feat: (non-l)erping

mandelbrot.ss

@@ -2,7 +2,7 @@
   (export make-ppm mandelbrot!
           steps
           make-rgb rgb-r rgb-g rgb-b
-          number->rgb)
+          number->rgb rgb-bin rgb-map rgb-lerp)
   (import (chezscheme))
 
 (define-record-type rgb (fields r g b))
@@ -11,6 +11,29 @@
   (make-rgb (bitwise-and #xff (bitwise-arithmetic-shift-right n 16))
             (bitwise-and #xff (bitwise-arithmetic-shift-right n 8))
             (bitwise-and #xff (bitwise-arithmetic-shift-right n 0))))
+(define (rgb-bin +)
+  (case-lambda
+    [(a) a]
+    [(a b) (make-rgb (+ (rgb-r a) (rgb-r b))
+                     (+ (rgb-g a) (rgb-g b))
+                     (+ (rgb-b a) (rgb-b b)))]
+    [(a . bs) (fold-left (rgb-bin +) a bs)]))
+
+(define (rgb-map c f)
+  (make-rgb (f (rgb-r c))
+            (f (rgb-g c))
+            (f (rgb-b c))))
+
+(define (rgb-mean . rgbs)
+  (if (null? rgbs)
+      (make-rgb 0 0 0)
+      (let* ([sum (apply (rgb-bin +) rgbs)]
+             [len (length rgbs)]
+             [scale (lambda (c) (inexact->exact (floor (/ c len))))])
+        (rgb-map sum scale))))
+
+(define (rgb-lerp i min max)
+  ((rgb-bin +) min (rgb-map ((rgb-bin -) max min) (lambda (x) (* i x)))))
 
 ;; proc : (x y) -> rgb
 (define (make-ppm path width height proc)
@@ -27,25 +50,45 @@
           (put-u8 p (rgb-b color))))))
   'done)
 
+
 (define (lerp i min max)
   (+ min (* i (- max min))))
 
 (define steps 100)
 (define power 2)
+(define samples-per-pixel 4)
 
+(define tau (* 4 (acos 0)))
+
+(define (rotate-about origin p angle)
+  (+ (* (- p origin)
+      (make-rectangular (cos angle) (sin angle)))
+     origin))
+
+;; let's rotate the sample?
 (define (mandelbrot! path width height color xmin xmax ymin ymax)
+  (define pixel-width  (exact->inexact (/ (- xmax xmin) width)))
+  (define pixel-height (exact->inexact (/ (- ymax ymin) height)))
+  (define sample-rotation (/ tau samples-per-pixel))
+  (define (sample-vals center)
+    (let ([top (+ center (make-rectangular 0 (- (/ pixel-height 2))))])
+      (map (lambda (i) (rotate-about center top (* i sample-rotation)))
+           (iota samples-per-pixel))))
   (make-ppm path width height
     (lambda (x y)
       (define ix (lerp (/ x width)  xmin xmax))
       (define iy (lerp (/ y height) ymin ymax))
-      (define c (exact->inexact (make-rectangular ix iy)))
-      (define (step z) (+ (expt z power) c))
+      (define center (exact->inexact (make-rectangular ix iy)))
+      (define (sample p)
+        (define (step z) (+ (expt z power) p))
         (let loop ([i 0]
                    [z (step 0)])
           (cond
            [(= i steps) (color -1)]
            [(> (magnitude z) 2) (color i)]
-         [else (loop (+ 1 i) (step z))]))))))
+           [else (loop (+ 1 i) (step z))])))
+      (define samples (map sample (sample-vals center)))
+      (apply rgb-mean samples)))))
 
 (top-level-program
  (import (chezscheme)
@@ -65,7 +108,7 @@
 
 (define (cli-fail)
   (format (standard-error-port 'line (current-transcoder))
-          "usage: ./mandelbrot.ss path width height [color:hex*]\n")
+          "usage: ./mandelbrot.ss PATH WIDTH HEIGHT [COLOR:hex+|--lerp INTERIOR:hex START:hex END:hex]\n")
   (exit 1))
 
 (define args (command-line-arguments))
@@ -83,19 +126,34 @@
   (cli-fail))
 
 (define (color i)
-  (define c (floor (* 256 (/ (+ 1 i) steps))))
+  (define c
+    (if (negative? i)
+        0
+        (floor (* 256 (/ i steps)))))
   (make-rgb c c c))
 
 (when (< 3 (length args))
-  (let* ([stripes
   (let* ([colors (cdddr args)]
+         [lerp? (equal? "--lerp" (car colors))]
+         [colors (if lerp? (cdr colors) colors)]
          [nums (map (lambda (n) (string->number n 16)) colors)]
          [_ (unless (for-all (lambda (x) (and (integer? x) (<= 0 x))) nums)
               (cli-fail))]
-                 [colors (map number->rgb nums)])
-            (list->vector colors))]
+         [stripes (list->vector (map number->rgb nums))]
          [stripe-count (vector-length stripes)])
-    (set! color (lambda (i) (vector-ref stripes (mod i stripe-count))))))
+    (when (and lerp? (< stripe-count 3))
+      (cli-fail))
+
+    (set! color
+      (if lerp?
+          (lambda (i)
+            (if (negative? i)
+                (vector-ref stripes 0)
+                (rgb-map (rgb-lerp (expt (/ i steps) 1.3)
+                                   (vector-ref stripes 1)
+                                   (vector-ref stripes 2))
+                         floor)))
+          (lambda (i) (vector-ref stripes (mod i stripe-count)))))))
 
 (mandelbrot! path width height color -2.2 1.1 -1 1))