Alright, so I'm trying to click and drag to rotate around an object using C++ and OpenGL. The way I have it is to use gluLookAt centered at the origin and I'm getting coordinates for the eye by using parametric equations for a sphere (eyex = 2* cos(theta) * sin(phi); eyey = 2* sin(theta) * sin(phi); eyez = 2* cos(phi);). This works mostly, as I can click and rotate horizontally, but when I try to rotate vertically it makes tight circles instead of rotating vertically. I'm trying to get the up vector by using the position of the camera and a vecter at a 90 degree angle along the x-z plane and taking the cross product of that.
The code I have is as follows:
double dotProduct(double v1[], double v2[]) {
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}
void mouseDown(int button, int state, int x, int y) {
if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN ) {
xpos = x;
ypos = y;
}
}
void mouseMovement(int x, int y) {
diffx = x - xpos;
diffy = y - ypos;
xpos = x;
ypos = y;
}
void camera (void) {
theta += 2*PI * (-diffy/glutGet(GLUT_SCREEN_HEIGHT));
phi += PI * (-diffx/glutGet(GLUT_WINDOW_WIDTH));
eyex = 2* cos(theta) * sin(phi);
eyey = 2* sin(theta) * sin(phi);
eyez = 2* cos(phi);
double rightv[3], rightt[3], eyes[3];
rightv[0] = 2* cos(theta + 2/PI) * sin(phi);
rightv[1] = 0;
rightv[2] = 2* cos(phi);
rightt[0] = rightv[0];
rightt[1] = rightv[1];
rightt[2] = rightv[2];
rightv[0] = rightv[0] / sqrt(dotProduct(rightt, rightt));
rightv[1] = rightv[1] / sqrt(dotProduct(rightt, rightt));
rightv[2] = rightv[2] / sqrt(dotProduct(rightt, rightt));
eyes[0] = eyex;
eyes[1] = eyey;
eyes[2] = eyez;
upx = (eyey/sqrt(dotProduct(eyes,eyes)))*rightv[2] + (eyez/sqrt(dotProduct(eyes,eyes)))*rightv[1];
upy = (eyez/sqrt(dotProduct(eyes,eyes)))*rightv[0] + (eyex/sqrt(dotProduct(eyes,eyes)))*rightv[2];
upz = (eyex/sqrt(dotProduct(eyes,eyes)))*rightv[1] + (eyey/sqrt(dotProduct(eyes,eyes)))*rightv[0];
diffx = 0;
diffy = 0;
}
I am somewhat basing things off of this but it doesn't work, so I tried my way instead.
This isn't exactly a solution for the way you are doing it but I did something similar the other day. I did it by using DX's D3DXMatrixRotationAxis and D3DXVec3TransformCoord The math behind the D3DXMatrixRotationAxis method can be found at the bottom of the following page: D3DXMatrixRotationAxis Math use this if you are unable to use DX. This will allow you to rotate around any axis you pass in. In my object code I keep track of a direction and up vector and I simply rotate each of these around the axis of movement(in your case the yaw and pitch).
To implement the fixed distance camera like this I would simply do the dot product of the current camera location and the origin location (if this never changes then you can simply do it once.) and then move the camera to the origin rotate it the amount you need then move it back with its new direction and up values.
Related
I am trying to do the equivalent of multiplying the velocity by the time between frames. I would imagine that doing this for quaternions would be done by raising them to a power. I have code to rotate an object based on my mouse movements. It has a main loop running at one frame rate and a physics loop running at a fixed frame rate. Here is the relevant part of the main loop:
glfwPollEvents();
Input::update();
window.clear(0,0,0,1);
rigidBody.angularVelocity *= glm::angleAxis(0.001f * Input::deltaMouse().x, glm::vec3(0,1,0));
rigidBody.angularVelocity *= glm::angleAxis(0.001f * Input::deltaMouse().y, glm::vec3(1,0,0));
if(Input::getKey(Input::KEY_A))
{
rigidBody.velocity -= float(Time::getDelta()) * glm::vec3(1,0,0);
}
if(Input::getKey(Input::KEY_D))
{
rigidBody.velocity += float(Time::getDelta()) * glm::vec3(1,0,0);
}
if(Input::getKey(Input::KEY_W))
{
rigidBody.velocity -= float(Time::getDelta()) * glm::vec3(0,0,1);
}
if(Input::getKey(Input::KEY_S))
{
rigidBody.velocity += float(Time::getDelta()) * glm::vec3(0,0,1);
}
if(Input::getKey(Input::KEY_LCONTROL))
{
rigidBody.velocity -= float(Time::getDelta()) * glm::vec3(0,1,0);
}
if(Input::getKey(Input::KEY_LSHIFT))
{
rigidBody.velocity += float(Time::getDelta()) * glm::vec3(0,1,0);
}
Here is the relevant part of the physics loop:
for(int i = 0; i < *numRigidBodies; i++)
{
rigidBodies[i].transform->getPos() += rigidBodies[i].velocity;
rigidBodies[i].transform->getRot() *= rigidBodies[i].angularVelocity;
}
rigidBodies[0].angularVelocity = glm::quat();
rigidBodies[0].velocity = glm::vec3();
This works fine, but when I try raising angular velocity to a power with glm::pow, the object rotates randomly and does not follow my mouse. I realize I could do this with a line of code like
rigidBodies[i].transform->getRot() *= glm::angleAxis((float)Time::getFixedDelta() * glm::angle(rigidBodies[i].angularVelocity), glm::axis(rigidBodies[i].angularVelocity));
but this seems needlessly complicated for the task. What is causing this issue, and how can I fix it?
Not sure exactly how to do it with the API you're using, but basically, you would use Quaternion::Slerp(). Slerp means "spherical linear interpolation".
Something like this(pseudocode) should work:
auto& rot = rigidBodies[i].transform->getRot();
auto goal = rigidBodies[i].angularVelocity * rot;
rot = rot.slerp(rot, goal, Time::deltaTime);
Edit:
I should note that this is not how I would approach this problem. I would just store the rotation around the X and Y axis as scalars and construct a new quaternion from them each frame.
Please excuse the sloppy pseudo code:
// previous x and y positions, could probably be set in MouseDown event
float lastX = ...;
float lastY = ...;
float xRotation = 0;
float yRotation = 0;
float rotationSpeed = 1.0;
void OnMouseMove(float x, float y) {
float dx = x - lastX;
float dy = y - lastY;
lastX = x;
lastY = y;
xRotation += dy * rotationSpeed * Time::deltaTime;
yRotation += dx * rotationSpeed * Time::deltaTime;
rigidBodies[i].transform->getRot() = eulerQuat(xRotation, yRotation, 0);
}
Turns out angular velocity is usually represented as a 3d vector where the direction is the axis and the magnitude is the angular speed. Replace this line of code:
rigidBodies[i].transform->getRot() *= rigidBodies[i].angularVelocity;
with this:
if(rigidBodies[i].angularVelocity != glm::vec3())
rigidBodies[i].transform->getRot() *= glm::quat(rigidBodies[i].angularVelocity * float(Time::getFixedDelta()));
and the physics system works as expected. The if check makes sure that angular speed is not 0.
I've asked this question over at GameDev but got not response so far and this question is a bit time sensitive unfortunately.
I'm pretty sure this is just me doing something stupid or not understanding something that I should but I cannot figure out what is wrong here.
I'm having a problem bouncing a projectile off a sprite, we've been asked to move the projectile using the equations of motions which makes things a little more difficult but as far as I can see what I have should work.
What I'm trying to do is change the angle of the collided projectile depending on which direction it is coming from.
Here is a video that is hopefully not too laggy for you to see what is happening:
Link
When the projectile collides with the left or right hand side of the sprite everything works as expected, it just switches X direction.
When it hit's the top or bottom of the sprite however it doesn't change, it just sort of rolls along the top and the shoots off.
Here is the movement code:
float nX = get_x() + cos(nGetAngle() * 3.14 / 180) * getU() * getT();
float nY = get_y() - sin(nGetAngle() * 3.14 / 180) * getU() * getT() + 0.5 * 9.8 * getT() * getT();
set_world_position(nX, nY);
Where U is initial velocity, T is time and nGetAngle() is the angle in degrees (which is set to radians whenever the angle is set).
Here is my collision for the top of the player:
//if the projectile is colliding in any way with the player sprite
if (projectiles[currProj]->get_y() < player->get_y()) // top of player
{
float vx = cos(projectiles[currProj]->nGetAngle());
float vy = sin(projectiles[currProj]->nGetAngle());
float newAngle = atan2(-vy, vx) * 180 / 3.14;
projectiles[currProj]->nSetAngle(newAngle);
projectiles[currProj]->set_world_position_y(player->get_y() - projectiles[currProj]->get_height() - 1);
}
and here is my collision for the left of the player:
else if (projectiles[currProj]->get_x() < player->get_x()) // left of player
{
projectiles[currProj]->set_world_position_x(player->get_x() - projectiles[currProj]->get_width());
float vx = cos(projectiles[currProj]->nGetAngle());
float vy = sin(projectiles[currProj]->nGetAngle());
float newAngle = atan2(vy, -vx) * 180 / 3.14;
projectiles[currProj]->nSetAngle(newAngle);
}
The left side collision works, the top does not and I have no idea why.
If necessary I can post the entire project somewhere.
Full collision code for player:
void Game::playerCollision()
{
if (projectiles[currProj]->bb_collision(player))
{
if (projectiles[currProj]->get_y() < player->get_y()) // top of player
{
float vx = cos(projectiles[currProj]->nGetAngle());
float vy = sin(projectiles[currProj]->nGetAngle());
float newAngle = atan2(-vy, vx) * 180 / 3.14;
projectiles[currProj]->nSetAngle(newAngle);
projectiles[currProj]->set_world_position_y(player->get_y() - projectiles[currProj]->get_height() - 1);
}
else if (projectiles[currProj]->get_y() + projectiles[currProj]->get_height() > player->get_y() + player->get_height() + 1) // bottom of player
{
projectiles[currProj]->set_world_position_y(player->get_y() + player->get_height());
float vx = cos(projectiles[currProj]->nGetAngle());
float vy = sin(projectiles[currProj]->nGetAngle());
float newAngle = atan2(-vy, vx) * 180 / 3.14;
projectiles[currProj]->nSetAngle(newAngle);
}
else if (projectiles[currProj]->get_x() < player->get_x()) // left of player
{
projectiles[currProj]->set_world_position_x(player->get_x() - projectiles[currProj]->get_width());
float vx = cos(projectiles[currProj]->nGetAngle());
float vy = sin(projectiles[currProj]->nGetAngle());
float newAngle = atan2(vy, -vx) * 180 / 3.14;
projectiles[currProj]->nSetAngle(newAngle);
}
else if (projectiles[currProj]->get_x() > player->get_x()) // right of player
{
projectiles[currProj]->set_world_position_x(player->get_x() + player->get_width());
float vx = cos(projectiles[currProj]->nGetAngle());
float vy = sin(projectiles[currProj]->nGetAngle());
float newAngle = atan2(vy, -vx) * 180 / 3.14;
projectiles[currProj]->nSetAngle(newAngle);
}
}
}
I think your collision detection is not sufficient. without knowing your representation in detail
you do not check where the projectile (pr) came from. a collision top left within the player (pl) might have entered through the top or from the left
you do not bounce the pr immediately, you just alter the direction. depending on the entry depth it might not be able to exit with the next iteration. this happens especially on the top where the pr accelerates downwards but slows down upwards.
so you must
detect the entry surface (determines angle)
and most important rebounce immediately
I am trying to rotate opengl scene using track ball. The problem i am having is i am getting rotations opposite to direction of my swipe on screen. Here is the snippet of code.
prevPoint.y = viewPortHeight - prevPoint.y;
currentPoint.y = viewPortHeight - currentPoint.y;
prevPoint.x = prevPoint.x - centerx;
prevPoint.y = prevPoint.y - centery;
currentPoint.x = currentPoint.x - centerx;
currentPoint.y = currentPoint.y - centery;
double angle=0;
if (prevPoint.x == currentPoint.x && prevPoint.y == currentPoint.y) {
return;
}
double d, z, radius = viewPortHeight * 0.5;
if(viewPortWidth > viewPortHeight) {
radius = viewPortHeight * 0.5f;
} else {
radius = viewPortWidth * 0.5f;
}
d = (prevPoint.x * prevPoint.x + prevPoint.y * prevPoint.y);
if (d <= radius * radius * 0.5 ) { /* Inside sphere */
z = sqrt(radius*radius - d);
} else { /* On hyperbola */
z = (radius * radius * 0.5) / sqrt(d);
}
Vector refVector1(prevPoint.x,prevPoint.y,z);
refVector1.normalize();
d = (currentPoint.x * currentPoint.x + currentPoint.y * currentPoint.y);
if (d <= radius * radius * 0.5 ) { /* Inside sphere */
z = sqrt(radius*radius - d);
} else { /* On hyperbola */
z = (radius * radius * 0.5) / sqrt(d);
}
Vector refVector2(currentPoint.x,currentPoint.y,z);
refVector2.normalize();
Vector axisOfRotation = refVector1.cross(refVector2);
axisOfRotation.normalize();
angle = acos(refVector1*refVector2);
I recommend artificially setting prevPoint and currentPoint to (0,0) (0,1) and then stepping through the code (with a debugger or with your eyes) to see if each part makes sense to you, and the angle of rotation and axis at the end of the block are what you expect.
If they are what you expect, then I'm guessing the error is in the logic that occurs after that. i.e. you then take the angle and axis and convert them to a matrix which gets multiplied to move the model. A number of convention choices happen in this pipeline --which if swapped can lead to the type of bug you're having:
Whether the formula assumes the angle is winding left or right handedly around the axis.
Whether the transformation is meant to rotate an object in the world or meant to rotate the camera.
Whether the matrix is meant to operate by multiplication on the left or right.
Whether rows or columns of matrices are contiguous in memory.
I am currently trying to work on getting my virtual trackball to work from any angle. When I am looking at it from the z axis, it seems to work fine. I hold my mouse down, and move the mouse up... the rotation will move accordingly.
Now, if I change my viewing angle / position of my camera and try to move my mouse. The rotation will occur as if I were looking from the z axis. I cannot come up with a good way to get this to work.
Here is the code:
void Renderer::mouseMoveEvent(QMouseEvent *e)
{
// Get coordinates
int x = e->x();
int y = e->y();
if (isLeftButtonPressed)
{
// project current screen coordinates onto hemi sphere
Point sphere = projScreenCoord(x,y);
// find axis by taking cross product of current and previous hemi points
axis = Point::cross(previousPoint, sphere);
// angle can be found from magnitude of cross product
double length = sqrt( axis.x * axis.x + axis.y * axis.y + axis.z * axis.z );
// Normalize
axis = axis / length;
double lengthPrev = sqrt( previousPoint.x * previousPoint.x + previousPoint.y * previousPoint.y + previousPoint.z * previousPoint.z );
double lengthCur = sqrt( sphere.x * sphere.x + sphere.y * sphere.y + sphere.z * sphere.z );
angle = asin(length / (lengthPrev * lengthCur));
// Convert into Degrees
angle = angle * 180 / M_PI;
// 'add' this rotation matrix to our 'total' rotation matrix
glPushMatrix(); // save the old matrix so we don't mess anything up
glLoadIdentity();
glRotatef(angle, axis[0], axis[1], axis[2]); // our newly calculated rotation
glMultMatrixf(rotmatrix); // our previous rotation matrix
glGetFloatv(GL_MODELVIEW_MATRIX, (GLfloat*) rotmatrix); // we've let OpenGL do our matrix mult for us, now get this result & store it
glPopMatrix(); // return modelview to its old value;
}
// Project screen coordinates onto a unit hemisphere
Point Renderer::projScreenCoord(int x, int y)
{
// find projected x & y coordinates
double xSphere = ((double)x/width)*2.0 - 1.0;
double ySphere = ( 1 - ((double)y/height)) * 2.0 - 1.0;
double temp = 1.0 - xSphere*xSphere - ySphere*ySphere;
// Do a check so you dont do a sqrt of a negative number
double zSphere;
if (temp < 0){ zSphere = 0.0;}
else
{zSphere = sqrt(temp);}
Point sphere(xSphere, ySphere, zSphere);
// return the point on the sphere
return sphere;
}
I am still fairly new at this. Sorry for the trouble and thanks for all the help =)
The usual way involves quaternions. E.g., in sample code originally from SGI.
Here is what I'm trying to do. I'm trying to make a bullet out of the center of the screen. I have an x and y rotation angle. The problem is the Y (which is modified by rotation on the x) is really not working as intended. Here is what I have.
float yrotrad, xrotrad;
yrotrad = (Camera.roty / 180.0f * 3.141592654f);
xrotrad = (Camera.rotx / 180.0f * 3.141592654f);
Vertex3f Pos;
// get camera position
pls.x = Camera.x;
pls.y = Camera.y;
pls.z = Camera.z;
for(float i = 0; i < 60; i++)
{
//add the rotation vector
pls.x += float(sin(yrotrad)) ;
pls.z -= float(cos(yrotrad)) ;
pls.y += float(sin(twopi - xrotrad));
//translate camera coords to cube coords
Pos.x = ceil(pls.x / 3);
Pos.y = ceil((pls.y) / 3);
Pos.z = ceil(pls.z / 3);
if(!CubeIsEmpty(Pos.x,Pos.y,Pos.z)) //remove first cube that made contact
{
delete GetCube(Pos.x,Pos.y,Pos.z);
SetCube(0,Pos.x,Pos.y,Pos.z);
return;
}
}
This is almost identical to how I move the player, I add the directional vector to the camera then find which cube the player is on. If I remove the pls.y += float(sin(twopi - xrotrad)); then I clearly see that on the X and Z, everything is pointing as it should. When I add pls.y += float(sin(twopi - xrotrad)); then it almost works, but not quite, what I observed from rendering out spheres of the trajector is that the furthur up or down I look, the more offset it becomes rather than stay alligned to the camera's center. What am I doing wrong?
Thanks
What basically happens is very difficult to explain, I'd expect the bullet at time 0 to always be at the center of the screen, but it behaves oddly. If i'm looking straight at the horizon to +- 20 degrees upward its fine but then it starts not following any more.
I set up my matrix like this:
void CCubeGame::SetCameraMatrix()
{
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(Camera.rotx,1,0,0);
glRotatef(Camera.roty,0,1,0);
glRotatef(Camera.rotz,0,0,1);
glTranslatef(-Camera.x , -Camera.y,-Camera.z );
}
and change the angle like this:
void CCubeGame::MouseMove(int x, int y)
{
if(!isTrapped)
return;
int diffx = x-lastMouse.x;
int diffy = y-lastMouse.y;
lastMouse.x = x;
lastMouse.y = y;
Camera.rotx += (float) diffy * 0.2;
Camera.roty += (float) diffx * 0.2;
if(Camera.rotx > 90)
{
Camera.rotx = 90;
}
if(Camera.rotx < -90)
{
Camera.rotx = -90;
}
if(isTrapped)
if (fabs(ScreenDimensions.x/2 - x) > 1 || fabs(ScreenDimensions.y/2 - y) > 1) {
resetPointer();
}
}
You need to scale X and Z by cos(xradrot). (In other words, multiply by cos(xradrot)).
Imagine you're pointing straight down the Z axis but looking straight up. You don't want the bullet to shoot down the Z axis at all, this is why you need to scale it. (It's basically the same thing that you're doing between X and Z, but now doing it on the XZ vector and Y.)
pls.x += float(sin(yrotrad)*cos(xrotrad)) ;
pls.z -= float(cos(yrotrad)*cos(xrotrad)) ;
pls.y += float(sin(twopi - xrotrad));