I have been playing around with OpenGL and matrix operations and I understand the concept of P * V * M but I cannot understand why changing the Z position of the 'camera' does not have the effect of zooming.
When using a perspective projection, changing the Z of the camera has the effect of zoom (as i'd expect).
glm::mat4 Projection = glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100.0f);
glm::mat4 View = glm::lookAt(
glm::vec3(0,0,3), // changing 3 to 8 will zoom out
glm::vec3(0,0,0),
glm::vec3(0,1,0)
);
glm::mat4 Model = glm::mat4(1.0f);
gml::mat4 MVP = Projection * View * Model;
However, when I use an ortho projection, changing the 3 to 8 or anything it does not have the effect of zooming out. I know they are very different projections but I am looking for an explanation (the math behind why it doesn't work would be especially helpful).
glm::mat4 Projection = glm::ortho(
0.0f,
128.0f,
0.0f,
72.0f,
0.0f,
100.0f
);
That's how orthographic projections work. Let's start with a perspective transform:
You get the projection of an object by following a straight line to the camera:
If you move the camera closer, then you will see that the projected area increases:
Orthographic projections work differently. You get the projection by following a straight line that is perpendicular to the image plane:
And obviously, the size of the projected area does not depend on how far the camera is away from the object. That's because the projection lines will always be parallel and preserve the size of the object in the two directions of the image plane.
When you change the Z coordinate from 3 to 8, you're not actually zooming out, you're just moving the camera farther away. You can zoom out without moving the camera by changing the first parameter for glm::perspective.
An orthographic camera doesn't have a location (you can think of it as infinitely far away), so it's not possible to "move" an orthographic camera in the same way. You can zoom out by changing the bounds passed to glm::ortho. Simply pass larger numbers to glm::ortho.
Look at what happens, when you move perspective camera:
Here: (xe, ye, ze) - point in eye coordinate system. (xp, yp, zp) - projection of that point
n - distance to near plane
t - distance to top plane of frustrum
You can see, that when you approach camera, xp and yp will grow.
In contrast, changing z position of orthogonal camera won't effect xp and yp, but still will effect zp, thus will change value in depth buffer.
Related
I am trying to orient a 3d object at the world origin such that it doesn't change its position wrt camera when I move the camera OR change its field of view. I tried doing this
Object Transform = Inverse(CameraProjectionMatrix)
How do I undo the perspective divide because when I change the fov, the object is affected by it
In detail it looks like
origin(0.0, 0.0, 0.0, 1.0f);
projViewInverse = Camera.projViewMatrix().inverse();
projectionMatrix = Camera.projViewMatrix();
projectedOrigin = projectionMatrix * origin;
topRight(0.5f, 0.5f, 0.f);
scaleFactor = 1.0/projectedOrigin.z();
scale(scaleFactor,scaleFactor,scaleFactor);
finalMatrix = projViewInverse * Scaling(w) * Translation(topRight);
if you use gfx pipeline where positions (w=1.0) and vectors (w=0.0) are transformed to NDC like this:
(x',y',z',w') = M*(x,y,z,w) // applying transforms
(x'',y'') = (x',y')/w' // perspective divide
where M are all your 4x4 homogenyuous transform matrices multiplied in their order together. If you want to go back to the original (x,y,z) you need to know w' which can be computed from z. The equation depends on your projection. In such case you can do this:
w' = f(z') // z' is usually the value encoded in depth buffer and can obtained
(x',y') = (x'',y'')*w' // screen -> camera
(x,y) = Inverse(M)*(x',y',z',w') // camera -> world
However this can be used only if you know the z' and can derive w' from it. So what is usually done (if we can not) is to cast ray from camera focal point through the (x'',y'') and stop at wanted perpendicular distance to camera. For perspective projection you can look at it as triangle similarity:
So for each vertex you want to transform you need its projected x'',y'' position on the znear plane (screen) and then just scale the x'',y'' by the ratio between distances to camera focal point (*z1/z0). Now all we need is the focal length z0. That one dependss on the kind of projection matrix you use. I usually encounter 2 versions when you are in camera coordinate system then point (0,0,0) is either the focal point or znear plane. However the projection matrix can be any hence also the focal point position can vary ...
Now when you have to deal with aspect ratio then the first method deals with it internally as its inside the M. The second method needs to apply inverse of aspect ratio correction before conversion. So apply it directly on x'',y''
I have fov angle = 60, width = 640 and height = 480 of window, near = 0.01 and far = 100 planes and I get projection matrix using glm::perspective()
glm::perspective(glm::radians(fov),
width / height,
zNear,
zFar);
It works well.
Then I want to change projection type to orthogonal, but I don't knhow how to compute input parameters of glm::ortho() properly.
I've tried many ways, but problem is after switching to orthographic projection size of model object become another.
Let I have a cube with center in (0.5, 0.5, 0.5) and length size 1, and camera with mEye in (0.5, 0.5, 3), mTarget in (0.5, 0.5, 0.5) and mUp (0, 1, 0). View matrix is glm::lookAt(mEye, mTarget, mUp)
With perspective projection it works well. With glm::ortho(-width, width, -height, height, zNear, zFar) my cube became a small pixel in the center of window.
Also I've tried implement this variant How to switch between Perspective and Orthographic cameras keeping size of desired object
but result is (almost) same as before.
So, first question is how to compute ortho parameters for saving original view size of object/position of camera?
Also, zooming with
auto distance = glm::length(mTarget - mEye)
mEye = mTarget - glm::normalize(mTarget - mEye) * distance;
have no effect with ortho. Thus second question is how to implement zooming in case of ortho projection?
P.s.
I assume I understand ortho correctly. Proportions of model doesn't depends on depth, but nevertheless I still can decide where camera is for setting size of model properly and using zoom. Also I assume it is simple and trivial task, for example, when developing a 3D-viewer/editor/etc. Correct me if it is not.
how to compute ortho parameters for saving original view size of object/position of camera?
At orthographic projection the 3 dimensional scene is parallel projection to the 2 dimensional viewport.
This means that the objects, which are projected on the viewport always have the same size, independent of their depth (distance to the camera).
The perspective projection describes the mapping from 3D points in the world as they are seen from of a pinhole camera, to 2D points of the viewport.
This means an object which is projected on the viewport becomes smaller, by its depth.
If you switch form perspective to orthographic projection only the objects in 1 plane, which is planar (parallel) to the viepwort, and keeps its depth. Note, a plane is 2 dimensional and has no "depth". This cause that a 3 dimensional object never can "look" the same, when the projection is switched. But a 2 dimensional billboard can keep it's size.
The ration of depth an size at perspective projection is linear and can be calculated. It depends on the field of view angle only:
float ratio_size_per_depth = atan(glm::radians(fov / 2.0f) * 2.0f;
If you want to set up an orthographic projection, which keeps the size for a certain distance (depth) then you have to define the depth first:
e.g. Distance to the target point:
auto distance = glm::length(mTarget - mEye);
the projection can be set up like this:
float aspect = width / height
float size_y = ratio_size_per_depth * distance;
float size_x = ratio_size_per_depth * distance * aspect;
glm::mat4 orthProject = glm::ortho(-size_x, size_x, -size_y, size_y, 0.0f, 2.0f*distance);
how to implement zooming in case of ortho projection?
Scale the XY components of the orthographic projection:
glm::mat4 orthProject = glm::ortho(-size_x, size_x, -size_y, size_y, 0.0f, 2.0f*distance);
float orthScale = 2.0f;
orthProject = glm::scale(orthProject, glm::vec3(orthScale, orthScale, 1.0f));
Set a value for orthScale which is > 1.0 for zoom in and a value which is < 1.0 for zoom out.
Can someone tell me how to make triangle vertices collide with edges of the screen?
For math library I am using GLM and for window creation and keyboard/mouse input I am using GLFW.
I created perspective matrix and simple array of triangle vertices.
Then I multiplied all this in vertex shader like:
gl_Position = projection * view * model * vec4(pos, 1.0);
Projection matrix is defined as:
glm::mat4 projection = glm::perspective(
45.0f, (GLfloat)screenWidth / (GLfloat)screenHeight, 0.1f, 100.0f);
I have fully working camera and projection. I can move around my "world" and see triangle standing there. The problem I have is I want to make sure that triangle collide with edges of the screen.
What I did was disable camera and only enable keyboard movement. Then I initialized translation matrix as glm::translate(model, glm::vec3(xMove, yMove, -2.5f)); and scale matrix to scale by 0.4.
Now all of that is working fine. When I press RIGHT triangle moves to the right when I press UP triangle moves up etc... The problem is I have no idea how to make it stop moving then it hits edges.
This is what I have tried:
triangleRightVertex.x is glm::vec3 object.
0.4 is scaling value that I used in scaling matrix.
if(((xMove + triangleRightVertex.x) * 0.4f) >= 1.0f)
{
cout << "Right side collision detected!" << endl;
}
When I move triangle to the right it does detect collision when x of the third vertex(bottom right corner of triangle) collides with right side but it goes little bit beyond before it detects. But when I tried moving up it detected collision when half of the triangle was up.
I have no idea what to do here can someone explain me this please?
Each of the vertex coordinates of the triangle is transformed by the model matrix form model space to world space, by the view matrix from world space to view space and by the projection matrix from view space to clip space. gl_Position is the Homogeneous coordinate in clip space and further transformed by a Perspective divide from clip space to normalized device space. The normalized device space is a cube, with right, bottom, front of (-1, -1, -1) and a left, top, back of (1, 1, 1).
All the geometry which is in this (volume) cube is "visible" on the viewport.
In clip space the clipping of the scene is performed.
A point is in clip space if the x, y and z components are in the range defined by the inverted w component and the w component of the homogeneous coordinates of the point:
-w <= x, y, z <= w
What you want to do is to check if a vertex x coordinate of the triangle is clipped. SO you have to check if the x component of the clip space coordinate is in the view volume.
Calculate the clip space position of the vertices on the CPU, as it does the vertex shader.
The glm library is very suitable for things like that:
glm::vec3 triangleVertex = ... ; // new model coordinate of the triangle
glm::vec4 h_pos = projection * view * model * vec4(triangleVertex, 1.0);
bool x_is_clipped = h_pos.x < -h_pos.w || h_pos.x > h_pos.w;
If you don't know how the orientation of the triangle is transformed by the model matrix and view matrix, then you have to do this for all the 3 vertex coordinates of the triangle-
The game is a top-down 2D space ship game -- think of "Asteroids."
Box2Dx is the physics engine and I extended the included DebugDraw, based on OpenTK, to draw additional game objects. Moving the camera so it's always centered on the player's ship and zooming in and out work perfectly. However, I really need the camera to rotate along with the ship so it's always facing in the same direction. That is, the ship will appear to be frozen in the center of the screen and the rest of the game world rotates around it as it turns.
I've tried adapting code samples, but nothing works. The best I've been able to achieve is a skewed and cut-off rendering.
Render loop:
// Clear.
Gl.glClear(Gl.GL_COLOR_BUFFER_BIT | Gl.GL_DEPTH_BUFFER_BIT);
// other rendering omitted (planets, ships, etc.)
this.OpenGlControl.Draw();
Update view -- centers on ship and should rotate to match its angle. For now, I'm just trying to rotate it by an arbitrary angle for a proof of concept, but no dice:
public void RefreshView()
{
int width = this.OpenGlControl.Width;
int height = this.OpenGlControl.Height;
Gl.glViewport(0, 0, width, height);
Gl.glMatrixMode(Gl.GL_PROJECTION);
Gl.glLoadIdentity();
float ratio = (float)width / (float)height;
Vec2 extents = new Vec2(ratio * 25.0f, 25.0f);
extents *= viewZoom;
// rotate the view
var shipAngle = 180.0f; // just a test angle for proof of concept
Gl.glRotatef(shipAngle, 0, 0, 0);
Vec2 lower = this.viewCenter - extents;
Vec2 upper = this.viewCenter + extents;
// L/R/B/T
Glu.gluOrtho2D(lower.X, upper.X, lower.Y, upper.Y);
Gl.glMatrixMode(Gl.GL_MODELVIEW);
}
Now, I'm obviously doing this wrong. Degrees of 0 and 180 will keep it right-side-up or flip it, but any other degree will actually zoom it in/out or result in only blackness, nothing rendered. Below are examples:
If ship angle is 0.0f, then game world is as expected:
Degree of 180.0f flips it vertically... seems promising:
Degree of 45 zooms out and doesn't rotate at all... that's odd:
Degree of 90 returns all black. In case you've never seen black:
Please help!
Firstly the 2-4 arguments are the axis, so please state them correctly as stated by #pingul.
More importantly the rotation is applied to the projection matrix.
// L/R/B/T
Glu.gluOrtho2D(lower.X, upper.X, lower.Y, upper.Y);
In this line your Orthogonal 2D projection matrix is being multiplied with the previous rotation and applied to your projection matrix. Which I believe is not what you want.
The solution would be move your rotation call to a place after the model view matrix mode is selected, as below
// L/R/B/T
Glu.gluOrtho2D(lower.X, upper.X, lower.Y, upper.Y);
Gl.glMatrixMode(Gl.GL_MODELVIEW);
// rotate the view
var shipAngle = 180.0f; // just a test angle for proof of concept
Gl.glRotatef(shipAngle, 0.0f, 0.0f, 1.0f);
And now your rotations will be applied to the model-view matrix stack. (I believe this is the effect you want). Keep in mind that glRotatef() creates a rotation matrix and multiplies it with the matrix at the top of the selected stack stack.
I would also strongly suggest you move away from fixed function pipeline if possible as suggested by #BDL.
I've just started playing with OpenGl to render a number of structure each comprising a number of polygon.
Basically I want to perform the equivalent of setting a camera at (0,0,z) in the world (structure) coordinates and rotate it about the x,y and z-axes of the world axes (in that order!) to render a view of each structure (as I understand it it common practice to do use the inverse camera matrix). Thus as I understand it I need to translate (to world origin i.e. (0,0,-z)) * rotateZrotateYrotateX * translate (re-define world origin see below)
So I think I need something like:
//Called when the window is resized
void handleResize(int w, int h) {
glViewport(0, 0, w, h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(9.148, (double)w / (double)h, 800.0, 1500.0);
}
float _Zangle = 10.0f;
float _cameraAngle = 90.0f;
//Draws the 3D scene
void drawScene() {
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW); //Switch to the drawing perspective
glLoadIdentity(); //Reset the drawing perspective
glTranslatef(0.0f, 0.0f, -z); //Move forward Z (mm) units
glRotatef(-_Zangle, 0.0f, 0.0f, 1.0f); //Rotate "camera" about the z-axis
glRotatef(-_cameraAngle, 0.0f, 1.0f, 0.0f); //Rotate the "camera" by camera_angle about y-axis
glRotatef (90.0f,1.0f,0.0f,0.0f); // rotate "camera" by 90 degrees about x-axis
glTranslatef(-11.0f,189.0f,51.0f); //re-define origin of world coordinates to be (11,-189,-51) - applied to all polygon vertices
glPushMatrix(); //Save the transformations performed thus far
glBegin(GL_POLYGON);
glVertex3f(4.91892,-225.978,-50.0009);
glVertex3f(5.73534,-225.978,-50.0009);
glVertex3f(6.55174,-225.978,-50.0009);
glVertex3f(7.36816,-225.978,-50.0009);
.......// etc
glEnd();
glPopMatrix();
However when I compile and run this the _angle and _cameraAngle seem to be reversed i.e. _angle seems to rotate about y-axis (Vertical) of Viewport and _cameraAngle about z-axis (into plane of Viewport)? What am I doing wrong?
Thanks for taking the time to read this
The short answer is: Use gluLookAt(). This utility function creates the proper viewing matrix.
The longer answer is that each OpenGL transformation call takes the current matrix and multiplies it by a matrix built to accomplish the transformation. By calling a series of OpenGL transformation function you build one transformation matrix that will apply the combination of transformations. Effectively, the matrix will be M = M1 * M2 * M3 . . . Mathematically, the transformations are applied from right to left in the above equation.
Your code doesn't move the camera. It stays at the origin, and looks down the negative z-axis. Your transformations move everything in model space to (11,-189,-51), rotates everything 90 degrees about the x-axis, rotates everything 90 degrees about the y-axis, rotates everything 10 degrees about the z-axis, then translates everything -z along the z-axis.
EDIT: More information
I'm a little confused about what you want to accomplish, but I think you want to have elements at the origin, and have the camera look at those elements. The eye coordinates would be where you want the camera, and the center coordinates would be where you want the objects to be. I'd use a little trigonometry to calculate the position of the camera, and point it at the origin.
In this type of situation I usually keep track of camera position using longitude, latitude, and elevation centered on the origin. Calculating x,y,z for the eye coordinates is simplyx = elv * cos(lat) * sin(lon), y = elv * sin(lat), z = elv * cos(lat) * cos(lat).
My gluLookAt call would be gluLookAt(x, y, z, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
You could rotate the up on the camera by changing the last three coordinates for gluLookAt.
The z axis is coming from the center of the monitor into you. So, rotating around the z-axis should make the camera spin in place (like a 2D rotation on just the xy plane). I can't tell, but is that what's happening here?
It's possible that you are encountering Gimbal Lock. Try removing one of the rotations and see if things work the way they should.
While it's true that you can't actually move the camera in OpenGL, you can simulate camera motion by moving everything else. This is why you hear about the inverse camera matrix. Instead of moving the camera by (0, 0, 10), we can move everything in the world by (0, 0, -10). If you expand those out into matrices, you will find that they are inverses of each other.
I also noticed that, given the code presented, you don't need the glPushMatrix()/glPopMatrix() calls. Perhaps there is code that you haven't shown that requires them.
Finally, can you provide an idea of what it is you are trying to render? Debugging rotations can be hard without some context.
Short answer :Good tip
Longer answer: Yes the order of matrix multiplication is clear... that's what I meant by inverse camera matrix to indicate moving all the world coordinates of structures into the camera coordinates (hence the use of "camera" in my comments ;-)) instead of actually translating and rotating camera into the world coordinates.
So if I read between the lines correctly you suggest something like:
void drawScene() {
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW); //Switch to the drawing perspective
glLoadIdentity(); //Reset the drawing perspective
gluLookAt(0.0,0.0,z,11.0,-189.0,-51.0,0.0,1.0,0.0); //eye(0,0,z) look at re-defined world origin(11,-189,-51) and up(0.0,1.0,0.0)
glRotatef(-_Zangle, 0.0f, 0.0f, 1.0f); //Rotate "camera" (actually structures) about the z-axis
glRotatef(-_cameraAngle, 0.0f, 1.0f, 0.0f); //Rotate the "camera" (actually structures!) by camera_angle about y-axis
glRotatef (90.0f,1.0f,0.0f,0.0f); // rotate "camera" (actually structures) by 90 degrees about x-axis
glPushMatrix();
Or am I still missing something?
I think you are mixing axes of your world with axes of the camera,
GLRotatef only uses axes of the camera, they are not the same as your the world axes once the camera is rotated.