Il giorno 04/giu/2015, alle ore 11.38, Michael Tiedtke ha scritto:
> All I wanted to do was to compute two or three color steps between two colors
> to fade from one to the other. Usually I would this with available
> compositing methods but in the current case it's easier to do maths and just
> redraw with the new color. The usual method to calculate the color steps is
> the linear one
> (http://stackoverflow.com/questions/27532/generating-gradients-programmatically).
> Wouldn't it be nice to define new methods for the usual arithmetic operation
> generics '(+ - * / < > = abs) to do color arithmetic?
>
> Example:
>
> (define color-1 (make-color r1 g1 b1))
> (define color-2 (make-color r2 g2 b2))
>
> (define color-delta (/ (- color-2 color-1) number-of-steps))
> (let loop ((color color-1))
> (cons color [if (= color color-2) '() (loop (+ color color-delta))] ))
>
> NB It's not the best example out there: delta should be computed like any
> other delta as the absolute numerical distance
> where the return value of the subtraction might be a negative
> color-distance% object but colors usually are only
> positive. Perhaps it's better to do without bigger than and less than when
> it comes to colors.
>
> Before I go ahead and just do it I wanted to ask:
>
> 1) Does such a thing exist somewhere for Scheme or Racket (I couldn't find
> anything)
> The only example I found was:
> https://www.wolframalpha.com/examples/ColorArithmetic.html
>
> 2) Does anyone know how this proposed color arithmetic would interact with
> color management / color spaces?
> 2a) Is it true that non-linear color arithmetic produces better results for
> gradients?
>
> 3) Any suggestions regarding the implementation of the generics?
>
> 4) Both Cairo and Quartz do have more sophisticated compositing methods - but
> they do not expose this low level functionality?
>
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Here is a first implementation: it's a bit awkward but does the job.
1) Some things that do not work: I can't provide + - etc. because this results
in really strange error messages where send doesn't see a color% object but a
number / rgb component at (define (rgb-delta rgb-1 rgb-2) (vector (- (send
rgb-1 red) ...
2) I can't compare colors in Racket - two (0 0 0) rgb color objects are neither
equal? nor object=?. Perhaps I should add an color equal predicate ...
#lang racket
;; Module In
(require racket/draw ; color%
plot/utils ; vector calculus)
;;;
;;; Delta Color: Color Distance Arithmetic
;;;
;;; Rationale: Colors are abstract concepts in the first place which
;;; we can't calculate with. Color distances are easy to define even
;;; for abstract unknown color spaces. The current definition is:
;;;
;;; If delta is the difference between color 2 and color 1, then
;;; you get color 2 by adding the delta to color 1.
;;;
;;; If you divide delta by n and add delta n times to color 1 you
;;; will get n color steps representing a smooth gradient from color
;;; 1 to color 2.
;;;
;;; Everything else is currently undefined. This Color Distance
;;; Arithmetic is currently only implemented for the usual virtual
;;; interval integer RGB color space (RGB32). Color Deltas are vectors
;;; of exact numbers. For this you can calculate with endless (memory
;;; limited) precision between the color points in the color space.
;;;
;;; Domain Entry and Exit:
;;;
;;; color - color -> color-delta
;;; color + color-delta -> color
;;; color - color-delta -> color
;; RGB Delta: Color Distance in our virtual RGB color space
;; The red, green and blue methods return byte data but we
;; use them as exact integers to allow further computation.
(define (rgb-delta rgb-1 rgb-2)
(vector (- (send rgb-1 red) (send rgb-2 red))
(- (send rgb-1 green) (send rgb-2 green))
(- (send rgb-1 blue) (send rgb-2 blue)) ))
(define (delta? a)
(and (vector? a)
(= (vector-length a) 3)))
(define (red delta) (vector-ref delta 0))
(define (green delta) (vector-ref delta 1))
(define (blue delta) (vector-ref delta 2))
;; RGB Delta Plus: Domain Exit
(define (rgb-delta-plus rgb delta)
(make-color (+ (send rgb red) (red delta))
(+ (send rgb green) (green delta))
(+ (send rgb blue) (blue delta))))
;; RGB Delta Minus: Domain Exit
(define (rgb-delta-minus rgb delta)
(make-color (- (send rgb red) (red delta))
(- (send rgb green) (green delta))
(- (send rgb blue) (blue delta))))
(define (color? a) (is-a? a color%))
(define (subtract a b)
(cond ([and (color? a) (color? b)] (rgb-delta a b))
([and (color? a) (delta? b)] (rgb-delta-minus a b))
([and (delta? a) (delta? b)] (v- a b))
(else
(error "Delta Color: subtract: out of domain error"))))
(define divide v/)
(define multiply v*)
(define (add a b)
(cond ([and (delta? a) (delta? b)] (v+ a b)) ; intra-domain
([and (delta? a) (color? b)] ; domain exit
(rgb-delta-plus b a))
([and (color? a) (delta? b)]
(rgb-delta-plus a b))
(else
(error "Delta Color: add: out of domain error"))))
;; Module Out
(provide add subtract multiply divide ; suggested prefix-in: deco-
delta?)
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