// 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); } }