Visualization of Coalescence of Multiple Small Bubbles with Closed B-Spline Curve

Algorithm 1: NDgBCA.

Input: the number of bubbles ; the coordinates of bubble contour control points; the number of iterates and the still rising speed ; the random factor

Output: the updated contour control points of bubbles .

Step 1: The current bubble number .

Step 2: while .

Step 3:  All bubbles rising according formula (12).

Step 4:  For each bubble, fit those contour points by the closed B-spline method [35].

Step 5:  Detect whether there are coalescence occurring in the new positions.

Step 6:  If there are coalescence,

Step 7:   Find the intersection points using Little’s method [23].

Step 8:   Detect and remove the inner points using Kpalma’ method [21];

Step 9:   Fit those contour points by the closed B-spline method [35];

Step 10:  Update the contour points and the current bubbles number .

Step 11:  End If

Step 12:  .

Step 13: End while.

return .

Algorithm 1: NDgBCA.