Imported Upstream version 2.14.2

[lilypond.git] / scm / bezier-tools.scm

diff --git a/scm/bezier-tools.scm b/scm/bezier-tools.scm
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+;;;; This file is part of LilyPond, the GNU music typesetter.
+;;;;
+;;;; Copyright (C) 2010--2011 Carl D. Sorensen <c_sorensen@byu.edu>
+;;;;
+;;;; LilyPond 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.
+;;;;
+;;;; LilyPond 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 LilyPond.  If not, see <http://www.gnu.org/licenses/>.
+
+(define (make-coord x-value y-value)
+ "Make a coordinate pair from @var{x-valye} and @var{y-value}."
+ (cons x-value y-value))
+
+(define (coord+ coord1 coord2)
+ "Add @var{coord1} to @var{coord2}, returning a coordinate."
+ (cons (+ (car coord1) (car coord2))
+       (+ (cdr coord1) (cdr coord2))))
+
+(define (coord- coord1 coord2)
+ "Subtract @var{coord2} from @var{coord1}."
+ (cons (- (car coord1) (car coord2))
+       (- (cdr coord1) (cdr coord2))))
+
+(define (coord* scalar coord)
+ "Multiply each component of @var{coord} by @var{scalar}."
+ (cons (* (car coord) scalar)
+       (* (cdr coord) scalar)))
+
+(define (make-bezier point-0 point-1 point-2 point-3)
+ "Create a cubic bezier from the four control points."
+ (list point-0 point-1 point-2 point-3))
+
+(define (interpolated-control-points control-points split-value)
+ "Interpolate @var{control-points} at @var{split-value}.  Return a
+set of control points that is one degree less than @var{control-points}."
+  (if (null? (cdr control-points))
+      '()
+      (let ((first (car control-points))
+            (second (cadr control-points)))
+       (cons* (coord+ first (coord* split-value (coord- second first)))
+             (interpolated-control-points
+              (cdr control-points)
+              split-value)))))
+
+(define (split-bezier bezier split-value)
+ "Split a cubic bezier defined by @var{bezier} at the value
+@var{split-value}.  @var{bezier} is a list of pairs; each pair is
+is the coordinates of a control point.  Returns a list of beziers.
+The first element is the LHS spline; the second
+element is the RHS spline."
+   (let* ((quad-points (interpolated-control-points
+                       bezier
+                       split-value))
+          (lin-points (interpolated-control-points
+                       quad-points
+                       split-value))
+          (const-point (interpolated-control-points
+                        lin-points
+                        split-value))
+          (left-side (list (car bezier)
+                           (car quad-points)
+                           (car lin-points)
+                           (car const-point)))
+          (right-side (list (car const-point)
+                            (list-ref lin-points 1)
+                            (list-ref quad-points 2)
+                            (list-ref bezier 3))))
+   (cons left-side right-side)))
+
+(define (multi-split-bezier bezier start-t split-list)
+ "Split @var{bezier} at all the points listed in @var{split-list}.
+@var{bezier} has a parameter value that goes from @var{start-t} to 1.
+Returns a list of @var{(1+ (length split-list))} beziers."
+  (let* ((bezier-split (split-bezier bezier
+                                     (/ (- (car split-list) start-t)
+                                        (- 1 start-t))))
+         (left-bezier (car bezier-split))
+         (right-bezier (cdr bezier-split)))
+    (if (null? (cdr split-list))
+        bezier-split
+        (cons* left-bezier
+               (multi-split-bezier right-bezier
+                                   (car split-list)
+                                   (cdr split-list))))))
+
+
+(define (bezier-sandwich-list top-bezier bottom-bezier)
+ "create the list of control points for a bezier sandwich consisting
+of @var{top-bezier} and @var{bottom-bezier}."
+ (list (list-ref bottom-bezier 1)
+       (list-ref bottom-bezier 2)
+       (list-ref bottom-bezier 3)
+       (list-ref bottom-bezier 0)
+       (list-ref top-bezier 2)
+       (list-ref top-bezier 1)
+       (list-ref top-bezier 0)
+       (list-ref top-bezier 3)))