4 nodes, 4 edges, one 3-cycle, 1 face, 1 selected node, 1 text label
Graphs are made of nodes, edges, and faces. A node has a size or radius, a shape (round dot, rectangle, custom shape, ...), a color and possibly a color gradient or an image, and a label (text). Nodes are denoted #0 (first node), #1, ...#last. Nodes are connected by edges, or links. An edge between #i and #j is denoted (#i,#j). There is at most one edge between two nodes. An edge is undirected : (#i,#j) is the same as (#j,#i). Edges can be displayed as lines, dotted lines, gradients, arrows, curves or springs. A path between two nodes a and b is a sequence of edges (#a,#i)(#i,#j)(#j,#k)...(#m,#b); A n-cycle is a closed path of n nodes from one node to itself : (#a,#i)(#i,#j)(#j,#k)...(#m,#a). Cycles may enclose faces, colored polygons. Faces may be drawn with color gradrients, or as 'smoothfaces' using Bezier curves. Faces are automatically found by GB_graph, or user-defined.
Meta keys notation : Cmd-Key denotes either ⌘-Key or Ctrl-Key. Cmd-A and Cmd-a, etc. are the same. 'A' denotes press the 'A' key = Shift-a, 'b' press the 'b' key, ... ESC is the ESCape key. Alt is the Alt or Option key. Useful commands : • Cmd-z : Undo last operation. GB-graph has an history stack to remember the 16 last graphs. The undoLevel - 0 to 16 - is displayed in the info area (top left of screen). Press Cmd-z, Cmd-z, Cmd-z, ...to go back in time. • 'Z' : clear all and start a new graph (undoable) • '?' : show help window • ESC : quit help window, quit text editor, stop animations, etc.
• Click on node : select/deselect node • Cmd-click on node : add/remove to/from selection • Alt-click anywhere : create a new node and connect it to current selection (use 'Backspace' to unlink if needed) • Click anywhere : deselect all • Cmd-click anywhere : move selection to click location (animated) • Click-and-drag anywhere : make a selection rectangle, enclosing nodes to select, then Cmd-a. The following apply to unselected nodes : • Alt-click on node : select node and connect to last selected • Double-click on node : select node and its closure • Click-and-drag : select and move node • Maj-click-and-drag : select and move node and its closure (cluster) • Alt-click-and-drag : select node and rotate its closure
• Menu Preferences|mouseWheel to enable/disable the wheel • Wheel to zoom +/- • Shift-wheel to rotate +/- • Alt-wheel to move left/right (X axis) • Cmd-wheel to move up/down (Y axis)
Menus items allow to launch menu actions : yellow background menus, eg. Faces, or to tune parameters values with sliders; The 'reset' action at the end of a menu resets parameters to default values. Menu are denoted by Name|<item name>. Ex : Nodes|radius • Click onto a menu name : Nodes,Random,... to open/close it • Clicking on a tagged menu name : • Anims,• Screens,.. will open/close its sub-menus. • 'm' : close all menus / submenus
Shapes, variant, sizes
- Clean everybody : 'Z' • NewNode : Add a node somewhere : Alt-click - Select it : Click or Cmd-click - Select a shape : Nodes|Shape - Change its radius : Set Nodes|radius = ... or keys '1', '2' - Select a variant : Nodes|variant - Try to set Nodes|rotate, Nodes|extent, Nodes|nColor • Goto NewNode.
Faces are delimited by cycles of any length > 2. Each face has a leader node which is used to set the face color or gradient. • NewFaces : Draw ...
- Clean everybody : 'Z' • Draw the (D) polygon - Unselect all : click anywhere - Draw faces : 'F' - Operations|QuadsToTriangles - Repeat : Operations|TrianglesToTriangles - [Add a few gradients] Notation : [... is an optional step] - [Try another palette : <space>,<space>,...] - Menu Nodes|radius = 0 or Key '0' - Menu Nodes|lineColor = 16 = black - Menu Nodes|lineWidth = 1 or 2 or 0
Homothety (n = 2 : two copies, scale = 0.5 , variant =1 : connect)
A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation. • Draw the generatrix path (G) - [insert intermediate nodes : select all, then 'I','I',...] - [Set MoreGraphs|variant to the minimal radius Rmin] -