static GfRay _ComputeUntransformedRay(GfFrustum::ProjectionType projectionType,
const GfRange2d &window,
const GfVec2d &windowPos)
{
// Compute position on window, from provided normalized
// (-1 to 1) coordinates.
double winX = _Rescale(windowPos[0], -1.0, 1.0,
window.GetMin()[0], window.GetMax()[0]);
double winY = _Rescale(windowPos[1], -1.0, 1.0,
window.GetMin()[1], window.GetMax()[1]);
// Compute the camera-space starting point (the viewpoint) and
// direction (toward the point on the window).
GfVec3d pos;
GfVec3d dir;
if (projectionType == GfFrustum::Perspective) {
pos = GfVec3d(0);
dir = GfVec3d(winX, winY, -1.0).GetNormalized();
}
else {
pos.Set(winX, winY, 0.0);
dir = -GfVec3d::ZAxis();
}
// Build and return the ray
return GfRay(pos, dir);
}
GfRay
GfFrustum::ComputeRay(const GfVec3d &worldSpacePos) const
{
GfVec3d camSpaceToPos = ComputeViewMatrix().Transform(worldSpacePos);
// Compute the camera-space starting point (the viewpoint) and
// direction (toward the point camSpaceToPos).
GfVec3d pos;
GfVec3d dir;
if (_projectionType == Perspective) {
pos = GfVec3d(0);
dir = camSpaceToPos.GetNormalized();
}
else {
pos.Set(camSpaceToPos[0], camSpaceToPos[1], 0.0);
dir = -GfVec3d::ZAxis();
}
// Transform these by the inverse of the view matrix.
const GfMatrix4d &viewInverse = ComputeViewInverse();
GfVec3d rayFrom = viewInverse.Transform(pos);
GfVec3d rayDir = viewInverse.TransformDir(dir);
// Build and return the ray
return GfRay(rayFrom, rayDir);
}
GfRay
GfFrustum::ComputePickRay(const GfVec3d &worldSpacePos) const
{
GfVec3d camSpaceToPos = ComputeViewMatrix().Transform(worldSpacePos);
// Compute the camera-space starting point (the viewpoint) and
// direction (toward the point camSpaceToPos).
GfVec3d pos;
GfVec3d dir;
if (_projectionType == Perspective) {
pos = GfVec3d(0);
dir = camSpaceToPos.GetNormalized();
}
else {
pos.Set(camSpaceToPos[0], camSpaceToPos[1], 0.0);
dir = -GfVec3d::ZAxis();
}
return _ComputePickRayOffsetToNearPlane(pos, dir);
}
GfQuaternion
GfMatrix3d::ExtractRotationQuaternion() const
{
// This was adapted from the (open source) Open Inventor
// SbRotation::SetValue(const SbMatrix &m)
int i;
// First, find largest diagonal in matrix:
if (_mtx[0][0] > _mtx[1][1])
i = (_mtx[0][0] > _mtx[2][2] ? 0 : 2);
else
i = (_mtx[1][1] > _mtx[2][2] ? 1 : 2);
GfVec3d im;
double r;
if (_mtx[0][0] + _mtx[1][1] + _mtx[2][2] > _mtx[i][i]) {
r = 0.5 * sqrt(_mtx[0][0] + _mtx[1][1] +
_mtx[2][2] + 1);
im.Set((_mtx[1][2] - _mtx[2][1]) / (4.0 * r),
(_mtx[2][0] - _mtx[0][2]) / (4.0 * r),
(_mtx[0][1] - _mtx[1][0]) / (4.0 * r));
}
else {
int j = (i + 1) % 3;
int k = (i + 2) % 3;
double q = 0.5 * sqrt(_mtx[i][i] - _mtx[j][j] -
_mtx[k][k] + 1);
im[i] = q;
im[j] = (_mtx[i][j] + _mtx[j][i]) / (4 * q);
im[k] = (_mtx[k][i] + _mtx[i][k]) / (4 * q);
r = (_mtx[j][k] - _mtx[k][j]) / (4 * q);
}
return GfQuaternion(GfClamp(r, -1.0, 1.0), im);
}
