The motivation behind the trackball aka arcball is to provide an intuitive user interface for complex 3D object rotation via a simple, virtual sphere - the screen space analogy to the familiar input device bearing the same name.

The sphere is a good choice for a virtual trackball because it makes a good enclosure for most any object; and its surface is smooth and continuous, which is important in the generation of smooth rotations in response to smooth mouse movements. Any smooth, continuous shape, however, could be used, so long as points on its surface can be generated in a consistent way. The first step in generating a trackball is defining the ball itself, which is simply a sphere at the origin.

Next we would like to center our sphere on the object we would like to rotate. To do this, we can project the object's center into screen space. The equation for our sphere then becomes.

This will place our sphere at the screen space origin, which, in OpenGL, is the lower left corner of the screen by default. Objects outside the view frustum could be culled via a sphere-frustum collision test, for example. As the mouse moves over the surface of our sphere it traces out a curve. Each position on this curve from the sphere's center is a vector, and any two consecutive vectors spans a plane through the center of the sphere.

The normal of this plane is our rotation axis, and the distance traveled by the mouse between any two points implicitly determines the amount of rotation. In detail, as the mouse moves over the screen we first need to generate points on the sphere. That's a simple matter of evaluating our equation. But what of points outside the sphere? Frustum culling restricts us to spheres at least partially visible, but we can still generate points outside of the sphere but within the screen's extent, which would generate complex results square roots of negative numbers.

This can be seen in the explicit form of the sphere. One nice way to get around this unpleasantness is to use a piecewise combination of surfaces in place of a single sphere.

In this way we can switch to one surface in a region where things are awkward in another.

Import tf2One surface that works well in this case is the hyperbolic sheet given by. This surface has the shape of an inverted trumpet, with the mouth piece at infinity along the z axis and the horn opening flaring out to cover the xy-plane. With the sphere nestled snugly at its opening, we can transition very smoothly from a ball to a flaring horn defined everywhere except the origin.

The crossover from sphere to sheet occurs at their intersection, which is defined by the circle. So in addition to avoiding negative numbers in our radical, the primary motivation for the transition is to make rotational falloff as graceful as possible: the farther the mouse ventures from the center of the sphere the less angular displacement is generated between any two mouse positions, which tapers off completely as the sheet flattens off to zero at infinity.

## Announcement

So now that we can generate points for our surface anywhere on the screen, there's still the matter of generating a rotation from them. The standard way to do this is through the use of quaternions, which provide a very compact, convenient and robust representation for rotations.

What makes quaternions particularly nice in this situation is the property that a normalized quaternion always represents a rotation -- as arbitrary, incremental rotations will be applied to our objects and in no particular order, the importance of this property can't be overstated. With quaternions in hand, object rotations are very straightforward. In fact, with our axis and angle from above, they're nigh automatic. Any two consecutive mouse positions on our surface are enough to generate two vectors, the cross product of which is the rotation axis, and the inverse cosine of the dot product of which is the angle.

The basic procedure is as follows:. While we can be sure our coordinate axes will remain orthogonal under rotation, due to limited floating point precision, we can't fully escape numeric drift in our calculations: After several arbitrary rotations, we can't guarantee that a reversal of the sequence will lead to our original basis exactly.

To help stem the numeric tide, it's possible to snap the rotation axes to the standard axes wherever they're very close to one another. Since a quaternion can be readily converted to and from an axis-angle representation, it's possible to first convert the quaternion to an axis-angle, snap the axis if very close to a standard axisangle snap, then convert the result back to a quaternion for rotation.

The angle snap must be performed in lockstep with the standard axis snap, otherwise a "stair casing" or rotational aliasing effect will ensue with each incremental rotation, the result of which is an ungainly bobble and teeter of the coordinate frame. The virtual trackball can provide an intuitive user interface for the interactive rotation of models in 3D.

From OpenGL Wiki. Jump to: navigationsearch.Need a tutorial that will make your OpenGL applications look better? A big problem we all run into is aliasing. That is, the square edged "jaggies" that exist on diagonal lines in relation to the square pixels that exist on your screen. In this tutorial you will use Anti-Aliasing to smudge those "jaggies" in order to create a smoother edge for objects. We achieve this through "Multisampling". Fullscreen AntiAliasing is something that non-realtime rendering programs have always had an advantage in.

However, with current hardware, we're able to pull off the same effect real time. Like any other Extension based tutorial, if your card does not support the extension used, the effect will not work on your machine or the program may fail to run.

If you enjoy it, let him know! Using vertex and fragment or pixel shaders to do some rendering dirty work can have numerous benefits. Cg provides a reasonably simple language for writing very powerful shaders.

This tutorial has multiple aims. The first is to present a simple vertex shader that actually does something, without introducing unnecessary lighting etcâ€¦ The second is to provide the basic mechanism for running the vertex shader with visible results using OpenGL.

As such, it is aimed at the beginner interested in Cg who has a little experience in OpenGL. This tutorial was written by Owen Bourne. If you enjoy it, please take the time to email him and let him know! With an ArcBall you can do just that.

In this tutorial Terence J. Grant will touch on his implementation and considerations for adding ArcBall rotation to your own projects. However, his version has some bug fixing and optimizations. The example code was originally based on lesson 5.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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I only just started learning OpenGL and even things like vector maths etc a couple of days ago, so I am having a bit of trouble figuring out exactly what to do to implement an arcball camera system.

I am using GLM to do things like get the cross product of two vectors etc, and I am using the glm::lookAt position, target, up method to set the view matrix. I have looked around on Google and the search on this site and even StackOverflow but since I am new to this I'm not exactly sure what I'm doing wrong probably a lot of things and what I should be searching for.

At the moment I am trying to follow the general steps outlined in this answer: How can I orbit a camera about it's target point?

But I am not sure if I am doing it correctly well, actually, I know I'm not doing it correctly because it's not working.

I can get the camera's normalized up and right vectors without any problem, and I can get a vector from the camera's target point to the camera position. I can then easily decide the angle of rotation in radians, but my main points of trouble come after that; creating a new vector to translate the camera with from a rotation matrix and then actually translating camera to get a new camera position.

Currently I have a cube that is drawn around the origin, three glm::vec3 objects which describe camera position, camera target and camera up, and the usual projectionview and model matrices which are multiplied together and given to glUniformMatrix4fv. Just before the main loop I also declare two glm::mat4 matrices to rotate with yaw and pitch and two more glm::vec3 objects to store the target to camera and camera right vectors, since that was one of the steps in the answer I linked above.

Create two rotation matrices. The 1st rotation matrix will use the up of the camera as the axis and yaw angle that you decided. The 2nd rotation matrix will use the right of the camera as the axis and pitch angle that you decided. Now rotate the camFocusVector with the new rotation matrices. This is now your new position of the camera relative to the origin. We of course, want it to be relative to the focus point Add the focus point position to camFocusVector.

This is now your camera's new position. Translate your camera accordingly. And having no idea how I should use this result to translate the vector, I make the, most likely wrong, assumption that I am supposed to do this. Afterwards I use the glm::lookAt method and recalculate the model view projection matrix to pass to glUniformMatrix4fv. But I think I mostly went wrong around the point where I had to rotate the matrices and translate the camera position.

Place your camera target at the center of the arc rotation That's usually where you want the camera to look anyway.I have been having a hard time making this work in an application and have stripped it down to the bare bones in a test application. It just draws a set of axes arrows at the origin, which the user can rotate. Still having the same problem. I thought I pretty much understood the whole matrix thingâ€¦ but maybe not.

Instead I am setting the sphere of rotation to a fixed size based on the window size. Start and end mouse coordinates are projected onto the surface of that sphere. The angle between them gives the rotation angle, and the normal vector gives the axis of rotation. Some of the methods e. MousePosToSphere are third party code, but from testing I think they are good. I believe my problem is at the final stage. The rotation seen is around some axis which is not aligned with the direction of mouse movement, which to me suggests a problem with the cumulative rotations.

In the above, I have tried both rotation sequences i.

### Object Mouse Trackball

I believe it should be active-then-completed in the code, since they are applied to the vertices in reverse order? Anyway, neither sequence worked. Thanks for the reply.

Extra utilities 2 grid is overloadedYes, I am aware of the rainwarrior page. In fact that was the source I initially referred to when first trying to implement this. Therefore I am not using the gluUnproject approach - although of course the principle is similar.

When it comes to applying the matrices, what I am doing is I think consistent with the rainwarrior description. Once you have your rotation matrix, however, you can multiply it by whatever matrix you were using when the starting vector was gathered, and pass the result to glMultMatrix.

**Euler (gimbal lock) Explained**

Rather than starting from square 1 with another method, I am hoping to pin down what is wrong with mine. It very nearly works, but there must be something I am missing somewhere.

It took me some time to get it right too. I had to do it in debug mode and output results at different steps. First you should make double sure that the conversion from screen to sphere coordinates is correct. I did this by clicking on the cardinal points North Pole, South Pole, equator, of the sphere. Check that it returns 3d points such as 0, r, 00,-r,0etc.

### The Industry's Foundation for High Performance Graphics

The matrices are of the type. At this stage again I tried to combine two simple rotations, sent the matrix to the debug output, and checked that it gave the intended result.

OpenGL: Basic Coding. Clear ClearBufferMask. DepthBufferBit ; GL.You seem to have CSS turned off. Please don't fill out this field. Arcball tracball OpenGL widgets for different toolkits now supported fltk 1 and 2 and gtkmm gtkglextmm.

Multi Toolkit Arcball Web Site. Do you have a GitHub project? Now you can sync your releases automatically with SourceForge and take advantage of both platforms. Please provide the ad click URL, if possible:. Help Create Join Login. Operations Management. IT Management. Project Management. Services Business VoIP. Resources Blog Articles Deals. Menu Help Create Join Login.

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Aerogarden catsPhone Number. Job Title. Company Size Company Size: 1 - 25 26 - 99 - - 1, - 4, 5, - 9, 10, - 19, 20, or More. Get notifications on updates for this project. Get the SourceForge newsletter. JavaScript is required for this form. No, thanks. BSD Linux. Project Activity. Categories User Interfaces3D Rendering. Then your future releases will be synced to SourceForge automatically.

Sync Now.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am using legacy OpenGL to draw a mesh. I am now trying to implement an arcball class to rotate the object with the mouse. However, when i move the mouse, the object either doesn't rotate or rotates by way too big an angle.

This method is meant to simply map the mouse coordinates to be centered at the center of the screen and map them to the bounding sphere, resulting in a starting vector. This method is again meant to map the mouse coordinates to be centered t the middle of the screen, then compute the new vector and compute a rotation axis and angle based on these two vectors.

I recommend to do store the mouse position at the point where you initially click in the view. Calculate the amount of the mouse movement in window coordinates. The distance of the movement has to be mapped to an angle. The rotation axis is perpendicular normal to the direction of the mouse movement. The result is a rotation of an object similar to this WebGL demo.

Store the current mouse position in startRotation. Note store the coordinates of the position mouse position not normalized vector:. Note even if the type of direction is QVector3Dit is still a 2 dimensional vector. It is a vector in the XY plane of the viewport representing the mouse movement on the viewport. The z coordinate is 0. A 2 dimensional vector x, ycan be 90 degrees counter clockwise rotated, by -y, x.

## Arcball OpenGL in C#

The length of the direction vector represents tha angle of rotation. A mouse motion over the entire screen results in a vector with length 2. So if a dragging over the full screen should result in a full rotation, the length of the vector has to be multiplied by PI. If you want a rotation around the upwards axis of the object a tilting the object along the view space x axis, then the calculation is different. First apply the rotation matrix around the y axis up vector then the current view matrix and finally the rotation on the x axis:.

Learn more. Asked 1 year, 2 months ago. Active 1 year, 1 month ago. Viewed times.It has been converted and modified for C. It utilizes the CsGL wrapper by default, but can be replaced with the Tao version as well. Arcball also know as Rollerball is probably the most intuitive method to view three dimensional objects. The principle of the Arcball is based on creating a sphere around the object and letting users to click a point on the sphere and drag it to a different location.

There is a bit of math involved, of course, and you can Google for it. Using this code is straightforward. Create a new form, create an instance of the Arcball class, and make if fill the form rectangle. I am plotting a torus in this example. Mouse left click rotates the object dynamically. Mouse right click resets it to its original orientation. You can easily control the mouse button too.

You don't need to change anything else and the code should work. You can also extend the keyboard control based on your needs. I have the Escape and R keys programmed here.

Note: For almost any code, you do not need to modify the Arcball class at all. Hope it comes useful to you.

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