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| ;;;; This file is part of LilyPond, the GNU music typesetter. | |
| ;;;; | |
| ;;;; Copyright (C) 2010--2020 Carl D. Sorensen <[email protected]> | |
| ;;;; | |
| ;;;; 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))) | |