// called on the parent object
// Should be synchronized so that the user thread does not modify the
// OrientedShape3D params while computing the transform
synchronized void updateOrientedTransform(Canvas3D canvas, int viewIndex) {
double angle = 0.0;
double sign;
boolean status;
Transform3D orientedxform = getOrientedTransform(viewIndex);
// get viewplatforms's location in virutal world
if (mode == OrientedShape3D.ROTATE_ABOUT_AXIS) { // rotate about axis
canvas.getCenterEyeInImagePlate(viewPosition);
canvas.getImagePlateToVworld(xform); // xform is imagePlateToLocal
xform.transform(viewPosition);
// get billboard's transform
xform.set(getCurrentLocalToVworld());
xform.invert(); // xform is now vWorldToLocal
// transform the eye position into the billboard's coordinate system
xform.transform(viewPosition);
// eyeVec is a vector from the local origin to the eye pt in local
eyeVec.set(viewPosition);
eyeVec.normalize();
// project the eye into the rotation plane
status = projectToPlane(eyeVec, nAxis);
if (status) {
// project the z axis into the rotation plane
zAxis.x = 0.0;
zAxis.y = 0.0;
zAxis.z = 1.0;
status = projectToPlane(zAxis, nAxis);
}
if (status) {
// compute the sign of the angle by checking if the cross product
// of the two vectors is in the same direction as the normal axis
vector.cross(eyeVec, zAxis);
if (vector.dot(nAxis) > 0.0) {
sign = 1.0;
} else {
sign = -1.0;
}
// compute the angle between the projected eye vector and the
// projected z
double dot = eyeVec.dot(zAxis);
if (dot > 1.0f) {
dot = 1.0f;
} else if (dot < -1.0f) {
dot = -1.0f;
}
angle = sign * Math.acos(dot);
// use -angle because xform is to *undo* rotation by angle
aa.x = nAxis.x;
aa.y = nAxis.y;
aa.z = nAxis.z;
aa.angle = -angle;
orientedxform.set(aa);
} else {
orientedxform.setIdentity();
}
} else if (mode == OrientedShape3D.ROTATE_ABOUT_POINT) { // rotate about point
// Need to rotate Z axis to point to eye, and Y axis to be
// parallel to view platform Y axis, rotating around rotation pt
// get the eye point
canvas.getCenterEyeInImagePlate(viewPosition);
// derive the yUp point
yUpPoint.set(viewPosition);
yUpPoint.y += 0.01; // one cm in Physical space
// transform the points to the Billboard's space
canvas.getImagePlateToVworld(xform); // xform is ImagePlateToVworld
xform.transform(viewPosition);
xform.transform(yUpPoint);
// get billboard's transform
xform.set(getCurrentLocalToVworld());
xform.invert(); // xform is vWorldToLocal
// transfom points to local coord sys
xform.transform(viewPosition);
xform.transform(yUpPoint);
// Make a vector from viewPostion to 0,0,0 in the BB coord sys
eyeVec.set(viewPosition);
eyeVec.normalize();
// create a yUp vector
yUp.set(yUpPoint);
yUp.sub(viewPosition);
yUp.normalize();
// find the plane to rotate z
zAxis.x = 0.0;
zAxis.y = 0.0;
zAxis.z = 1.0;
// rotation axis is cross product of eyeVec and zAxis
vector.cross(eyeVec, zAxis); // vector is cross product
// if cross product is non-zero, vector is rotation axis and
// rotation angle is acos(eyeVec.dot(zAxis)));
double length = vector.length();
if (length > 0.0001) {
double dot = eyeVec.dot(zAxis);
if (dot > 1.0f) {
dot = 1.0f;
} else if (dot < -1.0f) {
dot = -1.0f;
}
angle = Math.acos(dot);
aa.x = vector.x;
aa.y = vector.y;
aa.z = vector.z;
aa.angle = -angle;
zRotate.set(aa);
} else {
// no rotation needed, set to identity (scale = 1.0)
zRotate.set(1.0);
}
// Transform the yAxis by zRotate
yAxis.x = 0.0;
yAxis.y = 1.0;
yAxis.z = 0.0;
zRotate.transform(yAxis);
// project the yAxis onto the plane perp to the eyeVec
status = projectToPlane(yAxis, eyeVec);
if (status) {
// project the yUp onto the plane perp to the eyeVec
status = projectToPlane(yUp, eyeVec);
}
if (status) {
// rotation angle is acos(yUp.dot(yAxis));
double dot = yUp.dot(yAxis);
// Fix numerical error, otherwise acos return NULL
if (dot > 1.0f) {
dot = 1.0f;
} else if (dot < -1.0f) {
dot = -1.0f;
}
angle = Math.acos(dot);
// check the sign by looking a the cross product vs the eyeVec
vector.cross(yUp, yAxis); // vector is cross product
if (eyeVec.dot(vector) < 0) {
angle *= -1;
}
aa.x = eyeVec.x;
aa.y = eyeVec.y;
aa.z = eyeVec.z;
aa.angle = -angle;
xform.set(aa); // xform is now yRotate
// rotate around the rotation point
vector.x = rotationPoint.x;
vector.y = rotationPoint.y;
vector.z = rotationPoint.z; // vector to translate to RP
orientedxform.set(vector); // translate to RP
orientedxform.mul(xform); // yRotate
orientedxform.mul(zRotate); // zRotate
vector.scale(-1.0); // vector to translate back
xform.set(vector); // xform to translate back
orientedxform.mul(xform); // translate back
} else {
orientedxform.setIdentity();
}
}
// Scale invariant computation
if (constantScale) {
// Back Xform a unit vector to local world coords
canvas.getInverseVworldProjection(left_xform, right_xform);
// the two endpts of the vector have to be transformed
// individually because the Xform is not affine
im_vec[0].set(0.0, 0.0, 0.0, 1.0);
im_vec[1].set(1.0, 0.0, 0.0, 1.0);
left_xform.transform(im_vec[0]);
left_xform.transform(im_vec[1]);
left_xform.set(getCurrentLocalToVworld());
left_xform.invert();
left_xform.transform(im_vec[0]);
left_xform.transform(im_vec[1]);
lvec.set(im_vec[1]);
lvec.sub(im_vec[0]);
// We simply need the direction of this vector
lvec.normalize();
im_vec[0].set(0.0, 0.0, 0.0, 1.0);
im_vec[1].set(lvec);
im_vec[1].w = 1.0;
// Forward Xfrom to clip coords
left_xform.set(getCurrentLocalToVworld());
left_xform.transform(im_vec[0]);
left_xform.transform(im_vec[1]);
canvas.getVworldProjection(left_xform, right_xform);
left_xform.transform(im_vec[0]);
left_xform.transform(im_vec[1]);
// Perspective division
im_vec[0].x /= im_vec[0].w;
im_vec[0].y /= im_vec[0].w;
im_vec[0].z /= im_vec[0].w;
im_vec[1].x /= im_vec[1].w;
im_vec[1].y /= im_vec[1].w;
im_vec[1].z /= im_vec[1].w;
lvec.set(im_vec[1]);
lvec.sub(im_vec[0]);
// Use the length of this vector to determine the scaling
// factor
double scale = 1 / lvec.length();
// Convert to meters
scale *= scaleFactor * canvas.getPhysicalWidth() / 2;
// Scale object so that it appears the same size
scaleXform.setScale(scale);
orientedxform.mul(scaleXform);
}
}
