Sentence examples for plane translation from inspiring English sources

In connection with his studies of the work of Hilbert, he discovered the plane translation theorem, which characterizes topological mappings of the Cartesian plane, and the first of his fixed-point theorems, which later became important in the establishment of some fundamental theorems in branches of mathematics such as differential equations and game theory.

However, plate designs do not have any intrinsic features to their designs to assist with correction of coronal plane translation.

Each model was then placed in a reference pose (parallel to xy-plane, lateral view, out of plane translation = 200 mm) simulating a typical fluoroscopic frame.

This ensures the half pin and wire lie in line along the mid-sagittal axis and reduces the amount of sagittal plane translation that may arise from indiscriminate reference wire and half pin placement (these corresponding holes are easily identified as the Orthofix ring surface is marked).

They defined criteria for diagnosing instability from flexion-extension radiographs as "sagittal plane translation greater than 4.5 mm or greater than 15% of the vertebral body width, or sagittal plane rotation of greater than 15° at L1/L2, L2/L3 or L3/L4, greater than 20° at L4/L5, or greater than 25° at L5/S1" [ 23].

We then have that the homography transform can be decomposed into in-plane translation followed by roll rotation, yielding the following proposition.

For this purpose, three groups of DOF were formed: (i) in-plane pose parameters ; (ii) out-of-plane rotations ; (iii) out-of-plane translation (Tz).

Finally, the ground-plane translation is determined by seeking the location where the bi-variate shift histogram of point pairs with high curvature values (called CPSHs) peaks.

The first feature was used to evaluate a first guess for the bone model orientation around the projection axis , while the in-plane translation components were estimated using the second feature.

Experimental evaluation of the demonstrator showed that a gravity force of 34.4 N was balanced with a residual stiffness of 1.75 N/mm in a domain of 2 mm for the out-of-plane translation, while the out-of-plane rotational stiffness was less than 18.5 Nm/rad, caused by parasitic torsion of the bi-stable beams and v-shaped beams.

where θ t =[0,t x,t y ] T, (boldsymbol {K}_{{boldsymbol {theta }}_{boldsymbol {t}}} boldsymbol {x}phantom {dot {i}!}) denotes the in-plane translation operation, and PT and IPT stand for the polar transform and inverse polar transform [41], respectively.