;;;; 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-bezier-sandwich-stencil coords thick xext yext)
+ (let* ((command-list `(moveto
+ ,(car (list-ref coords 3))
+ ,(cdr (list-ref coords 3))
+ curveto
+ ,(car (list-ref coords 0))
+ ,(cdr (list-ref coords 0))
+ ,(car (list-ref coords 1))
+ ,(cdr (list-ref coords 1))
+ ,(car (list-ref coords 2))
+ ,(cdr (list-ref coords 2))
+ curveto
+ ,(car (list-ref coords 4))
+ ,(cdr (list-ref coords 4))
+ ,(car (list-ref coords 5))
+ ,(cdr (list-ref coords 5))
+ ,(car (list-ref coords 6))
+ ,(cdr (list-ref coords 6))
+ closepath)))
+ (ly:make-stencil
+ `(path ,thick `(,@' ,command-list) 'round 'round #t)
+ xext
+ yext)))
+
(define-public (stack-stencils axis dir padding stils)
"Stack stencils @var{stils} in direction @var{axis}, @var{dir}, using
@var{padding}."
(lower-inner-control-point
(cons inner-control-x lower-control-y)))
- (ly:make-stencil
- (list 'bezier-sandwich
- `(quote ,(list
- ;; Step 4: curve through inner control points
- ;; to lower end point.
- upper-inner-control-point
- lower-inner-control-point
- lower-end-point
- ;; Step 3: move to upper end point.
- upper-end-point
- ;; Step 2: curve through outer control points
- ;; to upper end point.
- lower-outer-control-point
- upper-outer-control-point
- upper-end-point
- ;; Step 1: move to lower end point.
- lower-end-point))
- line-width)
- (interval-widen x-extent (/ line-width 2))
- (interval-widen y-extent (/ line-width 2)))))
+ (make-bezier-sandwich-stencil
+ (list
+ ;; Step 4: curve through inner control points
+ ;; to lower end point.
+ upper-inner-control-point
+ lower-inner-control-point
+ lower-end-point
+ ;; Step 3: move to upper end point.
+ upper-end-point
+ ;; Step 2: curve through outer control points
+ ;; to upper end point.
+ lower-outer-control-point
+ upper-outer-control-point
+ upper-end-point
+ ;; Step 1: move to lower end point.
+ lower-end-point)
+ line-width
+ (interval-widen x-extent (/ line-width 2))
+ (interval-widen y-extent (/ line-width 2)))))
(define-public (parenthesize-stencil
stencil half-thickness width angularity padding)
(cons (min-max-crawler min cddr possible-extrema)
(min-max-crawler max cddr possible-extrema)))))
-(define (path-min-max origin pointlist)
+(define (line-part-min-max x1 x2)
+ (list (min x1 x2) (max x1 x2)))
+
+(define (bezier-part-min-max x1 x2 x3 x4)
+ ((lambda (x) (list (reduce min 10000 x) (reduce max -10000 x)))
+ (map
+ (lambda (x)
+ (+ (* x1 (expt (- 1 x) 3))
+ (+ (* 3 (* x2 (* (expt (- 1 x) 2) x)))
+ (+ (* 3 (* x3 (* (- 1 x) (expt x 2))))
+ (* x4 (expt x 3))))))
+ (if (< (+ (expt x2 2) (+ (expt x3 2) (* x1 x4)))
+ (+ (* x1 x3) (+ (* x2 x4) (* x2 x3))))
+ (list 0.0 1.0)
+ (filter
+ (lambda (x) (and (>= x 0) (<= x 1)))
+ (append
+ (list 0.0 1.0)
+ (map (lambda (op)
+ (if (not (eqv? 0.0
+ (exact->inexact (- (+ x1 (* 3 x3)) (+ x4 (* 3 x2))))))
+ ;; Zeros of the bezier curve
+ (/ (+ (- x1 (* 2 x2))
+ (op x3
+ (sqrt (- (+ (expt x2 2)
+ (+ (expt x3 2) (* x1 x4)))
+ (+ (* x1 x3)
+ (+ (* x2 x4) (* x2 x3)))))))
+ (- (+ x1 (* 3 x3)) (+ x4 (* 3 x2))))
+ ;; Apply L'hopital's rule to get the zeros if 0/0
+ (* (op 0 1)
+ (/ (/ (- x4 x3) 2)
+ (sqrt (- (+ (* x2 x2)
+ (+ (* x3 x3) (* x1 x4)))
+ (+ (* x1 x3)
+ (+ (* x2 x4) (* x2 x3)))))))))
+ (list + -))))))))
+
+(define (bezier-min-max x1 y1 x2 y2 x3 y3 x4 y4)
+ (map (lambda (x)
+ (apply bezier-part-min-max x))
+ `((,x1 ,x2 ,x3 ,x4) (,y1 ,y2 ,y3 ,y4))))
+
+(define (line-min-max x1 y1 x2 y2)
+ (map (lambda (x)
+ (apply line-part-min-max x))
+ `((,x1 ,x2) (,y1 ,y2))))
- (define (line-part-min-max x1 x2)
- (list (min x1 x2) (max x1 x2)))
-
- (define (bezier-part-min-max x1 x2 x3 x4)
- ((lambda (x) (list (reduce min 10000 x) (reduce max -10000 x)))
- (map
- (lambda (x)
- (+ (* x1 (expt (- 1 x) 3))
- (+ (* 3 (* x2 (* (expt (- 1 x) 2) x)))
- (+ (* 3 (* x3 (* (- 1 x) (expt x 2))))
- (* x4 (expt x 3))))))
- (if (< (+ (expt x2 2) (+ (expt x3 2) (* x1 x4)))
- (+ (* x1 x3) (+ (* x2 x4) (* x2 x3))))
- (list 0.0 1.0)
- (filter
- (lambda (x) (and (>= x 0) (<= x 1)))
- (append
- (list 0.0 1.0)
- (map (lambda (op)
- (if (not (eqv? 0.0
- (- (+ x1 (* 3 x3)) (+ x4 (* 3 x2)))))
- ;; Zeros of the bezier curve
- (/ (+ (- x1 (* 2 x2))
- (op x3
- (sqrt (- (+ (expt x2 2)
- (+ (expt x3 2) (* x1 x4)))
- (+ (* x1 x3)
- (+ (* x2 x4) (* x2 x3)))))))
- (- (+ x1 (* 3 x3)) (+ x4 (* 3 x2))))
- ;; Apply L'hopital's rule to get the zeros if 0/0
- (* (op 0 1)
- (/ (/ (- x4 x3) 2)
- (sqrt (- (+ (* x2 x2)
- (+ (* x3 x3) (* x1 x4)))
- (+ (* x1 x3)
- (+ (* x2 x4) (* x2 x3)))))))))
- (list + -))))))))
-
- (define (bezier-min-max x1 y1 x2 y2 x3 y3 x4 y4)
- (map (lambda (x)
- (apply bezier-part-min-max x))
- `((,x1 ,x2 ,x3 ,x4) (,y1 ,y2 ,y3 ,y4))))
-
- (define (line-min-max x1 y1 x2 y2)
- (map (lambda (x)
- (apply line-part-min-max x))
- `((,x1 ,x2) (,y1 ,y2))))
+(define (path-min-max origin pointlist)
((lambda (x)
(list
projects / lilypond.git / blobdiff