If now we compare D ( H L, 1 2 ) and D ( H L 2, 1 ), we see that x ∈ D ( H L 2, 1 ) implies that L x ∈ l 2. For any x ∈ l 2 satisfying L 2 x ∈ l 2, we can redefine (if necessary) the values of x on [ − 2, 2 ] Z, which are finite points, so that the boundary conditions in (3.5) are satisfied.
The one difference in the initialization step is that W is now defined as the region within the supplied boundary B. We seek to refine the control points so that they are equidistant from the left and right boundaries and well spaced along the length of the worm.
Given six boundary B-spline surfaces for a solid, this approach finds the internal control points so that the resulting trivariate B-spline solid is valid in the sense the minimal Jacobian of the solid is positive.
The minimum distance constraint and the shortest residence time constraint are accomplished by adding the protection zones around key-points so that sector boundary cannot extend beyond these protection zones.
Hysteresis thresholding [ 26] is applied next in order to remove all weak boundary points that are not connected to strong boundary points.
An important limitation of the beta regression is that it does not contain the boundary points 0 and 1 so that quite arbitrary transformation methods need to be applied.
Relative points with respect to the center and cone boundary were chosen so that three points fell outside the cone boundary (277, 173, and 69 km), three points fell within the cone boundary (416, 520, and 659 km), and so that no points appeared to touch the visible center line or boundary lines.
So, the boundary points are located on edge rather than in the protection zones.
In [20], He and Zhu have observed that, if (0 notin M), calculating (h u_{n})) implies determining (h u_{n})u_{n}), a boundary point of M, so iteration (1.9) is known as the boundary point method.
