Draw waves to fill every unshaded cell on the board. A wave is a repeating pair of lines that continues until hitting the edges of the board or—if allowed by the puzzle creator?—shaded cells. Otherwise shaded cells are off-limits: no line goes into one.
Each of the two line types that constitute a wave must be straight 8-directional orthogonal or diagonal lines. All lines go through cell centers, with any given line’s 2 endpoints (which may be clued by unshaded pearls) being in the centers of cells. The two line types constituting a wave must share exactly one endpoint, and must not overlap. They must have an angle that isn't 180 degrees between them.
A wave is formed from its constituents by repeating the pattern of its lines—for example, imagine a line that goes from a given cell to the cell 2 up and 2 right from it, forming a length-2 diagonal line. The second line starts at the endpoint of the first and goes 1 cell down, forming a length-1 orthogonal line. Then, to continue the wave, from the unshared endpoint of the second line, the first line is copied, meaning the 2-diagonal 1-down pattern continues until the wave is stopped.
When the wave is stopped, it must go through its barrier, meaning—for example—that a wave that hits the edge of the board must end by continuing its pattern into the edge of the board rather than stopping on an edge-border cell.
Uniquely, waves can have endpoints that aren’t on the board. A wave could just look like a straight line if both endpoints are technically off the board; one endpoint could connect to a “cell” 30 diagonal steps off the board. A puzzle’s solution may require keeping track of a wave as it dips off and onto the board, but will never require actually filling any off-board “cells”—any player who draws these lines is just keeping notes. Because waves can go off and back onto the board, but waves may also end when they reach a board edge, a line hitting the edge of the board does not necessarily mean the wave is complete in that direction—however, if the proportions of a wave’s constituents make it obvious that the pattern could not double back (for example, a simple 1-up-1-right pattern could not possibly come back onto the board after it exits), this dilemma may be avoided.
Waves may cross and may share cells, but two waves never draw the same line.
Unshaded pearls carry a number if they mark more than 1 corner. Each wave goes through exactly one shaded pearl, and no other wave goes through it (can't overlap an unshaded pearl).