opengl trackball - opengl

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.

Related

Ray vs ellipsoid intersection

I am trying to implement ray vs ellipsoid intersection by "squishing" space and doing ray vs sphere:
create mat3 S with ellipsoid radius at diagonal
squish ray by multiplying start and direction by an inverse of S
intersect ray with sphere of radius 1.0 in local space
multiply hitPoint by S to unsquish it.
Here is ray vs sphere:
float P = glm::dot(dir, sphereCenter-start);
float L = glm::distance(start, sphereCenter);
float d = sqrt(L*L - P*P);
if (d < radius) {
float x0 = sqrt(1.f - d*d);
hitPoint = start + dir*(P - x0);
hitNormal = glm::normalize(hitPoint - sphereCenter);
}
else if (d == radius) {
hitPoint = start + dir*P;
hitNormal = glm::normalize(hitPoint - sphereCenter);
}
else {
return false;
}
if (glm::distance(start, hitPoint) > dist) return false;
return true;
Here is the squishing part:
glm::vec3 S = start;
glm::vec3 Dir = dir;
auto sphereCenter = thisEntity()->transform()->getPosition();
auto scale = thisEntity()->transform()->getScale();
glm::mat3 q = glm::mat3(0);
float x = _radius.x * scale.x;
float y = _radius.y * scale.y;
float z = _radius.z * scale.z;
q[0][0] = x;
q[1][1] = y;
q[2][2] = z;
glm::mat3 qI = glm::inverse(q);
S = qI * S;
Dir = qI * Dir;
//calculate hit point in world space squished
glm::vec3 hitPoint, hitNormal;
if (!IntersectionsMath::instance()->segmentVsSphere(sphereCenter, S, Dir, dist, 1.f, hitPoint, hitNormal)) return;
hitPoint = q * hitPoint;
hit.pushHit(hitPoint, hitNormal, this);
Current ray sphere code is for world position, i'm trying to make it work at the origin so it shouldn't matter. Ray vs regular sphere works fine, ellipsoid is the problem.
I spent a lot of time on this and something somewhere is wrong.
Problem:
The center of scaling matters.
Solution:
Perform the scaling about the center of the ellipsoid.
... and not the origin as you are doing right now. This is because, although the direction of the ray will be the same (it is just a directional vector), the relative displacement between the scaled source and center of the sphere will be different:
Scaling about origin (current code):
Source S' = qI * S, center C' = qI * C --- S' - C' = qI * (S - C)
Scaling about ellipsoid center (correct procedure):
Source S" = qI * (S - C), center C" = C --- S" - C" = qI * (S - C) - C
The two displacements differ by the position of the original ellipsoid; thus your current ray will likely miss / give false positives.
Corrected code:
// scale about the ellipsoid's position by subtracting before multiplying
// more appropriate name would be "ellipseCenter" to avoid confusion
S_ = qI * (S - sphereCenter);
// this ::normalize should really be in the intersection function
Dir_ = glm::normalize(qI * Dir);
// calculate hit point in world space squished
// ... but around the origin in the squashed coordinate system
glm::vec3 hitPoint, hitNormal;
if (!IntersectionsMath::instance()->segmentVsSphere(
glm::vec3::ZERO, S_, Dir_,
dist, 1.f,
hitPoint, hitNormal)) return;
// re-apply the offset
hitPoint = q * hitPoint + sphereCenter
// problem: hitNormal will not be correct for the ellipsoid when scaled
// solution: divide through each component by square of respective semi-axis
// (will provide proof upon request)
hitNormal.x /= (x * x); hitNormal.y /= (y * y); hitNormal.z /= (z * z);

Rotating around a sphere using OpenGL and gluLookAt

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.

I need to implement a 2d shape rotate function

this is the formular but i dont know how to implement it. can someone please help
rectangle::rectangle() //rectangle constructor
{
bl.real() = 0; //bottom
bl.imag() = 0; //left
tr.real() = 1; //top
tr.imag() = 1; //right
}
complex<double> rectangle::get_bl() const
{
return bl;
}
complex<double> rectangle::get_tr() const
{
return tr;
}
void rectangle::rotate(double angle)
{
//not sure how to do it tr = tr.real() * cos(angle) + tr.imag() *cos(angle);
}
main
rectangle r;
r.rotate(90);
expected output (not 100% sure)
0 0 -1 1
Move your shape to (0, 0) temporarily (formula assumes you are rotating about origin, so move the bottom-left corner to (0, 0)).
Apply formula.
Move it back.
if (tr.real() < bl.real()) {
float tempX = tr.real() - bl.real();
float tempY = tr.imag() - bl.imag();
} else {
float tempX = bl.real() - tr.real();
float tempY = bl.imag() - tr.imag();
}
tr.real() = tempX * cos(theta) - tempY * sin(theta)
tr.imag() = tempx * sin(theta) + tempY * cos(theta)
The formula is basically saying:
new_x = shape.point[i].x*cos(angle) - shape.point[i].y*sin(angle)
new_y = shape.point[i].x*sin(angle) + shape.point[i].y*cos(angle)
shape.point[i].x = new_x
shape.point[i].y = new_y
angle is in radians, to convert from degrees to radians use
degree*pi/180 where pi is the constant 3.14...
you will need to do this for each point on the shape to fully rotate the shape by the desired degree.
This formula also assumes that the points are centered around (0,0), i.e. the center of the shape is (0,0) and all points are relative to that center.
One tip, if applicable, try and store shapes as points, going clockwise from the 0th point. for instance, this rectangle will be:
point[0] = {-1, 1}
point[1] = { 1, 1}
point[2] = { 1,-1}
point[3] = {-1,-1}
To convert from tl, br to points you will need to do something similar to:
point[0] = {tl.x, tl.y}
point[1] = {br.x, tl.y}
point[2] = {br.x, br.y}
point[3] = {tl.x, br.y}

Getting a Virtual Trackball to work from any viewing angle

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.

Bullet algorithm having trouble with rotation on the X

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));