How to get X/Y-extent of a bezier-curve?

[Thomas Morley]

Hi all,

I'm going to write a generic bow-stencil.
Below you'll find a boiled down example.

The main problem: how to determine the correct extents.
Looks like I need to calculate the actual X/Y-extents of the resulting
bezier-curve.
Though, obviously my maths-skills are not sufficient.

Any hints?

\version "2.18.2"

%% `overlay' is in the source for 2.19.28
%% for lower versions use:
#(define-markup-command (overlay layout props args) (markup-list?)
  (apply ly:stencil-add (interpret-markup-list layout props args)))

#(define (make-simple-bezier-stencil coords)
  (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))
                        )))
  (ly:make-stencil
    `(path 0.1 `(,@' ,command-list) 'round 'round #f)
    ;;;; TODO
    ;;;; How to get correct extents?
    ;; xext:
    (cons
      (car (list-ref coords 2))
      (car (list-ref coords 3)))
    ;;yext:
    (cons
      (cdr (list-ref coords 2))
      (cdr (list-ref coords 1)))
    )))

%%%%%%%%%%%%%%%%%
%% EXAMPLE
%%%%%%%%%%%%%%%%%

#(define pts-list
  '((12 . 8)
    (5 . 8)
    (2 . 2)
    (15 . 2)))

#(define (rotated-pts-list degree)
  (map
    (lambda (c)
      ;;;; TODO
      ;; coord-rotate rotates around '(0 . 0)
      ;; make it generic
      (coord-rotate c (degrees->radians degree)))
    pts-list))

\markup
  \column {
    \vspace #3
     \fill-line {
       \overlay {
         \circle \null %% representing point '(0 . 0)
         \override #'(box-padding . 0)
         \box \with-color #red {
           \stencil
             #(make-simple-bezier-stencil pts-list)
           \stencil
             #(make-simple-bezier-stencil (rotated-pts-list 90))
           \stencil
             #(make-simple-bezier-stencil (rotated-pts-list 60))
         }
       }
     }
  }



Cheers,
  Harm