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(in-package :2d-geometry)
;;;; This file contains functions to decompose a complex polygons into simple ones.
;;; Brute force decomposition into non-disjoint simple polygons
;;; The main problem is efficient finding of intersections. Bentley-Ottmann algorithm can do this in
;;; O((n+k)logn), but it is somewhat complicated. As it is, brute force should be quadratic, maybe
;;; n^3 if I create one loop too many... actually, I will be glad if it's subexponential at the
;;; moment.
(defun find-intersection (edge-list)
(labels ((recurse-edge-list (edge-list-1 edge-list-2)
(if (null edge-list-1)
nil
(if (null edge-list-2)
(recurse-edge-list (cdr edge-list-1) (cddr edge-list-1))
(let ((edge1 (car edge-list-1))
(edge2 (car edge-list-2)))
(if (intersect-proper-p (start edge1)(end edge1)
(start edge2)(end edge2))
(list edge1 edge2 (line-segments-intersection-point edge1 edge2))
(recurse-edge-list edge-list-1 (cdr edge-list-2))))))))
(recurse-edge-list edge-list (cdr edge-list))))
(defun decompose-complex-polygon-nondisjoint (polygon)
"Decomposes a complex polygon into a set of simple ones, possibly some entirely contained in others."
(let ((ring-head (double-linked-ring-from-point-list (point-list polygon)))
(simple-polys nil))
(let ((ring-index (collect-ring-nodes ring-head))
(edge-list (ring-to-list-of-edges ring-head)))
(iterate (while ring-index)
(iterate (for inters next (find-intersection edge-list))
(while inters)
(destructuring-bind (edge1 edge2 i-point) inters
(let ((v1 (make-instance 'poly-ring-node
:val i-point
:prev (start edge1)
:next (end edge2)))
(v2 (make-instance 'poly-ring-node
:val i-point
:prev (start edge2)
:next (end edge1))))
(push v1 ring-index)
(push v2 ring-index)
(setf (next-node (start edge1)) v1)
(setf (prev-node (end edge1)) v2)
(setf (next-node (start edge2)) v2)
(setf (prev-node (end edge2)) v1)
(setf edge-list (append
(list (make-instance 'line-segment
:start (start edge1)
:end v1)
(make-instance 'line-segment
:start v1
:end (end edge2))
(make-instance 'line-segment
:start (start edge2)
:end v2)
(make-instance 'line-segment
:start v2
:end (end edge1)))
(remove-if #'(lambda (e)
(or (eql e edge1)
(eql e edge2)))
edge-list))))))
(push (point-list-from-ring ring-head) simple-polys)
(setf ring-index (set-difference ring-index
(collect-ring-nodes ring-head)
:test #'point-equal-p))
(setf ring-head (car ring-index))))
(mapcar #'make-polygon-from-point-list simple-polys)))
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