I have a scene which is basically a square floor measuring 15x15 (a quad with coordinates (0,0,0) (0,0,15) (15,0,15) (15,0,0) ).
I 've set the center-of-scene to be at (7.5,0,7.5). Problem is I can't figure out how to rotate the camera horizontally around that center of scene (aka make the camera do a 360 horizontal circle around center-of-scene). I know you need to do something with sin and cos, but don't know what exactly.
Here is the code (plain C):
//set camera position
//camera height is 17
GLfloat camx=0, camy=17, camz=0;
//set center of scene
GLfloat xref=7.5, yref=0, zref=7.5;
gluLookAt(camx, camy, camz, xref, yref, zref, 0, 1, 0);
//projection is standard gluPerspective, nothing special
gluPerspective(45, (GLdouble)width/(GLdouble)height, 1, 1000);
You need to modify the camx and camz variables.
The points you want to walk through lie on the circle and their coordinates are determined by x = r*sin(alpha) + 7.5, z = r*cos(alpha) + 7,5, where r is the radius of the circle and alpha is the angle between xy plane and the current position of your camera.
Of course the angle depends on the rotation speed and also on the time from the beginning of the animation. Basically, the only thing you need to do is to set the right angle and then calculate the coordinates from the expressions above.
For more info about the circle coordinates, see Wiki : http://en.wikipedia.org/wiki/Unit_circle
I think there are two ways you can use:
You can use sin/cos to compute your camx and camz position. This picture is a good example how this works.
An alternative would be to move the camera to 7.5, 0, 7.5, then rotate the camera with the camera angle you want. After that you move the camera by -7.5, 0, -7.5.
Related
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 managed to acquire camera's intrinsic and extrinsic parameters using OpenCV, thus I have fx, fy, cx and cy. And I also have the screen / image's width and height.
But how do I create an OpenGL perspective projection matrix from these parameters?
glFrustrum shows how to create projection matrix, given Z near, Z far and the image width and height. But how do I include focal points and camera centers in this matrix?
You can check the following links
Kyle Simek's explanation
My explanation
Here is the code to obtain the OpenGL projection matrix equivalent to a computer vision camera with camera matrix K=[fx, s, cx; 0, fy, cy; 0, 0, 1] and image size [W, H]:
glMatrixMode(GL_PROJECTION); // Select The Projection Matrix
glLoadIdentity(); // Reset The Projection Matrix
GLdouble perspMatrix[16]={2*fx/W,0,0,0,2*s/W,2*fy/H,0,0,2*(cx/W)-1,2*(cy/H)-1,(zmax+zmin)/(zmax-zmin),1,0,0,2*zmax*zmin/(zmin-zmax),0};
glMultMatrixd(perspMatrix);
NB: zmin and zmax represent the near and far Z clipping planes. This formulation assumes that the OpenGL world coordinate frame is chosen as follows:
The OpenGL camera is assumed to be located at the origin, looking towards positive Z axis, with a down vector collinear and towards the positive Y axis.
In relation to the AldurDisciple answer this is the formulation you need to use if the world coordinate frame is choosen with inverted z axe
glMatrixMode(GL_PROJECTION); // Select The Projection Matrix
glLoadIdentity(); // Reset The Projection Matrix
GLdouble perspMatrix[16]={2*fx/w,0,0,0,0,2*fy/h,0,0,2*(cx/w)-1,2*(cy/h)-1,-(far+near)/(far-near),-1,0,0,-2*far*near/(far-near),0};
glMultMatrixd(perspMatrix);
Open GL operates with a frustum which is related to perspective projection with some limits in depth referred as near and far values. Imagine a pyramid lying on its side - this is frustum. Another analogy is a projector beam that extends in its width and height with the distance - this is frustum too. So right, left, bottom, and top are your image coordinates while near and far are your depth limits with the near beint your focal plane. OpenGL will put Cx and Cy in the center of the image plane so you can skip them. The alternative and more natural way to specify frustum is based on viewing angle or field of view (50-60 deg is typical); the function you call is glPerspective() where you still have near and far but instead of sizes specify the angle and aspect ratio. Good luck.
You have cx, cy, fx, fy, width, height.
And you need left, right, top, bottom in your equations.
You can calculate these value using this way.
left = cx * near / -fx
top = cy * near / fy
right = -(width - cx) * near / -fx
bottom = -(height - cy) * near / fy
I am working on an application that has similar functionality to MotionBuilder in its viewport interactions. It has three buttons:
Button 1 rotates the viewport around X and Y depending on X/Y mouse drags.
Button 2 translates the viewport around X and Y depending on X/Y mouse drags.
Button 3 "zooms" the viewport by translating along Z.
The code is simple:
glTranslatef(posX,posY,posZ);
glRotatef(rotX, 1, 0, 0);
glRotatef(rotY, 0, 1, 0);
Now, the problem is that if I translate first, the translation will be correct but the rotation then follows the world axis. I've also tried rotating first:
glRotatef(rotX, 1, 0, 0);
glRotatef(rotY, 0, 1, 0);
glTranslatef(posX,posY,posZ);
^ the rotation works, but the translation works according to world axis.
My question is, how can I do both so I achieve the translation from code snippet one and the rotation from code snippet 2.
EDIT
I drew this rather crude image to illustrate what I mean by world and local rotations/translations. I need the camera to rotate and translate around its local axis.
http://i45.tinypic.com/2lnu3rs.jpg
Ok, the image makes things a bit clearer.
If you were just talking about an object, then your first code snippet would be fine, but for the camera it's quite different.
Since there's technically no object as a 'camera' in opengl, what you're doing when building a camera is just moving everything by the inverse of how you're moving the camera. I.e. you don't move the camera up by +1 on the Y axis, you just move the world by -1 on the y axis, which achieves the same visual effect of having a camera.
Imagine you have a camera at position (Cx, Cy, Cz), and it has x/y rotation angles (CRx, CRy). If this were just a regular object, and not the camera, you would transform this by:
glTranslate(Cx, Cy, Cz);
glRotate(CRx, 1, 0, 0);
glRotate(CRy, 0, 1, 0);
But because this is the camera, we need to do the inverse of this operation instead (we just want to move the world by (-Cx, -Cy, and -Cz) to emulate the moving of a 'camera'. To invert the matrix, you just have to do the opposite of each individual transform, and do them in reverse order.
glRotate(-CRy, 0, 1, 0);
glRotate(-CRx, 1, 0, 0);
glTranslate(-Cx, -Cy, -Cz);
I think this will give you the kind of camera you're mentioning in your image.
I suggest that you bite the apple and implement a camera class that stores the current state of the camera (position, view direction, up vector, right vector) and manipulate that state according to your control scheme. Then you can set up the projection matrix using gluLookAt(). Then, the order of operations becomes unimportant. Here is an example:
Let camPos be the current position of the camera, camView its view direction, camUp the up vector and camRight the right vector.
To translate the camera by moveDelta, simply add moveDelta to camPos. Rotation is a bit more difficult, but if you understand quaternions you'll be able to understand it quickly.
First you need to create a quaternion for each of your two rotations. I assume that your horizontal rotation is always about the positive Z axis (which points at the "ceiling" if you will). Let hQuat be the quaternion representing the horizontal rotation. I further assume that you want to rotate the camera about its right axis for your vertical rotation (creating a pitch effect). For this, you must apply the horizontal rotation to the camera's current angle. The result is the rotation axis for your vertical rotation hQuat. The total rotation quaternion is then rQuat = hQuat * vQuat. Then you apply rQuat to the camera's view direction, up, and right vectors.
Quat hRot(rotX, 0, 0, 1); // creates a quaternion that rotates by angle rotX about the positive Z axis
Vec3f vAxis = hRot * camRight; // applies hRot to the camera's right vector
Quat vRot(rotY, vAxis); // creates a quaternion that rotates by angle rotY about the rotated camera's right vector
Quat rQuat = hRot * vRot; // creates the total rotation
camUp = rQuat * camUp;
camRight = rQuat * camRight;
camView = rQuat * camView;
Hope this helps you solve your problem.
glRotate always works around the origin. If you do:
glPushMatrix();
glTranslated(x,y,z);
glRotated(theta,1,0,0);
glTranslated(-x,-y,-z);
drawObject();
glPopMatrix();
Then the 'object' is rotate around (x,y,z) instead of the origin, because you moved (x,y,z) to the origin, did the rotation, and then pushed (x,y,z) back where it started.
However, I don't think that's going to be enough to get the effect you're describing. If you always want transformations to be done with respect to the current frame of reference, then you need to keep track of the transformation matrix yourself. This why people use Quaternion based cameras.
I'm having some trouble with the eyeZ value of gluLookAt.
The way I'd imagine it to work is like moving a camera further away, thus shrinking the object in your field of view.
I have a simple setup with a simple shape in 3d space draw via glDrawElements with an 100x100x100 ortho where 0, 0, 0 is the center of the universe. The object is at 0, 0, 0.
I'm trying to make it so when you scroll the mouse wheel you get further away/closer to the object. Here's how glulookat is called.
float eyeX = 0;
float eyeY = 0;
float eyeZ = differenceInMouseWheel();
float centerX = 0;
float centerY = 0;
float centerZ = 0;
float upX = 0;
float upY = 1;
float upZ = 0;
gluLookAt(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ);
The only thing changing here is eyeZ.
The effect is strange, I scroll for about 10 seconds and then suddenly half of the object disappears. From there more and more of it disappears. This is probably because the camera is going out off into the 50 z distance limit, but I can't understand why the object doesn't scale like it would in 3D space.
Maybe I'm misunderstanding how the center values work?
I've also tried applying differenceInMouseWheel() to centerZ but that changed nothing, I'm going to assume the center values are just so glu can get a direction and nothing more.
Maybe the up vector should change? I don't know at this point.
You are using an orthographic projection. This means that no matter how great the distance, your objects will always appear to have the same size. Your object will disappear once it reaches the far clipping plane however, which is what you are seeing when you scroll for a long time.
You have two options: Either you use a perspective projection or you implement a zoom by modifying the orthographic projection matrix like so:
Let zoom be in (0, 1], and let viewport be a rectangle that is set to your current viewport. Let near be your near clipping plane distance and far be your far clipping plane distance.
glOrtho(zoom * viewport.width / 2, zoom * viewport.width / 2, zoom * viewport.height / 2, zoom * viewport.height / 2, near, far);
Are you using a perspective projection matrix, or an orthographic one? If you don't use a perspective matrix the object's wont appear to change in size as you move the camera around.
I am wondering if gluLookAt together with glFrustum is distorting the rendered picture.
This is how a scene is rendered:
And here's the code that rendered it.
InitCamera is called once and should, as I understand it now, set up a matrix so as if I looked from a position 2 units above and 3 units in front of the origin towards the origin. Also glFrustum is used in order to create a perspective`.
void InitCamera() {
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
gluLookAt (
0, 2 , 3,
0, 0 , 0,
0, 1 , - 0
);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glFrustum (- 1, 1,
- 1, 1,
1,1000.0);
glMatrixMode(GL_MODELVIEW);
}
Then TheScene is what actually draws the picture:
void TheScene() {
glClear(
GL_COLOR_BUFFER_BIT |
GL_DEPTH_BUFFER_BIT
);
glMatrixMode(GL_MODELVIEW);
// Draw red circle around origin and radius 2 units:
glColor3d(1,0,0);
glBegin(GL_LINE_LOOP);
for (double i = 0; i<=2 * M_PI; i+=M_PI / 20.0) {
glVertex3d(std::sin(i) * 2.0, 0, std::cos(i) * 2.0);
}
glEnd();
// draw green sphere at origin:
glColor3d(0,1,0);
glutSolidSphere(0.2,128, 128);
// draw pink sphere a bit away
glPushMatrix();
glColor3d(1,0,1);
glTranslated(8, 3, -10);
glutSolidSphere(0.8, 128, 128);
glPopMatrix();
SwapBuffers(hDC_opengl);
}
The red ball should be drawn in the origin and at the center of the red circle around it. But looking at it just feels wierd, and gives me the imprssion that the green ball is not in the center at all.
Also, the pink ball should, imho, be drawn as a perfect circle, not as an ellipse.
So, am I wrong, and the picture is drawn correctly, or am I setting up something wrong?
Your expectations are simply wrong
The perspective projection of a 3d circle (if the circle is fully visible) is an ellipse, however the projection of the center of the circle is NOT in general the center of the ellipse.
The outline of the perspective projection of a sphere is in general a conic section i.e. can be a circle, an ellipse, a parabola or an hyperbola depending on the position of viewpoint, projection plane and sphere in 3D. The reason is that the outline of the sphere can be imagined as a cone starting from the viewpoint and touching the sphere being intersected with the projection plane.
Of course if you're looking at a circle with a perfectly perpendicular camera the center of the circle will be projected to the center of the circle projection. In the same manner if your camera is pointing exactly to a sphere the sphere outline will be a circle, but those are special cases, not the general case.
These differences between the centers are more evident with strong perspective (wide angle) cameras. With a parallel projection instead this apparent distortion is absent (i.e. the projection of the center of a circle is exactly the center of the projection of the circle).
To see the green sphere in the centre of the screen with a perfect circle around it you need to change the camera location like so:
gluLookAt (
0, 3, 0,
0, 0, 0,
0, 0, 1
);
Not sure what's causing the distortion of the purple sphere though.
The perspective is correct, it just looks distorted because that's how things fell together here.
try this for gluLookAt, and play around a bit more.:
gluLookAt (
0, 2 , 10,
0, 0 , 0,
0, 1 , 0
);
The way I tried it out was with a setup that allows me to adjust the position and view direction with the mouse, so you get real time motion. Your scene looks fine when I move around. If you want I can get you the complete code so you can do that too, but it's a bit more than I want to shove into an answer here.