_THE DESIGN AND IMPLEMENTATION OF PIE MENUS_
by Don Hopkins

[LISTING ONE]

% Code to implement the "8 Days a Week" Pie Menu 
% by Don Hopkins

/pie framebuffer /new ClassPieMenu send def
[ (Today)
  (Sunday)
  (Monday) (Tuesday) (Wednesday) (Thursday) (Friday)
  (Saturday)
] /setitemlist pie send
90 /setinitialangle pie send
false /setclockwise pie send

/can framebuffer /new ClassPieMenuCanvas send def
pie /setpiemenu can send
/minsize {100 100} /installmethod can send
/win can framebuffer /new ClassBaseWindow send def
/new ClassEventMgr send /activate win send
/place win send /map win send


[LISTING TWO]

    /Layout { % - => -
        PieGSave self setcanvas
            /LayoutInit self send
            /LayoutValidateItems self send
            /LayoutItemRadius self send
            /LayoutOuterRadius self send
        grestore
    } def

    /LayoutInit { % - => -
        % Deflate the menu.
        /Radius 0 def
        % Figure the slice width.
        /SliceWidth 360 /itemcount self send 1 max div def
        % Point the initial slice in the initial angle.
        /ThisAngle InitialAngle store
    } def

 
    /LayoutValidateItems { % - => -
        % Loop through the items, validating each one.
        ItemList {
            begin % item

                % Measure the item.
                /DisplayItem load DisplayItemSize
                /ItemHeight exch def
                /ItemWidth exch def

                % Remember the angle and the direction.
                /Angle ThisAngle def
                /DX Angle cos def
                /DY Angle sin def

                % Figure the offset from the tip of the inner radius
                % spoke to the lower left item corner, according to
                % the direction of the item.
                %
                % Items at the very top (bottom) are centered on their
                % bottom (top) edge. Items to the left (right) are
                % centered on their right (left) edge.
                %
                DX abs .05 lt { % tippy top or bippy bottom

                    % Offset to the North or South edge of the item.
                    /XOffset ItemWidth -.5 mul def
                    /YOffset
                        DY 0 lt {ItemHeight neg} {0} ifelse
                    def
 
                } { % left or right

                    % Offset to the East or West edge of the item.
                    /XOffset
                        DX 0 lt {ItemWidth neg} {0} ifelse
                    def
                    /YOffset ItemHeight -.5 mul def

                } ifelse

                % Twist around to the next item.
                /ThisAngle
                    ThisAngle SliceWidth
                    Clockwise? {sub} {add} ifelse
                    NormalAngle
                store

            end % item
        } forall
    } def
 
    /LayoutItemRadius { % - => -
        % Figure the inner item radius, at least enough to prevent

        % the items from overlapping.
        /ItemRadius RadiusMin def
        /itemcount self send 3 gt { % No sweat if 3 or less.

            % Check each item against its next neighbor.
            0 1 /itemcount self send 1 sub {

                /I exch def
                /NextI I 1 add /itemcount self send mod def

                % See if these two items overlap.
                % If they do, keep pushing the item radius out
                % by RadiusStep until they don't.
                {   I /CalcRect self send
                    NextI /CalcRect self send
                    rectsoverlap not {exit} if % They don't overlap!

                    % They overlap. Push them out a notch and try again.
                    /ItemRadius ItemRadius RadiusStep add def
                } loop
 
            } for
            % Now that we've gone around once checking each pair,
            % none of them overlap any more!
        } if

        % Add in some more space to be nice.
        /ItemRadius ItemRadius RadiusExtra add def
    } def
 
    /LayoutOuterRadius { % - => -
        % Now we need to calculate the outer radius, based on the radius
        % of the farthest item corner. During the loop, Radius actually
        % holds the square of the radius, since we're comparing it against
        % squared item corner radii anyway.
        /Radius ItemRadius dup mul def
        ItemList {
            begin % item

                % Remember the location to center the item edge.
                /x DX ItemRadius mul def
                /y DY ItemRadius mul def

                % Remember the location of the item's SouthWest corner.
                /ItemX x XOffset add round def
                /ItemY y YOffset add round def
 
                % Figure the distance of the item's farthest corner.
                % This is easy 'cause we can fold all the items into
                % the NorthEast quadrant and get the same result.
                DX abs .05 lt { % tippy top or bippy bottom

                    % (|x|,|y|) is South edge: radius^2 of NorthEast corner
                    x abs ItemWidth .5 mul add dup mul
                    y abs ItemHeight add dup mul add


                } { % left or right

                    % (|x|,|y|) is West edge: radius^2 of NorthEast corner
                    x abs ItemWidth add dup mul
                    y abs ItemHeight .5 mul add dup mul add

                } ifelse

                % Remember the maximum corner radius seen so far.
                Radius max /Radius exch store
            end % item
        } forall
 
        % Take the square root and add some extra space.
        /Radius
            Radius sqrt Gap add Border add ceiling cvi
        store % Whew, we're done! Time to party!
    } def