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Basic 2D Geometry Routines

From: "andrew cooke" <andrew@...>

Date: Sat, 18 Aug 2007 16:28:41 -0400 (CLT)

I *think* this is fairy efficient, but haven't actually done any profiling
(I know...)

":";exec snow -- "$0" "$@"

(package* napito-base/v1.0.0

  (provide:
   (define (nap-default-transform)))

  (author: "Andrew Cooke <andrew at acooke.org>")
  (homepage: "http://www.acooke.org")
  (description: "Napito drawing description language - support routines")
  (keywords: graphics)
  (license: gpl/v3.0))

(define (nap-default-transform) '(1 0 0 0 1 0))

(define-syntax dot
  (syntax-rules ()
    ((_ (op1 arg1 ...) (op2 arg2 ...))
     (receive (a b c) (op1 arg1 ...)
       (receive (x y z) (op2 arg2 ...)
         (+ (* a x) (* b y) (* c z)))))))

(define-syntax row1 (syntax-rules () ((_ a b c d e f) (values a b c))))
(define-syntax row2 (syntax-rules () ((_ a b c d e f) (values d e f))))
(define-syntax col1 (syntax-rules () ((_ a b c d e f) (values a d 0))))
(define-syntax col2 (syntax-rules () ((_ a b c d e f) (values b e 0))))
(define-syntax col3 (syntax-rules () ((_ a b c d e f) (values c f 1))))
(define-syntax xyz  (syntax-rules () ((_ x y)         (values x y 1))))

(define-syntax split (syntax-rules () ((_ lst) (values (car lst) (cdr
lst)))))

(define (unpack6 lst)
  (receive (a as) (split lst)
    (receive (b bs) (split as)
      (receive (c cs) (split bs)
        (receive (d ds) (split cs)
          (receive (e es) (split ds)
            (receive (f fs) (split es)
              (values a b c d e f))))))))

(define (unpack2 lst)
  (receive (a as) (split lst)
    (receive (b bs) (split as)
      (values a b))))

(define (nap-transform-point transform point)
  (receive (a b c d e f) (unpack6 transform)
    (receive (x y) (unpack2 point)
      (list (dot (row1 a b c d e f) (xyz x y))
            (dot (row2 a b c d e f) (xyz x y))))))

(define (nap-join-transforms before extra)
  (receive (p q r s t u) (unpack6 before)
    (receive (a b c d e f) (unpack6 extra)
      (list (dot (row1 p q r s t u) (col1 a b c d e f))
            (dot (row1 p q r s t u) (col2 a b c d e f))
            (dot (row1 p q r s t u) (col3 a b c d e f))
            (dot (row2 p q r s t u) (col1 a b c d e f))
            (dot (row2 p q r s t u) (col2 a b c d e f))
            (dot (row2 p q r s t u) (col3 a b c d e f))))))

(test*
 (let ((unit '(1 0 0 0 1 0))
       (doublex '(2 0 0 0 1 0))
       (incx '(1 0 1 0 1 0))
       (one '(1 1)))
   (expect* (equal? '(1 1) (nap-transform-point unit one)))
   (expect* (equal? '(2 1) (nap-transform-point doublex one)))
   (expect* (equal? '(2 1) (nap-transform-point incx one)))
   (expect* (equal? unit (nap-join-transforms unit unit)))
   (expect* (equal? '(4 1)
                    (nap-transform-point
                     (nap-join-transforms doublex incx) one)))
   (expect* (equal? '(3 1)
                    (nap-transform-point
                     (nap-join-transforms incx doublex) one)))))

More Specific Operations

From: "andrew cooke" <andrew@...>

Date: Sat, 18 Aug 2007 17:00:31 -0400 (CLT)

(define (nap-shift-x d) (list 1 0 d 0 1 0))
(define (nap-shift-y d) (list 1 0 0 0 1 d))
(define (nap-scale f) (list f 0 0 0 f 0))
(define (nap-scale-x f) (list f 0 0 0 1 0))
(define (nap-scale-y f) (list 1 0 0 0 f 0))
(define pi 3.1415926)
(define (nap-rotate-deg d)
  (let* ((r (/ (* pi d) 180))
         (c (cos r))
         (s (sin r)))
    (list c (- s) 0 s c 0)))

(test*
 (define (almost-equal? ab pq)
   (define (close x y) (< (abs (- x y)) 0.01))
   (receive (a b) (unpack2 ab)
     (receive (p q) (unpack2 pq)
       (and (close a p) (close b q)))))
 (let ((unit '(1 0 0 0 1 0))
       (incx2 (nap-shift-x 2))
       (incy3 (nap-shift-y 3))
       (double (nap-scale 2))
       (scalex3 (nap-scale-x 3))
       (scaley4 (nap-scale-y 4))
       (rot90 (nap-rotate-deg 90))
       (one '(1 1)))
   (expect* (equal? '(3 1) (nap-transform-point incx2 one)))
   (expect* (equal? '(1 4) (nap-transform-point incy3 one)))
   (expect* (equal? '(2 2) (nap-transform-point double one)))
   (expect* (equal? '(3 1) (nap-transform-point scalex3 one)))
   (expect* (equal? '(1 4) (nap-transform-point scaley4 one)))
   (expect* (almost-equal? '(0.999 -0.001) '(1 0)))
   (expect* (almost-equal? '(-1 1) (nap-transform-point rot90 one)))))

Andrew

Not Efficient!

From: "andrew cooke" <andrew@...>

Date: Sun, 19 Aug 2007 18:00:57 -0400 (CLT)

The values/receive code is constructing and discarding vectors,
apparently.  need to rewrite...

Andrew

Significantly Faster

From: "andrew cooke" <andrew@...>

Date: Sun, 19 Aug 2007 21:15:33 -0400 (CLT)

I've removed values/receive by (1) using CPS in the macros that select
particular elements and (2) using vectors, which simplifies unpacking.

":";exec snow -- "$0" "$@"

; this is about 40% faster than napito-base.scm

; qp6 napito: ./napito-vector.scm
; warming up
; 100000 timing
; (time (speed 1 %%n1414))
;     1403 ms real time
;     1316 ms cpu time (1316 user, 0 system)
;     95 collections accounting for 571 ms real time (548 user, 0 system)
;     891208784 bytes allocated
;     no minor faults
;     no major faults

(package* napito-vector/v1.0.0

  (provide:
   (define nap-default-transform)
   (define (nap-transform-handler engine))
   (define (nap-join-transforms before extra))
   (define (nap-transform-point transform point)))

  (author: "Andrew Cooke <andrew at acooke.org>")
  (homepage: "http://www.acooke.org")
  (description: "Napito drawing description language - support routines")
  (keywords: graphics)
  (license: gpl/v3.0))

(define nap-default-transform '#(1 0 0 0 1 0))

(define (dot a b c) (lambda (p q r) (+ (* a p) (* b q) (* c r))))

(define-syntax row1 (syntax-rules () ((_ a b c d e f fun) (fun a b c))))
(define-syntax row2 (syntax-rules () ((_ a b c d e f fun) (fun d e f))))
(define-syntax col1 (syntax-rules () ((_ a b c d e f fun) (fun a d 0))))
(define-syntax col2 (syntax-rules () ((_ a b c d e f fun) (fun b e 0))))
(define-syntax col3 (syntax-rules () ((_ a b c d e f fun) (fun c f 1))))
(define-syntax xyz  (syntax-rules () ((_ x y fun)         (fun x y 1))))

; this is *much* slower
; (define (row1 a b c d e f fun) (fun a b c))
; (define (row2 a b c d e f fun) (fun d e f))
; (define (col1 a b c d e f fun) (fun a d 0))
; (define (col2 a b c d e f fun) (fun b e 0))
; (define (col3 a b c d e f fun) (fun c f 1))
; (define (xyz  x y fun)         (fun x y 1))

(define (unpack6 vec fun)
  (let* ((a (vector-ref vec 0))
         (b (vector-ref vec 1))
         (c (vector-ref vec 2))
         (d (vector-ref vec 3))
         (e (vector-ref vec 4))
         (f (vector-ref vec 5)))
    (fun a b c d e f)))

(define (unpack2 vec fun)
  (let* ((a (vector-ref vec 0))
         (b (vector-ref vec 1)))
    (fun a b)))

(define (nap-transform-point transform point)
  (unpack6 transform (lambda (a b c d e f)
    (unpack2 point (lambda (x y)
      (vector (row1 a b c d e f (xyz x y dot))
              (row2 a b c d e f (xyz x y dot))))))))

(define (nap-join-transforms before extra)
  (unpack6 before (lambda (p q r s t u)
    (unpack6 extra (lambda (a b c d e f)
      (vector (row1 p q r s t u (col1 a b c d e f dot))
              (row1 p q r s t u (col2 a b c d e f dot))
              (row1 p q r s t u (col3 a b c d e f dot))
              (row2 p q r s t u (col1 a b c d e f dot))
              (row2 p q r s t u (col2 a b c d e f dot))
              (row2 p q r s t u (col3 a b c d e f dot))))))))

(test*
 (let ((unit '#(1 0 0 0 1 0))
       (doublex '#(2 0 0 0 1 0))
       (incx '#(1 0 1 0 1 0))
       (one '#(1 1)))
   (expect* (equal? '#(1 1) (nap-transform-point unit one)))
   (expect* (equal? '#(2 1) (nap-transform-point doublex one)))
   (expect* (equal? '#(2 1) (nap-transform-point incx one)))
   (expect* (equal? unit (nap-join-transforms unit unit)))
   (expect* (equal? '#(4 1)
                    (nap-transform-point
                     (nap-join-transforms doublex incx) one)))
   (expect* (equal? '#(3 1)
                    (nap-transform-point
                     (nap-join-transforms incx doublex) one)))))

(define (nap-shift-x d) (list 1 0 d 0 1 0))
(define (nap-shift-y d) (list 1 0 0 0 1 d))
(define (nap-scale f) (list f 0 0 0 f 0))
(define (nap-scale-x f) (list f 0 0 0 1 0))
(define (nap-scale-y f) (list 1 0 0 0 f 0))
(define pi 3.1415926)
(define (nap-rotate-deg d)
  (let* ((r (/ (* pi d) 180))
         (c (cos r))
         (s (sin r)))
    (list c (- s) 0 s c 0)))

(test*
 (define (almost-equal? ab pq)
   (define (close x y) (< (abs (- x y)) 0.01))
   (receive (a b) (unpack2 ab)
     (receive (p q) (unpack2 pq)
       (and (close a p) (close b q)))))
 (let ((unit '#(1 0 0 0 1 0))
       (incx2 (nap-shift-x 2))
       (incy3 (nap-shift-y 3))
       (double (nap-scale 2))
       (scalex3 (nap-scale-x 3))
       (scaley4 (nap-scale-y 4))
       (rot90 (nap-rotate-deg 90))
       (one '#(1 1)))
   (expect* (equal? '#(3 1) (nap-transform-point incx2 one)))
   (expect* (equal? '#(1 4) (nap-transform-point incy3 one)))
   (expect* (equal? '#(2 2) (nap-transform-point double one)))
   (expect* (equal? '#(3 1) (nap-transform-point scalex3 one)))
   (expect* (equal? '#(1 4) (nap-transform-point scaley4 one)))
   (expect* (almost-equal? '#(0.999 -0.001) '#(1 0)))
   (expect* (almost-equal? '#(-1 1) (nap-transform-point rot90 one)))
   (expect* (equal? '#(3 4) (nap-transform-point
                            (nap-join-transforms incx2 incy3) one)))))

; this wraps an engine and normalizes all transform actions
(define (nap-transform-handler engine)
  (define (forward transform)
    (engine 'nap-transform transform))
  (lambda (action args)
    (case action
      ((nap-shift-x) (forward (nap-shift-x (car args))))
      ((nap-shift-y) (forward (nap-shift-y (car args))))
      ((nap-scale) (forward (nap-scale (car args))))
      ((nap-scale-x) (forward (nap-scale-x (car args))))
      ((nap-scale-y) (forward (nap-scale-y (car args))))
      ((nap-rotate-deg) (forward (nap-rotate-deg (car args))))
      (else (engine action args)))))

(define (speed n limit)
  (if (> n limit)
      '()
      (let ((a (vector n n n n n n))
            (b (vector n n n n n n)))
        (nap-join-transforms a b)
        (speed (+ n 1) limit))))

(define (measure n)
  (display "warming up\n")
  (speed 1 n)
  (display (list n " timing\n"))
  (time (speed 1 n)))

(measure 100000)

Andrew

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