So I currently use quaternions to store and modify the orientation of the objects in my OpenGL scene, as well as the orientation of the camera. When rotating these objects directly (i.e. saying I want to rotate the camera Z amount around the Z-axis, or I want to rotate an object X around the X-axis and then translate it T along its local Z-axis), I have no problems, so I can only assume my fundamental rotation code is correct.
However, I am now trying to implement a function to make my camera orbit an arbitrary point in space, and am having quite a hard time of it. Here is what I have come up with so far, which doesn't work (this takes place within the Camera class).
//Get the inverse of the orientation, which should represent the orientation
//"from" the focal point to the camera
Quaternion InverseOrient = m_Orientation;
InverseOrient.Invert();
///Rotation
//Create change quaternions for each axis
Quaternion xOffset = Quaternion();
xOffset.FromAxisAngle(xChange * m_TurnSpeed, 1.0, 0.0, 0.0);
Quaternion yOffset = Quaternion();
yOffset.FromAxisAngle(yChange * m_TurnSpeed, 0.0, 1.0, 0.0);
Quaternion zOffset = Quaternion();
zOffset.FromAxisAngle(zChange * m_TurnSpeed, 0.0, 0.0, 1.0);
//Multiply the change quats into the inversed orientation quat
InverseOrient = yOffset * zOffset * xOffset * InverseOrient;
//Translate according to the focal distance
//Start with a vector relative to the position being looked at
sf::Vector3<float> RelativePos(0, 0, -m_FocalDistance);
//Rotate according to the quaternion
RelativePos = InverseOrient.MultVect(RelativePos);
//Add that relative position to the focal point
m_Position.x = m_FocalPoint->x + RelativePos.x;
m_Position.y = m_FocalPoint->y + RelativePos.y;
m_Position.z = m_FocalPoint->z + RelativePos.z;
//Now set the orientation to the inverse of the quaternion
//used to position the camera
m_Orientation = InverseOrient;
m_Orientation.Invert();
What ends up happening is that the camera rotates around some other point - certainly not the object, but apparently not itself either, as though it were looping through space in a spiral path.
So this is clearly not the way to go about orbiting a camera around a point, but what is?
I would operate on the camera first in spherical coordinates and convert to quaternions as necessary.
Given the following assumptions:
The camera has no roll
The point you are looking at is [x, y, z]
You have yaw, pitch angles
[0, 1, 0] is "up"
Here is how to calculate some important values:
The view vector: v = [vx, vy, vz] = [cos(yaw)*cos(pitch), sin(pitch), -sin(yaw)*cos(pitch)]
The camera location: p = [x, y, z] - r*v
The right vector: cross product v with [0, 1, 0]
The up vector: cross product v with the right vector
Your view quaternion is [0, vx, vy, vz] (that's the view vector with a 0 w-component)
Now in your simulation you can operate on pitch/yaw, which are pretty intuitive. If you want to do interpolation, convert the before and after pitch+yaws into quaternions and do quaternion spherical linear interpolation.
Related
I want to determine the horizontal and vertical angle, from a camera's position to a world point, in respect to the camera's forward axis.
My linear algebra is a bit rusty, but given the camera's forward, up, and right vector, for example:
camForward = [0 0 1];
camUp = [0 1 0];
camRight = [1 0 0];
And the camera position and world point, for example:
camPosition = [1 2 3];
worldPoint = [5 6 4];
The sought-after angles should be determinable by first taking the difference of the positions:
delta = worldPoint-camPosition;
Then projecting it on the camera axes using the dot products:
deltaHorizontal = dot(delta,camRight);
deltaVertical = dot(delta,camUp);
deltaDepth = dot(delta,camForward);
And finally computing angles as:
angleHorizontal = atan(deltaHorizontal/deltaDepth);
angleVertical = atan(deltaVertical/deltaDepth);
In the example case, this yields that both angles become ~76°, which seems reasonable; varying the positions and axes also seem to give reasonable results.
Thus, if I am not getting the angles I expect, it should be due to that I am using either incorrect position and/or camera axes. It is worth noting that the 3D engine is using OpenGL and GLM.
I am fairly certain that the positions are correct, as moving around in the scene and inspecting the positions in relation to known reference points give consistent and correct results. Leading me to believe that I am using the wrong camera axes. To get the angles I am using (the equivalent of):
glm::vec3 worldPoint = glm::unProject( glm::vec3(windowX, windowY, windowZ), viewMatrix, projectionMatrix, glm::vec4(0,0,windowWidth,windowHeight));
glm::vec3 delta = glm::vec3(worldPoint.x, worldPoint.y, worldPoint.z);
float horizontalDistance = glm::dot(delta, cameraData->right);
float verticalDistance = glm::dot(delta, cameraData->up);
float depthDistance = glm::dot(delta, cameraData->forward);
float horizontalAngle = glm::atan(horizontalDistance/depthDistance)
float verticalAngle = glm::atan(verticalDistance/depthDistance)
Each frame, forward, up, and right are read from a view matrix, viewMatrix which in turn is produced by a converting a quaternion, Q, which holds the camera rotation which is controlled by mouse:
void updateView(CameraData * cameraData, MouseData * mouseData, MouseParameters * mouseParameters){
float deltaX = mouseData->currentX - mouseData->lastX;
float deltaY = mouseData->currentY - mouseData->lastY;
mouseData->lastX = mouseData->currentX;
mouseData->lastY = mouseData->currentY;
float pitch = mouseParameters->sensitivityY * deltaY;
float yaw = mouseParameters->sensitivityX * deltaX;
glm::quat pitch_Q = glm::quat(glm::vec3(pitch, 0.0f, 0.0f));
glm::quat yaw_Q = glm::quat(glm::vec3(0.0f, yaw, 0.0f));
cameraData->Q = pitch_Q * cameraData->Q * yaw_Q;
cameraData->Q = glm::normalize(cameraData->Q);
glm::mat4 rotation = glm::toMat4(cameraData->Q);
glm::mat4 translation = glm::mat4(1.0f);
translation = glm::translate(translation, -(cameraData->position));
cameraData->viewMatrix = rotation * translation;
cameraData->forward = (cameraData->viewMatrix)[2];
cameraData->up = (cameraData->viewMatrix)[1];
cameraData->right = (cameraData->viewMatrix)[0];
}
However, something goes wrong, and the correct angles are seemingly only produced while looking along, or perpendicular to, the world z-axis ([0 0 1]). Where am I mistaken?
I'm trying to implement a camera that follows a moving object. I've implemented these functions:
void Camera::espheric_yaw(float degrees, glm::vec3 center_point)
{
float lim_yaw = glm::radians(89.0f);
float radians = glm::radians(degrees);
absoluteYaw += radians;
... clamp absoluteYaw
float radius = 10.0f;
float camX = cos(absoluteYaw) * cos(absoluteRoll) * radius;
float camY = sin(absoluteRoll)* radius;
float camZ = sin(absoluteYaw) * cos(absoluteRoll) * radius;
eyes.x = camX;
eyes.y = camY;
eyes.z = camZ;
lookAt = center_point;
view = glm::normalize(lookAt - eyes);
up = glm::vec3(0, 1, 0);
right = glm::normalize(glm::cross(view, up));
}
I want to use this function (and the pitch version) for a camera that follows a moving 3d model. Right now, it works when the center_point is the (0,1,0). I think i'm getting the position right but the up vector is clearly not always (0,1,0).
How can I get my up, view and right vector for the camera? And then, if I update the eyes position of the camera this way, how will my camera move when the other object (centered at center_position parameter) moves?
The idea is to update this each time I have mouse input with centered_value = center of the moving object. Then use gluLookAt with view, eyes and up values of my camera (and lookAt which will be eyes+view).
Following a moving object is matter of pointing the camera to that object. This is what typical lookAt function does. See the maths here and then use glm::lookAt().
The 'Arcball' technic is for rotating with the mouse. See some maths here.
The idea is to get two vectors (first, second) from positions on screen. For each vector, X,Y are taking depending on pixels "travelled" by mouse and the size of the window. Z is calculated by 'trackball' maths. With these two vectors (after normalizing them), its cross product gives the axis of rotation in camera coordinates, and its dot product gives the angle. Now, you can rotate the camera by glm::rotate()
If you go another route (e.g. calculating camera matrix on your own), then the "up" direction of the camera must be updated by yourself. Remember it's perpendicular to the other two axis of the camera.
I am implementing a first-person camera to move about a scene using the arrow keys on my keyboard. It seems to work OK when I am only rotating about a single axis (X or Y), however if I am rotating about both axes it also gives me rotation about the third, Z, axis. I am fairly sure that the problem is that my camera does not rotate about global axis but instead its local ones, resulting in 'roll' when I just want yaw and pitch. In my code I deduce a forward vector from the X and Y rotation, stored in two variables. The most relevant code snippet is as follows:
glm::mat4 CameraManager::rotateWorld(float angle, glm::vec3 rot){
static float yRot = 0.0f;
static float xRot = 0.0f;
glm::vec3 degrees = rot * angle;
glm::vec3 radians = glm::vec3(degrees.x * (M_PI/180.0f),
degrees.y * (M_PI/180.0f),
degrees.z * (M_PI/180.0f));
yRot += radians.y;
xRot += radians.x;
forwardVector = glm::vec3(sinf(yRot) * cosf(xRot),
-sinf(xRot),
-cosf(yRot) * cosf(xRot));
return glm::rotate(glm::mat4(1.0f), angle, rot);
}
the rotateWorld function is complemented by the moveForwardfunction:
glm::mat4 CameraManager::moveForward(float dist){
glm::vec3 translation = forwardVector/glm::vec3(sqrt(forwardVector.x * forwardVector.x +
forwardVector.y * forwardVector.y +
forwardVector.z * forwardVector.z)) * dist;
return glm::translate(glm::mat4(1.0f), -translation);
}
where yRot is equivalent to yaw and xRot is equivalent to pitch.
The rotation and translation matrices are simply multiplied together in the main section of the program.
I then go on to multiply a distance d by this vector to update the position.
xRot and yRot are static doubles that get incremented/decremented when the user presses an arrow key.
When the program starts, this is the view. The plane and the monkey head are facing the 'right way' up. incrementing/decrementing the pitch and yaw individually work as expected. But when I, say, increase the pitch and then yaw, the scene flips sideways! (Picture below.) Any ideas how to fix this?
If I understand you correctly, the problem you're experiencing is that your "up" vector is not always pointing vertically upwards with respect to the intended Y axis of your viewing plane.
Determining a correct "up" vector usually requires a combination of cross product operations against the vector you have against the viewport's X and Y axes.
You may find some useful hints in the documentation for the gluLookAt function whose purpose is to calculate a view matrix with desired orientation (i.e. without roll) given an eye position and the coordinates of the intended centre of the field.
I am using glm to create a camera class, and I am running into some problems with a lookat function. I am using a quaternion to represent rotation, but I want to use glm's prewritten lookat function to avoid duplicating code. This is my lookat function right now:
void Camera::LookAt(float x, float y, float z) {
glm::mat4 lookMat = glm::lookAt(position, glm::vec3(x, y, z), glm::vec3(0, 1, 0));
rotation = glm::toQuat(lookMat);
}
However when I call LookAt(0.0f,0.0f,0.0f), my camera is not rotated to that point. When I call glm::eulerangles(rotation) after the lookat call, I get a vec3 with the following values: (180.0f, 0.0f, 180.0f). position is (0.0f,0.0f,-10.0f), so I should not have any rotation at all to look at 0,0,0. This is the function which builds the view matrix:
glm::mat4 Camera::GetView() {
view = glm::toMat4(rotation) * glm::translate(glm::mat4(), position);
return view;
}
Why am I not getting the correct quaternion, and how can I fix my code?
Solution:
You have to invert the rotation of the quaternion by conjugating it:
using namespace glm;
quat orientation = conjugate(toQuat(lookAt(vecA, vecB, up)));
Explanation:
The lookAt function is a replacement for gluLookAt, which is used to construct a view matrix.
The view matrix is used to rotate the world around the viewer, and is therefore the inverse of the cameras transform.
By taking the inverse of the inverse, you can get the actual transform.
I ran into something similar, the short answer is your lookMat might need to be inverted/transposed, because it is a camera rotation (at least in my case), as opposed to a world rotation. Rotating the world would be a inverse of a camera rotation.
I have a m_current_quat which is a quaternion that stores the current camera rotation. I debugged the issue by printing out the matrix produced by glm::lookAt, and comparing with the resulting matrix that I get by applying m_current_quat and a translation by m_camera_position. Here is the relevant code for my test.
void PrintMatrix(const GLfloat m[16], const string &str)
{
printf("%s:\n", str.c_str());
for (int i=0; i<4; i++)
{
printf("[");
//for (int j=i*4+0; j<i*4+4; j++) // row major, 0, 1, 2, 3
for (int j=i+0; j<16; j+=4) // OpenGL is column major by default, 0, 4, 8, 12
{
//printf("%d, ", j); // print matrix index
printf("%.2f, ", m[j]);
}
printf("]\n");
}
printf("\n");
}
void CameraQuaternion::SetLookAt(glm::vec3 look_at)
{
m_camera_look_at = look_at;
// update the initial camera direction and up
//m_initial_camera_direction = glm::normalize(m_camera_look_at - m_camera_position);
//glm::vec3 initial_right_vector = glm::cross(m_initial_camera_direction, glm::vec3(0, 1, 0));
//m_initial_camera_up = glm::cross(initial_right_vector, m_initial_camera_direction);
m_camera_direction = glm::normalize(m_camera_look_at - m_camera_position);
glm::vec3 right_vector = glm::cross(m_camera_direction, glm::vec3(0, 1, 0));
m_camera_up = glm::cross(right_vector, m_camera_direction);
glm::mat4 lookat_matrix = glm::lookAt(m_camera_position, m_camera_look_at, m_camera_up);
// Note: m_current_quat quat stores the camera rotation with respect to the camera space
// The lookat_matrix produces a transformation for world space, where we rotate the world
// with the camera at the origin
// Our m_current_quat need to be an inverse, which is accompolished by transposing the lookat_matrix
// since the rotation matrix is orthonormal.
m_current_quat = glm::toQuat(glm::transpose(lookat_matrix));
// Testing: Make sure our model view matrix after gluLookAt, glmLookAt, and m_current_quat agrees
GLfloat current_model_view_matrix[16];
//Test 1: gluLookAt
gluLookAt(m_camera_position.x, m_camera_position.y, m_camera_position.z,
m_camera_look_at.x, m_camera_look_at.y, m_camera_look_at.z,
m_camera_up.x, m_camera_up.y, m_camera_up.z);
glGetFloatv(GL_MODELVIEW_MATRIX, current_model_view_matrix);
PrintMatrix(current_model_view_matrix, "Model view after gluLookAt");
//Test 2: glm::lookAt
lookat_matrix = glm::lookAt(m_camera_position, m_camera_look_at, m_camera_up);
PrintMatrix(glm::value_ptr(lookat_matrix), "Model view after glm::lookAt");
//Test 3: m_current_quat
glLoadIdentity();
glMultMatrixf( glm::value_ptr( glm::transpose(glm::mat4_cast(m_current_quat))) );
glTranslatef(-m_camera_position.x, -m_camera_position.y, -m_camera_position.z);
glGetFloatv(GL_MODELVIEW_MATRIX, current_model_view_matrix);
PrintMatrix(current_model_view_matrix, "Model view after quaternion transform");
return;
}
Hope this helps.
I want to use glm's prewritten lookat function to avoid duplicating code.
But it's not duplicating code. The matrix that comes out of glm::lookat is just a mat4. Going through the conversion from a quaternion to 3 vectors, only so that glm::lookat can convert it back into an orientation is just a waste of time. You've already done 85% of lookat's job; just do the rest.
You are getting the (or better: a) correct rotation.
When I call glm::eulerangles(rotation) after the lookat call, I get a
vec3 with the following values: (180.0f, 0.0f, 180.0f). position is
(0.0f,0.0f,-10.0f), so I should not have any rotation at all to look
at 0,0,0.
glm is following the conventions of the old fixed-function GL. And there, eye space was defined as the camera placed at origin, with x pointng to the right, y up and looking in -z direction. Since you want to look in positive z direction, the camera has to turn. Now, as a human, I would have described that as a rotation of 180 degrees around y, but a rotation of 180 degrees around x in combination with another 180 degrees rotation aroundz will have the same effect.
When multiplied by the LookAt view matrix, the world-space vectors are rotated (brought) into the camera's view while the camera's orientation is kept in place.
So an actual rotation of the camera by 45 degress to the right is achieved with a matrix which applies a 45 degree rotation to the left to all the world-space vertices.
For a Camera object you would need to get its local forward and up direction vectors in order to calculate a lookAt view matrix.
viewMatrix = glm::lookAtLH (position, position + camera_forward, camera_up);
When using quaternions to store the orientation of an object (be it a camera or anything else), usually this rotation quat is used to calculate the vectors which define its local-space (left-handed one in the below example):
glm::vec3 camera_forward = rotation * glm::vec3(0,0,1); // +Z is forward direction
glm::vec3 camera_right = rotation * glm::vec3(1,0,0); // +X is right direction
glm::vec3 camera_up = rotation * glm::vec3(0,1,0); // +Y is up direction
Thus, the world-space directions should be rotated 45 degress to the right in order to reflect the correct orientation of the camera.
This is why the lookMat or the quat obtained from it cannot be directly used for this purpose, since the orientation they describe is a reversed one.
Correct rotation can be done in two ways:
Calculate the inverse of the lookAt matrix and multiply the world-space direction vectors by this rotation matrix
(more efficient) Convert the LookAt matrix into a quaternion and conjugate it instead of applying glm::inverse, since the result is a unit quat and for such quats the inverse is equal to the conjugate.
Your LookAt should look like this:
void Camera::LookAt(float x, float y, float z) {
glm::mat4 lookMat = glm::lookAt(position, glm::vec3(x, y, z), glm::vec3(0, 1, 0));
rotation = glm::conjugate( glm::quat_cast(lookMat));
}
So I've been having trouble with a camera I've implemented in OpenGL and C++ using the GLM library. The type of camera I'm aiming for is a fly around camera which will allow easy exploration of a 3D world. I have managed to get the camera pretty much working, it's nice and smooth, looks around and the movement seems to be nice and correct.
The only problem I seem to have is that the rotation along the camera's X and Y axis (looking up and down) introduces some rotation about it's Z axis. This has the result of causing the world to slightly roll whilst travelling about.
As an example... if I have a square quad in front of the camera and move the camera in a circular motion, so as if looking around in a circle with your head, once the motion is complete the quad will have rolled slightly as if you've tilted your head.
My camera is currently a component which I can attach to an object/entity in my scene. Each entity has a "Frame" which is basically the model matrix for that entity. The Frame contains the following attributes:
glm::mat4 m_Matrix;
glm::vec3 m_Position;
glm::vec3 m_Up;
glm::vec3 m_Forward;
These are then used by the camera to create the appropriate viewMatrix like this:
const glm::mat4& CameraComponent::GetViewMatrix()
{
//Get the transform of the object
const Frame& transform = GetOwnerGO()->GetTransform();
//Update the viewMatrix
m_ViewMatrix = glm::lookAt(transform.GetPosition(), //position of camera
transform.GetPosition() + transform.GetForward(), //position to look at
transform.GetUp()); //up vector
//return reference to the view matrix
return m_ViewMatrix;
}
And now... here are my rotate X and Y methods within the Frame object, which I'm guessing is the place of the problem:
void Frame::RotateX( float delta )
{
glm::vec3 cross = glm::normalize(glm::cross(m_Up, m_Forward)); //calculate x axis
glm::mat4 Rotation = glm::rotate(glm::mat4(1.0f), delta, cross);
m_Forward = glm::normalize(glm::vec3(Rotation * glm::vec4(m_Forward, 0.0f))); //Rotate forward vector by new rotation
m_Up = glm::normalize(glm::vec3(Rotation * glm::vec4(m_Up, 0.0f))); //Rotate up vector by new rotation
}
void Frame::RotateY( float delta )
{
glm::mat4 Rotation = glm::rotate(glm::mat4(1.0f), delta, m_Up);
//Rotate forward vector by new rotation
m_Forward = glm::normalize(glm::vec3(Rotation * glm::vec4(m_Forward, 0.0f)));
}
So somewhere in there, there's a problem which I've been searching around trying to fix. I've been messing with it for a few days now, trying random things but I either get the same result, or the z axis rotation is fixed but other bugs appear such as incorrect X, Y rotation and camera movement.
I had a look at gimbal lock but from what I understood of it, this problem didn't seem quite like gimbal lock to me. But I may be wrong.
Store the current pitch/yaw angles and generate the camera matrix on-the-fly instead of trying to accumulate small changes on the intermediate vectors.
In your RotateY function, change it from this:
glm::mat4 Rotation = glm::rotate(glm::mat4(1.0f), delta, m_Up);
to this:
glm::mat4 Rotation = glm::rotate(glm::mat4(1.0f), delta, glm::vec3(0,1,0));