I am implementing a 3D engine for spatial visualisation, and am writing a camera with the following navigation features:
- Rotate the camera (ie, analogous to rotating your head)
- Rotate around an arbitrary 3D point (a point in space, which is probably not in the center of the screen; the camera needs to rotate around this keeping the same relative look direction, ie the look direction changes too. This does not look directly at the chosen rotation point)
- Pan in the camera's plane (so move up/down or left/right in the plane orthogonal to the camera's look vector)
The camera is not supposed to roll - that is, 'up' remains up. Because of this I represent the camera with a location and two angles, rotations around the X and Y axes (Z would be roll.) The view matrix is then recalculated using the camera location and these two angles. This works great for pan and rotating the eye, but not for rotating around an arbitrary point. Instead I get the following behaviour:
- The eye itself apparently moving further up or down than it should
- The eye not moving up or down at all when
m_dRotationXis 0 or pi. (Gimbal lock? How can I avoid this?) - The eye's rotation being inverted (changing the rotation makes it look further up when it should look further down, down when it should look further up) when
m_dRotationXis between pi and 2pi.
(a) What is causing this 'drift' in rotation?
This may be gimbal lock. If so, the standard answer to this is 'use quaternions to represent rotation', said many times here on SO (1, 2, 3 for example), but unfortunately without concrete details (example. This is the best answer I've found so far; it's rare.) I've struggled to implemented a camera using quaternions combining the above two types of rotations. I am, in fact, building a quaternion using the two rotations, but a commenter below said there was no reason - it's fine to immediately build the matrix.
This occurs when changing the X and Y rotations (which represent the camera look direction) when rotating around a point, but does not occur simply when directly changing the rotations, i.e. rotating the camera around itself. To me, this doesn't make sense. It's the same values.
(b) Would a different approach (quaternions, for example) be better for this camera? If so, how do I implement all three camera navigation features above?
If a different approach would be better, then please consider providing a concrete implemented example of that approach. (I am using DirectX9 and C++, and the D3DX* library the SDK provides.) In this second case, I will add and award a bounty in a couple of days when I can add one to the question. This might sound like I'm jumping the gun, but I'm low on time and need to implement or solve this quickly (this is a commercial project with a tight deadline.) A detailed answer will also improve the SO archives, because most camera answers I've read so far are light on code.
Thanks for your help :)
Some clarifications
Thanks for the comments and answer so far! I'll try to clarify a few things about the problem:
The view matrix is recalculated from the camera position and the two angles whenever one of those things changes. The matrix itself is never accumulated (i.e. updated) - it is recalculated afresh. However, the camera position and the two angle variables are accumulated (whenever the mouse moves, for example, one or both of the angles will have a small amount added or subtracted, based on the number of pixels the mouse moved up-down and/or left-right onscreen.)
Commenter JCooper states I'm suffering from gimbal lock, and I need to:
add another rotation onto your transform that rotates the eyePos to be completely in the y-z plane before you apply the transformation, and then another rotation that moves it back afterward. Rotate around the y axis by the following angle immediately before and after applying the yaw-pitch-roll matrix (one of the angles will need to be negated; trying it out is the fastest way to decide which).
double fixAngle = atan2(oEyeTranslated.z,oEyeTranslated.x);
Unfortunately, when implementing this as described, my eye shoots off above the scene at a very fast rate due to one of the rotations. I'm sure my code is simply a bad implementation of this description, but I still need something more concrete. In general, I find unspecific text descriptions of algorithms are less useful than commented, explained implementations. I am adding a bounty for a concrete, working example that integrates with the code below (i.e. with the other navigation methods, too.) This is because I would like to understand the solution, as well as have something that works, and because I need to implement something that works quickly since I am on a tight deadline.
Please, if you answer with a text description of the algorithm, make sure it is detailed enough to implement ('Rotate around Y, then transform, then rotate back' may make sense to you but lacks the details to know what you mean. Good answers are clear, signposted, will allow others to understand even with a different basis, are 'solid weatherproof information boards.')
In turn, I have tried to be clear describing the problem, and if I can make it clearer please let me know.
My current code
To implement the above three navigation features, in a mouse move event moving based on the pixels the cursor has moved:
// Adjust this to change rotation speed when dragging (units are radians per pixel mouse moves)
// This is both rotating the eye, and rotating around a point
static const double dRotatePixelScale = 0.001;
// Adjust this to change pan speed (units are meters per pixel mouse moves)
static const double dPanPixelScale = 0.15;
switch (m_eCurrentNavigation) {
case ENavigation::eRotatePoint: {
// Rotating around m_oRotateAroundPos
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dRotatePixelScale * D3DX_PI;
const double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dRotatePixelScale * D3DX_PI;
// To rotate around the point, translate so the point is at (0,0,0) (this makes the point
// the origin so the eye rotates around the origin), rotate, translate back
// However, the camera is represented as an eye plus two (X and Y) rotation angles
// This needs to keep the same relative rotation.
// Rotate the eye around the point
const D3DXVECTOR3 oEyeTranslated = m_oEyePos - m_oRotateAroundPos;
D3DXMATRIX oRotationMatrix;
D3DXMatrixRotationYawPitchRoll(&oRotationMatrix, dX, dY, 0.0);
D3DXVECTOR4 oEyeRotated;
D3DXVec3Transform(&oEyeRotated, &oEyeTranslated, &oRotationMatrix);
m_oEyePos = D3DXVECTOR3(oEyeRotated.x, oEyeRotated.y, oEyeRotated.z) + m_oRotateAroundPos;
// Increment rotation to keep the same relative look angles
RotateXAxis(dX);
RotateYAxis(dY);
break;
}
case ENavigation::ePanPlane: {
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dPanPixelScale;
const double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dPanPixelScale;
m_oEyePos += GetXAxis() * dX; // GetX/YAxis reads from the view matrix, so increments correctly
m_oEyePos += GetYAxis() * -dY; // Inverted compared to screen coords
break;
}
case ENavigation::eRotateEye: {
// Rotate in radians around local (camera not scene space) X and Y axes
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dRotatePixelScale * D3DX_PI;
const double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dRotatePixelScale * D3DX_PI;
RotateXAxis(dX);
RotateYAxis(dY);
break;
}
The RotateXAxis and RotateYAxis methods are very simple:
void Camera::RotateXAxis(const double dRadians) {
m_dRotationX += dRadians;
m_dRotationX = fmod(m_dRotationX, 2 * D3DX_PI); // Keep in valid circular range
}
void Camera::RotateYAxis(const double dRadians) {
m_dRotationY += dRadians;
// Limit it so you don't rotate around when looking up and down
m_dRotationY = std::min(m_dRotationY, D3DX_PI * 0.49); // Almost fully up
m_dRotationY = std::max(m_dRotationY, D3DX_PI * -0.49); // Almost fully down
}
And to generate the view matrix from this:
void Camera::UpdateView() const {
const D3DXVECTOR3 oEyePos(GetEyePos());
const D3DXVECTOR3 oUpVector(0.0f, 1.0f, 0.0f); // Keep up "up", always.
// Generate a rotation matrix via a quaternion
D3DXQUATERNION oRotationQuat;
D3DXQuaternionRotationYawPitchRoll(&oRotationQuat, m_dRotationX, m_dRotationY, 0.0);
D3DXMATRIX oRotationMatrix;
D3DXMatrixRotationQuaternion(&oRotationMatrix, &oRotationQuat);
// Generate view matrix by looking at a point 1 unit ahead of the eye (transformed by the above
// rotation)
D3DXVECTOR3 oForward(0.0, 0.0, 1.0);
D3DXVECTOR4 oForward4;
D3DXVec3Transform(&oForward4, &oForward, &oRotationMatrix);
D3DXVECTOR3 oTarget = oEyePos + D3DXVECTOR3(oForward4.x, oForward4.y, oForward4.z); // eye pos + look vector = look target position
D3DXMatrixLookAtLH(&m_oViewMatrix, &oEyePos, &oTarget, &oUpVector);
}
