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;;;
;;; GRAPHS - graph theory package for Maxima
;;;
;;; Copyright (C) 2007-2011 Andrej Vodopivec <andrej.vodopivec@gmail.com>
;;;
;;; This program is free software; you can redistribute it and/or modify
;;; it under the terms of the GNU General Public License as published by
;;; the Free Software Foundation; either version 2 of the License, or
;;; (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;;; GNU General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program; if not, write to the Free Software
;;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;;; force-based graph embedding algorithm
;;;
;;; Based on:
;;; T.M.J. Fruchterman, E.M. Reingold, Graph drawing by force-directed
;;; placement, Software practice and experience 21 (1991), 11, 1129--1164.
;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-package :maxima)
(defvar *vertex-position*)
(defvar *optimal-distance*)
(defvar *epsilon-distance* 0.5)
(defvar *frame-width* 10.0)
(defvar *fixed-vertices* nil)
(defun attractive-force (d)
(/ (* d d) *optimal-distance*))
(defun repulsive-force (d)
(let ((d (max d *epsilon-distance*)))
(/ (* *optimal-distance* *optimal-distance*) d 100)))
(defun distance (p1 p2)
(let ((d (mapcar #'- p1 p2)))
(sqrt (apply #'+ (mapcar #'* d d)))))
(defun random-positions (v-list dimension)
(when *fixed-vertices*
(let ((n (length *fixed-vertices*)))
(dotimes (i (length *fixed-vertices*))
(let ((v (nth i *fixed-vertices*))
(x (* *frame-width* ($sin (/ (* 2 i pi) n))))
(y (* *frame-width* ($cos (/ (* 2 i pi) n)))))
(setf (gethash v *vertex-position*)
(list x y))))))
(dolist (v v-list)
(unless (member v *fixed-vertices*)
(let* ((x (- *frame-width* (random (* 2 *frame-width*))))
(y (- *frame-width* (random (* 2 *frame-width*))))
(z (- *frame-width* (random (* 2 *frame-width*)))))
(setf (gethash v *vertex-position*)
(if (= dimension 3)
(list x y z)
(list x y)))))))
(defmfun $spring_embedding (g depth fixed-vertices dimension continue)
(let ((*vertex-position* (make-hash-table))
(vertex-displacement (make-hash-table))
(*fixed-vertices* (cdr fixed-vertices))
(*optimal-distance* (/ (* 2 *frame-width*)
(sqrt ($graph_order g)))))
;; Start with current positions if we already have some.
(if (and continue
(> (length ($get_positions g)) 1)
(= ($length ($first ($get_positions g))) dimension))
(dolist (v (cdr ($get_positions g)))
(setf (gethash (cadr v) *vertex-position*) (cdaddr v)))
(random-positions (vertices g) dimension))
(let* ((step (/ *frame-width* 5))
(d-step (/ step (1+ depth))))
(dotimes (i depth)
(setq step (- step d-step))
(dolist (v (vertices g))
(setf (gethash v vertex-displacement) (if (= dimension 2) (list 0 0) (list 0 0 0))))
;; calculate repulsive forces
(when (null *fixed-vertices*)
(let ((v-vrt (vertices g)))
(loop while v-vrt do
(let* ((v (car v-vrt))
(u-vrt (cdr v-vrt))
(v-pos (gethash v *vertex-position*)))
(loop while u-vrt do
(let* ((u (car u-vrt))
(u-pos (gethash u *vertex-position*))
(delta (mapcar #'- v-pos u-pos))
(delta-abs (distance v-pos u-pos))
(force (repulsive-force delta-abs))
(vu-disp (mapcar
#'(lambda (u) (* (/ u (max delta-abs *epsilon-distance*)) force))
delta))
(v-disp (gethash v vertex-displacement))
(u-disp (gethash u vertex-displacement)))
(setf (gethash v vertex-displacement)
(mapcar #'+ v-disp vu-disp)
(gethash u vertex-displacement)
(mapcar #'- u-disp vu-disp))
(setq u-vrt (cdr u-vrt)))))
(setq v-vrt (cdr v-vrt)))))
;; calculate attractive forces
(dolist (e (edges g))
(let* ((v (first e))
(u (second e))
(v-pos (gethash v *vertex-position*))
(u-pos (gethash u *vertex-position*))
(delta (mapcar #'- v-pos u-pos))
(delta-abs (distance v-pos u-pos))
(v-disp (gethash v vertex-displacement))
(u-disp (gethash u vertex-displacement))
(force (attractive-force delta-abs))
(vu-disp (mapcar
#'(lambda (u)
(* (/ u (max delta-abs *epsilon-distance*)) force))
delta)))
(setf (gethash v vertex-displacement)
(mapcar #'- v-disp vu-disp)
(gethash u vertex-displacement)
(mapcar #'+ u-disp vu-disp))))
;; Limit the displacement
(dolist (v (vertices g))
(unless (member v *fixed-vertices*)
(let* ((v-disp (gethash v vertex-displacement))
(v-disp (mapcar #'(lambda (u) (/ u 2)) v-disp))
(v-disp-abs (sqrt (apply #'+ (mapcar #'* v-disp v-disp))))
(v-pos (gethash v *vertex-position*)))
(if (> v-disp-abs step)
(setq v-pos (mapcar #'(lambda (u v)
(+ u (* (/ v v-disp-abs) step)))
v-pos v-disp))
(setq v-pos (mapcar #'+ v-pos v-disp)))
(setq v-pos (mapcar #'(lambda (u) (min *frame-width* (max u (- *frame-width*))))
v-pos))
(setf (gethash v *vertex-position*) v-pos))))
))
(let (result)
(maphash #'(lambda (vrt pos)
(setq result
(cons `((mlist simp) ,vrt ((mlist simp) ,@pos))
result)))
*vertex-position*)
(cons '(mlist simp) result)) ))
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