-;;; Dungeon Master --- RPG Adventure Generator
-;;; Copyright © 2019 Javier Sancho <jsf@jsancho.org>
-;;;
-;;; Dungeon Master 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 3 of the License, or
-;;; (at your option) any later version.
-;;;
-;;; Dungeon Master 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 Dungeon Master. If not, see <http://www.gnu.org/licenses/>.
-
-
-(define-module (dungeon-master geom bowyer-watson)
- #:use-module (ice-9 receive)
- #:use-module (srfi srfi-1)
- #:use-module (srfi srfi-9)
- #:use-module (dungeon-master geom point)
- #:use-module (dungeon-master geom triangle)
- #:export (bowyer-watson))
-
-"
-Compute the Delaunay triangulation using Bowyer–Watson algorithm
-https://en.wikipedia.org/wiki/Bowyer-Watson_algorithm
-"
-
-(define (bowyer-watson vertices)
- (receive (minx miny maxx maxy)
- (calculate-limits vertices)
- (let ((c1 (make-point minx miny))
- (c2 (make-point minx maxy))
- (c3 (make-point maxx miny))
- (c4 (make-point maxx maxy)))
- (let ((frame (list c1 c2 c3 c4)))
- (receive (points triangles)
- (calculate-triangulation
- (list c4 c3 c2 c1)
- (list (make-triangle c1 c2 c3)
- (make-triangle c2 c3 c4))
- vertices)
- (values triangles points frame))))))
-
-(define (calculate-limits vertices)
- (let ((xs (map (lambda (p) (point-x p)) vertices))
- (ys (map (lambda (p) (point-y p)) vertices)))
- (let ((minx (apply min (cons (expt 10 10) xs)))
- (miny (apply min (cons (expt 10 10) ys)))
- (maxx (apply max (cons (- (expt 10 9)) xs)))
- (maxy (apply max (cons (- (expt 10 9)) ys))))
- (let ((dx (* (- maxx minx) 0.5))
- (dy (* (- maxy miny) 0.5)))
- (values (- minx (/ dx 2))
- (- miny (/ dy 2))
- (+ maxx (/ dx 2))
- (+ maxy (/ dy 2)))))))
-
-(define (calculate-triangulation points triangles vertices)
- (cond ((null? vertices)
- (values points triangles))
- (else
- (let ((vertice (car vertices)))
- (receive (to-split to-keep)
- (triangles-contains-point triangles vertice)
- (cond ((null? to-split)
- (calculate-triangulation points triangles (cdr vertices)))
- (else
- (calculate-triangulation
- (cons vertice points)
- (concatenate
- (list (calculate-new-triangles to-split vertice)
- to-keep))
- (cdr vertices)))))))))
-
-(define (calculate-new-triangles to-split p1)
- (receive (a b)
- (calculate-new-edges to-split)
- (let loop ((p2-list a)
- (p3-list b)
- (triangles '()))
- (cond ((null? p2-list)
- triangles)
- (else
- (let ((p2 (car p2-list))
- (p3 (car p3-list)))
- (loop (cdr p2-list)
- (cdr p3-list)
- (cons (make-triangle p1 p2 p3) triangles))))))))
-
-(define* (calculate-new-edges triangles #:optional (original-t triangles) (a '()) (b '()))
- (cond ((null? triangles)
- (values a b))
- (else
- (let* ((triangle (car triangles))
- (common-edge (triangles-has-common-edge triangle original-t)))
- (let ((points (triangle-points triangle)))
- (let ((p1 (car points))
- (p2 (cadr points))
- (p3 (caddr points))
- (e1 (car common-edge))
- (e2 (cadr common-edge))
- (e3 (caddr common-edge)))
- (cond (e1
- (set! a (cons p1 a))
- (set! b (cons p2 b))))
- (cond (e2
- (set! a (cons p2 a))
- (set! b (cons p3 b))))
- (cond (e3
- (set! a (cons p3 a))
- (set! b (cons p1 b))))
- (calculate-new-edges (cdr triangles) original-t a b)))))))
-
-(define* (triangles-has-common-edge triangle triangles #:optional (e1 #t) (e2 #t) (e3 #t))
- (cond ((not (or e1 e2 e3))
- (list e1 e2 e3))
- ((null? triangles)
- (list e1 e2 e3))
- (else
- (let ((t (car triangles)))
- (cond ((equal? t triangle)
- (triangles-has-common-edge triangle (cdr triangles) e1 e2 e3))
- (else
- (let ((points (triangle-points triangle)))
- (let ((p1 (car points))
- (p2 (cadr points))
- (p3 (caddr points)))
- (when (and e1 (triangle-has-edge t p2 p1))
- (set! e1 #f))
- (when (and e2 (triangle-has-edge t p3 p2))
- (set! e2 #f))
- (when (and e3 (triangle-has-edge t p1 p3))
- (set! e3 #f))))
- (triangles-has-common-edge triangle (cdr triangles) e1 e2 e3)))))))
-
-(define (triangles-contains-point triangles point)
- (partition
- (lambda (triangle)
- (< (points-distance point (triangle-center triangle))
- (triangle-radius triangle)))
- triangles))