the rotation and maybe flip. You can do that by multiplying a vector with matrix1, I'd suggest before any translation to the correct location.
Vector3 anchor=new vector3(-3,0,0);
anchor.mul(matrix1); //after this operation anchor is now set to the correct location
//for the new rotation and flipping of the model. This offset should
//be applied to your translation if your anchor point is not at 0,0,0
//of the model.
This can all be a bit of a pain, particularly if you don't like matrices. It doesn't help that everything is done in a different way to what you've tried so far, but this is the method I use to display all the 3D models in my game and will work if you can adapt it to your code. Hopefully it'll help someone anyway.
Here is the deal, I'm programming a 2D framework/game engine with opengl ES. I am using VBOs and an ortho projection to draw an arrangement of sprites throughout the screen (as part of the testing), and everything was going nice and smooth until I had to play with translations and rotations. The specific problem I am having is that when I apply a translation with glTranslatef() prior to the rotation, the function does not only move the sprite, but also my origin, messing up my whole transformation. I am 100% sure it is working this way, because I used glTranslatef() to move to the right and bottom the sprite half of the size of the screen (yes, my origin is in the top left) and then apply a constant rotation and the thing just keeps mooving in a circular path around the center of the screen (actually rotating, but not as I expect.
If you want some code, here we go:
gl.glTranslatef(-(x+width/2), -(y+height/2), -layer);
gl.glRotatef(angle, 0.0f, 0.0f, -1.0f);
gl.glTranslatef(x+width/2, y+height/2, layer);
In this fragment of code, x and y are the position of the sprite, height and width are the size of the sprite, angle the angle of rotation, and layer just a form of organizing the sprites into several layers, pretty straight forward, right?
Again, my problem is that glTranslatef(); is moving both, the sprite and the origin, am I doing something wrong or misunderstanding something about the translation?
Thanks in advance.
you might need to use glPushMatrix and glPopMatrix since anything you do after those translations and rotations will be affected by them
but what you are describing is actually how it works, if you use a translate, that sort of becomes your new origin because once you do a translate, everything after that is affected by that translate, thats why you need to push and pop, so that you can go, push -> translate object and/or rotate -> pop, and then you can go about with whatever other translations you need to do without having that previous translation affecting everything else
its a bit confusing at first but google around and you'll see how to use them properly
http://www.khronos.org/opengles/sdk/1.1/docs/man/glPushMatrix.xml
I think you misunderstood how matrices work in openGL. When you do a matrix operation such as glRotatef and glTranslatef the matrices are being multiplied, resulting in affecting the base vectors.. For instance, let's say we are only drawing a point that starts at (0,0,0). If you call translate(1,0,0) the point will be in (1,0,0), after that you call rotate(90, 0, 0, 1) and your point will be on the same place as before but rotated. Now the last call is translate(-1,0,0) and your point is at (1,-1,0) (and not where you started)!
And that is what you did in your "fragment of code". The thing is you did not specify what you really want to do and how do you define your verices is relative as well.. If you want something like a view with some image that you want to control in sense of changing the position and rotation, you might want to create a square vertex buffer with values from -1 to 1 in both dimensions (or (-width/2, -height/2) to (width/2, height/2)). In this case the base center of your object is in (0,0,0) and that is probably the point you want to rotate it around (or am I wrong here?). So when you want to define the position of the object with origin point, you will need to write translatef(x+width/2,y+height/2,..).
As for the whole process of drawing in this case: If you want the origin to be at (x,y,z), with a (width, height) and rotated by (angle) here is the sequence
glTranslatef(x,y,z)
glTranslatef(width/2,height/2,0)
glScalef(width/2,height/2, 1) //only if verices defined at (-1,1)
glRotatef(angle, 0, 0, 1)
Do note in this case that since you rotate the object around its center its origin will not be at (x,y,z) anymore.
In general I would suggest to stay away from glRotate, glTranslate and glScale if possible. They tend to make things very nasty. So another way is to construct a matrix directly from base vectors: With little math you can compute all 4 points of your "square view" based on parameters such as origin, width, height and rotation.. The 4 points being (A-origin), (B-lower left point), (C-lower right point), (D-upper right point) your base vectors are (B-A), (D-A) and normalized(dotProduct((B-A), (D-A))) this 3 vectors can be inserted int top left 3x3 matrix of the GL matrix (witch is 4x4 or float[16]) and they represent both, rotation and scale so all you need to add is the translation part (just google around a bit for this approach).
I'm creating an HTML5 canvas 3D renderer, and I'd say I've gotten pretty far without the help of SO, but I've run into a showstopper of sorts. I'm trying to implement backface culling on a cube with the help of some normals calculations. Also, I've tagged this as WebGL, as this is a general enough question that it could apply to both my use case and a 3D-accelerated one.
At any rate, as I'm rotating the cube, I've found that the wrong faces are being hidden. Example:
I'm using the following vertices:
https://developer.mozilla.org/en/WebGL/Creating_3D_objects_using_WebGL#Define_the_positions_of_the_cube%27s_vertices
The general procedure I'm using is:
Create a transformation matrix by which to transform the cube's vertices
For each face, and for each point on each face, I convert these to vec3s, andn multiply them by the matrix made in step 1.
I then get the surface normal of the face using Newell's method, then get a dot-product from that normal and some made-up vec3, e.g., [-1, 1, 1], since I couldn't think of a good value to put in here. I've seen some folks use the position of the camera for this, but...
Skipping the usual step of using a camera matrix, I pull the x and y values from the resulting vectors to send to my line and face renderers, but only if they have a dot-product above 0. I realize it's rather arbitrary which ones I pull, really.
I'm wondering two things; if my procedure in step 3 is correct (it most likely isn't), and if the order of the points I'm drawing on the faces is incorrect (very likely). If the latter is true, I'm not quite sure how to visualize the problem. I've seen people say that normals aren't pertinent, that it's the direction the line is being drawn, but... It's hard for me to wrap my head around that, or if that's the source of my problem.
It probably doesn't matter, but the matrix library I'm using is gl-matrix:
https://github.com/toji/gl-matrix
Also, the particular file in my open source codebase I'm using is here:
http://code.google.com/p/nanoblok/source/browse/nb11/app/render.js
Thanks in advance!
I haven't reviewed your entire system, but the “made-up vec3” should not be arbitrary; it should be the “out of the screen” vector, which (since your projection is ⟨x, y, z⟩ → ⟨x, y⟩) is either ⟨0, 0, -1⟩ or ⟨0, 0, 1⟩ depending on your coordinate system's handedness and screen axes. You don't have an explicit "camera matrix" (that is usually called a view matrix), but your camera (view and projection) is implicitly defined by your step 4 projection!
However, note that this approach will only work for orthographic projections, not perspective ones (consider a face on the left side of the screen, facing rightward and parallel to the view direction; the dot product would be 0 but it should be visible). The usual approach, used in actual 3D hardware, is to first do all of the transformation (including projection), then check whether the resulting 2D triangle is counterclockwise or clockwise wound, and keep or discard based on that condition.
I'm a fresh in cocos3d, now I have a problem.
In cocos3d, I want to rotate a node. I got the angles in x axis, y axis, z axis, then I used the property:rotation to rotate, like this:
theNodeToBeRotated.rotation = cc3v(x,y,z);
But I found out it didn't rotate as I expected, because the document said the rotate order is y-x-z.
I want to change the order to x-y-z. Can anyone let me know how?
You might need to clarify further regarding the following: "it didn't rotate as I expected"
OpenGL ES (and ergo, cocos3D) uses the y-axis as up so the rotation order is still x-y-z. If you are importing a model, you then need to take into account the 3D editor's co-ordinate system and adapt accordingly.
If you are not used to working with three-dimensional representations, the leap from 2D to 3D can be a significant hurdle. Within Cocos3D:
the x-axis is positive on the right and negative on the left
the y-axis is positive upwards and negative downwards
the z-axis is positive moving towards you and negative moving away from you
Envisage those three lines of axis, or even better, a piece of string.
If you are rotating around the x-axis, hold the string horizontally from left to right: the object would rotating towards you or away from you.
If you are rotating around the y-axis, hold the string vertically from feet to head: the object would rotate as if like a revolving door.
If you are rotating around the z-axis, hold one end close to your chest and the other end as far away as possible: the object would rotate similar to a clock face.
-- Update
I heavily wouldn't recommend changing the rotation order as it is the OpenGL standard to use Y-X-Z. If you wish to modify it, take a look at CC3GLMatrixMath and look for kmMat4RotationYXZ - there is also kmMat4RotationZYX. If you want to have X-Y-Z, you would need to construct your own rotation matrix and update accordingly in CC3GLMatrix and CC3GLMatrixMath.
As a reference, you also have the OpenGL Red book - it should have some suggestions for you.