DROP FUNCTION IF EXISTS MidPoint;
DELIMITER //

CREATE FUNCTION MidPoint(ls LINESTRING)
RETURNS POINT
DETERMINISTIC
BEGIN
    DECLARE len double;
    DECLARE workLength double DEFAULT 0;
    DECLARE workPoint int DEFAULT 1;
    DECLARE point0 POINT;
    DECLARE point1 POINT;
    DECLARE distanceOver double;
    DECLARE segmentLength double;

    IF (NumPoints(ls) = 1) THEN return PointN(ls, 1); END IF;

    -- find half the length of the linestring
    SET len := GLength(ls) / 2;

    -- walk the linestring until we exceed the distance
    WHILE (workLength < len) DO
        SET point0 = PointN(ls, workPoint);
        SET workPoint := workPoint + 1;
        SET point1 = PointN(ls, workPoint);
        SET segmentLength = GLength(LineString(point0, point1));
        SET workLength := workLength + segmentLength;
    END WHILE;

    -- distance to backup
    SET distanceOver = workLength - len;

    -- midpoint is distanceOver back down the last segement
    RETURN POINT(
            X(point1) - distanceOver / segmentLength * (X(point1) - X(point0)),
            Y(point1) - distanceOver / segmentLength * (Y(point1) - Y(point0))
        );

END//
DELIMITER ;