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giugio

OpenGL orbit camera

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can you recommend to me a good orbit camera that i can include in a my project opengl 4?
may be based on the math library glt that i have already integrated?
thanks

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The math itself is relatively simple:

 

1.) Rotate the camera into the new orientation.

2.) Translate it in direction of the forward vector by the negated desired distance between camera and point of interest.

3.) Add the world position of the point of interest.

 

How to implement point 1., however, depends on how your camera control works.

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The math itself is relatively simple:

 

1.) Rotate the camera into the new orientation.

2.) Translate it in direction of the forward vector by the negated desired distance between camera and point of interest.

3.) Add the world position of the point of interest.

 

How to implement point 1., however, depends on how your camera control works.

only a question: why many people uses quaternion on point 1?

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only a question: why many people uses quaternion on point 1?

In principle there is no reason for this perhaps until knowing how the camera control is done. Performing a rotation is simpler when using a matrix. A quaternion may have advantages as intermediary during computing the rotation, especially is it fine if rotational interpolation is to be done. The technical reason then is that a quaternion with its 4 parameters is closer to the 3 parameters (what's needed for a rotation) compared to the 9 parameters of a matrix, so the additionally required constraints (count just 4-3=1 for quaternions, but 9-3=6 for matrices) are far easier to maintain for quaternions than for matrices.

 

However, as said, the preparation of point 1. depends heavily on how your camera control works. Maybe quaternions are advantageously there, maybe not.

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only a question: why many people uses quaternion on point 1?

In principle there is no reason for this perhaps until knowing how the camera control is done. Performing a rotation is simpler when using a matrix. A quaternion may have advantages as intermediary during computing the rotation, especially is it fine if rotational interpolation is to be done. The technical reason then is that a quaternion with its 4 parameters is closer to the 3 parameters (what's needed for a rotation) compared to the 9 parameters of a matrix, so the additionally required constraints (count just 4-3=1 for quaternions, but 9-3=6 for matrices) are far easier to maintain for quaternions than for matrices.

 

However, as said, the preparation of point 1. depends heavily on how your camera control works. Maybe quaternions are advantageously there, maybe not.

 

A question: with the mouse how i can obtain an angle of rotation for the pitch and the yaw?
I get a mouse position in x and y .
I would understand, not only copy from an example.

with atan2 i can get the angle , but 1 angle and what angle i use for pitch and for roll?

i use math library glm .
Thanks

Edited by giugio

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ok, this is my code:

void Camera::updateMouse(double x, double y)
{    
    glm::vec3 mouse_position = glm::vec3(x, y, 0.0);
    if (m_mousePressed)
    {       
        m_mousePosition = mouse_position; 
        m_mouseButton = false;    }   
        if (m_mouseButton){
            glm::vec3 mouseDelta = mouse_position - m_mousePosition;
        if (mouseDelta.length() < 0.1f)    
        {            return; // don't do tiny rotations.        
        }
        float angle = glm::atan(mouseDelta.y, mouseDelta.x);    
        glm::degrees(angle);
        if (angle < 0) angle += 360;    
}

i obtain an angle , but what is the angle for yaw and what is the angle for roll ? I need two angles?

thanks

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i obtain an angle , but what is the angle for yaw and what is the angle for roll ?

When you calculate an angle that way, it is most obviously interpreted as rolling.

 

There are some ways to compute 2 angles from mouse movement, but all of them suffer in the one or other way. The very basic ways are these:

 

a) Use the delta in mouse movement along x axis, scale it by some factor, and add it as delta yaw. Do the same with the y direction and pitch. Here screen axes and rotation axes are related only logically. The rotations are relative because only deltas are used.

 

b) Think of a hemisphere centered on the screen, having a radius so that the circumference is close inside the screen borders. The point under the mouse and inside the projected circle of the hemisphere is then projected onto the hemisphere. This is then interpreted as spherical coordinates, hence giving you 2 angles. This method gives an orientation rather than a rotation. It returns one angle with [0,2pi] and the other with [0,pi/2] only (matching a hemisphere, of course), and suffers from inaccuracies when pointing close to the border of the projected circle. (Lookout for "turntable" implementations.)

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i obtain an angle , but what is the angle for yaw and what is the angle for roll ?

When you calculate an angle that way, it is most obviously interpreted as rolling.

 

There are some ways to compute 2 angles from mouse movement, but all of them suffer in the one or other way. The very basic ways are these:

 

a) Use the delta in mouse movement along x axis, scale it by some factor, and add it as delta yaw. Do the same with the y direction and pitch. Here screen axes and rotation axes are related only logically. The rotations are relative because only deltas are used.

 

b) Think of a hemisphere centered on the screen, having a radius so that the circumference is close inside the screen borders. The point under the mouse and inside the projected circle of the hemisphere is then projected onto the hemisphere. This is then interpreted as spherical coordinates, hence giving you 2 angles. This method gives an orientation rather than a rotation. It returns one angle with [0,2pi] and the other with [0,pi/2] only (matching a hemisphere, of course), and suffers from inaccuracies when pointing close to the border of the projected circle. (Lookout for "turntable" implementations.)

 

thanks

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i obtain an angle , but what is the angle for yaw and what is the angle for roll ?

When you calculate an angle that way, it is most obviously interpreted as rolling.

 

There are some ways to compute 2 angles from mouse movement, but all of them suffer in the one or other way. The very basic ways are these:

 

a) Use the delta in mouse movement along x axis, scale it by some factor, and add it as delta yaw. Do the same with the y direction and pitch. Here screen axes and rotation axes are related only logically. The rotations are relative because only deltas are used.

 

b) Think of a hemisphere centered on the screen, having a radius so that the circumference is close inside the screen borders. The point under the mouse and inside the projected circle of the hemisphere is then projected onto the hemisphere. This is then interpreted as spherical coordinates, hence giving you 2 angles. This method gives an orientation rather than a rotation. It returns one angle with [0,2pi] and the other with [0,pi/2] only (matching a hemisphere, of course), and suffers from inaccuracies when pointing close to the border of the projected circle. (Lookout for "turntable" implementations

 

only two questions :

1)the quaternion need only one angle for create a angular displacement , is correct? why now two angles?for the two quaternions that must be interpolated?

2)i see the squad and there is two quaternion and a variable t time? then i must get the time for each step ? and how i can convert the t to [0-1]

thanks and sorry for my ignorance

 

ps. and how i can transform the position of the mouse to the hypersfere? i must project? how? do you have a link on google.

thanks again

Edited by giugio

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I had some problem to decipher your post (no offending), so bear with me if I misunderstood what you meant ...

 

1)the quaternion need only one angle for create a angular displacement , is correct? why now two angles?for the two quaternions that must be interpolated?

A quaternion, in fact a unit-quaternion, is a kind of representation for rotations. As such it encodes an axis of rotation and an angle of rotation (and it has a constraint that its 2-norm is 1, else it would be a unit-quaternion and shearing would appear).

 

Interpolation means to calculate an in-between, having 2 supporting points (or key values) at the limits. Whether these 2 supporting points are spatially or temporally or whatever related plays no role for the interpolation. What "2 quaternions" do you want to interpolate? The control schemes described above do by themselves not have an urge to use quaternions. If you speak of a smooth transition of the current orientation to the next, then the one support point is the last recently used quaternion and the other is the newly determined (from mouse position / movement) one.

 

2)i see the squad and there is two quaternion and a variable t time? then i must get the time for each step ? and how i can convert the t to [0-1]

The 2 quaternions are the said support points, and the free variable (you used t, I will use k below) denotes where the in-between is located between the support points. You can compute an in-between only when you provide a value for k, yes. (But, as said, t need not be a time value.) How to determine a suitable k depends on what you want to achieve. For example, if you want N interpolation steps that are equally distributed within the allowed range [0,1], then you would use

    kn := n / N   with   n = 0, 1, 2, …, N

where kn is the value for k at step n. Notice that n increments by 1 from 0 up to N, inclusively; this would be implemented as counting loop, of course. So you get

    k0 = 0 / N = 0

    kN = N / N = 1

as is required for the interpolation factor by definition.

 

If, on the other hand, you want the interpolation run over a duration T and started at moment in time t0 (measured by a continuously running clock), now at a measured moment t, then

    k( t ) := ( t - t0 ) / T   with   t0 <= t <= t0+T

so that, as required by the interpolation factor definition,

    k( t0 ) = ( t0 - t0 ) / T = 0

    k( t0 + T ) = ( t0 + T - t0 ) / T = 1

 

As you can see in both examples above, the allowed range [0,1] is achieved by normalizing (division by N or T) and, in the case of the timed interpolation, by first shifting the real interval (subtraction of t0) so that it originates at 0; the latter part was not necessary in the first example because it already originates at 0.

 

and how i can transform the position of the mouse to the hypersfere? i must project? how? [...]

Well, a hemisphere (half of a full sphere) is luckily not a hypersphere (a sphere in more than 3 dimensions)!

 

Let's say the mouse position is the tuple (mx,my) and the screen size is given by (w,h) in the same co-ordinate system as (mx,my). Then the relative mouse position is

   s := min( w, h ) * 0.5    << EDIT: must be halved to yield in a proper [-1,+1] normalization, hence the 0.5

   x' := ( mx - w / 2 ) / s

   y' := ( my - h / 2 ) / s

 
The position is within a circle as described in a previous post only if
   x'2 + y'2 <= 1
otherwise the mouse is out of the range of our gizmo! If inside, then the tuple (x',y') denote a normalized position within the projected circle.
 
A point (x,y,z) on a hemisphere is described by spherical co-ordinates by 
   x := r * sin( theta ) * cos( phi )

   y := r * sin( theta ) * sin( phi )

   z := r * cos( theta )

Due to normalization we can ignore the radius because it is 1.

 

If we divide y by x we achieve

   y / x = sin( phi ) / cos( phi ) = tan( phi )

and hence we can compute phi' for our relative mouse position (x',y') using the famous atan2 function as

   phi' = atan2( y', x' )

 

For theta or z, resp., we have 2 ways. One of them is derived from the fact that each point on the unit sphere is 1 length unit away from its center. That means for use

   x'2 + y'2 + z'2 == 1

so that for our z', considering that we use the "upper" hemisphere, have

   z' = +sqrt( 1 - x'2 - y'2 )

This is valid due to our above formulated condition that the mouse position is within the circle.

 

Hence we can calculate

   theta' = acos( z' )

 

Now we have 2 angles, phi' and theta'. What is left over is how to map that onto yaw and pitch, a question you need to answer.

Edited by haegarr

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