Supersampling

- Random supersampling (prettier but quite slow)
- WIP: bette color gradient

6 files changed, 85 insertions, 22 deletions

diff --git a/Makefile b/Makefile
index 85660a0..11997f9 100644
--- a/Makefile
+++ b/Makefile
@@ -1,7 +1,7 @@
 NAME = mandel
 CC = gcc
 CCFLAGS = -Wall -Wextra
-LDFLAGS = -lpthread $(shell sdl2-config --libs --cflags)
+LDFLAGS = -lm -lpthread $(shell sdl2-config --libs --cflags)
 
 HEADER = header.h
 SRC = main.c graphics.c mandelbrot.c helper.c
diff --git a/README.md b/README.md
index 24a5002..0cae1d4 100644
--- a/README.md
+++ b/README.md
@@ -17,10 +17,13 @@ SDL2: `sudo apt install libsdl2-dev`
 
 ## TODO
 
-- [ ] Create color spectrum.
+- [ ] Color gradient with control points and cubic iterpolation
+      like <https://stackoverflow.com/a/25816111>
 - [ ] Smooth shading for out of set iteration colors.
 - [ ] Draw to bmp image.
 - [x] Create pixel array and update the render line by line.
 - [ ] Display coordinates and other useful info.
 - [x] Computation done in parallel.
 - [x] Command line options
+- [x] Anti-aliasing with supersampling
+- [ ] Other (not random?) supersampling algorithm
diff --git a/graphics.c b/graphics.c
index d8c6997..e422071 100644
--- a/graphics.c
+++ b/graphics.c
@@ -17,6 +17,8 @@
 #define IN_SET_COLOR 0x050505
 #define PALETTE_START 0x000022
 #define PALETTE_END 0xd62f2f
+/* #define PALETTE_START 0x000000 */
+/* #define PALETTE_END 0xffffff */
 #define SET_DRAW_COLOR(renderer, c) ( \
         SDL_SetRenderDrawColor(renderer, c.rgb.r, c.rgb.g, c.rgb.b, SDL_ALPHA_OPAQUE));
 
@@ -185,7 +187,7 @@ static void event_handler(GState *state)
                     zoom_out(state, ZOOM_RATIO);
                 break;
             case SDL_MOUSEBUTTONDOWN:
-                    printf("> %d, %d\n", e.button.x, e.button.y);
+                    /* printf("> %d, %d\n", e.button.x, e.button.y); */
                 if (e.button.button == SDL_BUTTON_RIGHT)
                     recenter(state, e.button.x, e.button.y);
             // TODO
@@ -222,6 +224,8 @@ static void event_handler(GState *state)
         return NULL;
     for (int i = 0; i < MAX_ITERATION; i++)
     {
+        /* palette[i] = helper_HSL_to_RGB(i, 0.6, 1.0); */
+        /* printf("%x\n", palette[i].hexcode); */
         palette[i].rgb.r = i * red_step + start.rgb.r;
         palette[i].rgb.g = i * green_step + start.rgb.g;
         palette[i].rgb.b = i * blue_step + start.rgb.b;
diff --git a/header.h b/header.h
index fbaca08..92b4d83 100644
--- a/header.h
+++ b/header.h
@@ -4,8 +4,8 @@
 # include <stdbool.h>
 # include <SDL2/SDL.h>
 
-# define MAX_ITERATION 210
-# define ESCAPE_RADIUS 2
+# define MAX_ITERATION 200
+# define ESCAPE_RADIUS 10
 # define ESCAPE_RADIUS_SQUARED (ESCAPE_RADIUS * ESCAPE_RADIUS)
 
 # define PIXELS_CHANELS 3
@@ -62,6 +62,7 @@ typedef struct
 {
     double real_lo;
     double real_hi;
+    double imag_step;
     int width;
     double imag;
     Color *palette;
@@ -81,6 +82,7 @@ void graphics_run(GState *state);
 
 // helper.c
 double map_range(double x, double src_lo, double src_hi, double dest_lo, double dest_hi);
-int *inclusive_range(int start, int end);
+Color helper_HSL_to_RGB(int hue, double saturation, double lightness);
+double double_rand(void);
 
 #endif
diff --git a/helper.c b/helper.c
index 0290563..3e02182 100644
--- a/helper.c
+++ b/helper.c
@@ -1,22 +1,48 @@
 #include <math.h>
 #include "header.h"
 
+#define MAX(x, y) ((x) > (y) ? (x) : (y))
+#define MIN(x, y) ((x) < (y) ? (x) : (y))
+#define MIN3(x, y, z) (MIN(x, MIN(y, z)))
+
 double map_range(double x, double src_lo, double src_hi, double dest_lo, double dest_hi)
 {
-    double src_len = fabs(src_hi - src_lo);
-    double dest_len = fabs(dest_hi - dest_lo);
-
+    double src_len = src_hi - src_lo;
+    double dest_len = dest_hi - dest_lo;
     return (x - src_lo) / src_len * dest_len + dest_lo;
 }
 
-int *inclusive_range(int start, int end)
+Color helper_HSL_to_RGB(int hue, double saturation, double lightness)
+{
+    /* double chroma = (1 - fabs(2 * lightness - 1)) * saturation; */
+    /* int hue_p = hue / 60; */
+    /* double x = chroma * (1 - abs(hue_p % 2 - 1)); */
+    Color color;
+
+    /* if (hue == 0) */
+    /* { */
+    /*     color.hexcode = 0x000000; */
+    /*     return color; */
+    /* } */
+    /*  */
+    /* if (hue_p */
+
+    double a = saturation * MIN(lightness, 1 - lightness);
+    int kn0 = (0 + hue / 30) % 12;
+    int kn8 = (8 + hue / 30) % 12;
+    int kn4 = (4 + hue / 30) % 12;
+    Byte f0 = lightness - a * MAX(MIN3(kn0 - 3, 9 - kn0, 1), -1);
+    Byte f8 = lightness - a * MAX(MIN3(kn8 - 3, 9 - kn8, 1), -1);
+    Byte f4 = lightness - a * MAX(MIN3(kn4 - 3, 9 - kn4, 1), -1);
+
+    color.rgb.r = f0;
+    color.rgb.g = f8;
+    color.rgb.b = f4;
+
+    return color;
+}
+
+double double_rand(void)
 {
-    if (end < start)
-        return NULL;
-    int *range = malloc(sizeof(int) * (end - start + 1));
-    if (range == NULL)
-        return NULL;
-    for (int i = 0; start < end; i++)
-        range[i] = start++;
-    return range;
+    return (double)rand() / RAND_MAX;
 }
diff --git a/mandelbrot.c b/mandelbrot.c
index 1112575..7017a54 100644
--- a/mandelbrot.c
+++ b/mandelbrot.c
@@ -1,4 +1,5 @@
 #include <stdio.h>
+#include <math.h>
 #include <pthread.h>
 #include "header.h"
 
@@ -9,6 +10,7 @@
 #define AXIS_DIV 46.0
 #define REAL_AXIS_STEP ((PRINT_REAL_HI - PRINT_REAL_LO) / AXIS_DIV)
 #define IMAG_AXIS_STEP ((PRINT_IMAG_HI - PRINT_IMAG_LO) / AXIS_DIV)
+#define SAMPLES 1
 
 #define IN_CHAR '*'
 #define OUT_CHAR ' '
@@ -37,6 +39,16 @@ int mandelbrot_in_set(double ca, double cb)
     return n;
 }
 
+
+int mandelbrot_in_set_super_sampled(double ca, double cb, double real_step, double imag_step)
+{
+    int total = 0;
+    for (int i = 0; i < SAMPLES; i++)
+        total += mandelbrot_in_set(ca - (double_rand() * real_step) / 2,
+                                   cb - (double_rand() * imag_step) / 2);
+    return total / SAMPLES;
+}
+
 void *mandelbrot_pixels(double real_lo, double real_hi, double imag_lo,
                         double imag_hi, int width, int height, Color *palette)
 {
@@ -55,6 +67,7 @@ void *mandelbrot_pixels(double real_lo, double real_hi, double imag_lo,
         args->real_hi = real_hi;
         args->width = width;
         args->imag = map_range((double)y, 0, height, imag_lo, imag_hi);
+        args->imag_step = (imag_hi - imag_lo) / (0.5 + (height - 1));
         args->palette = palette;
         args->row = pixels + PIXELS_CHANELS * width * y;
         pthread_create(&threads[y], NULL, pixel_row, args);
@@ -68,13 +81,28 @@ void *mandelbrot_pixels(double real_lo, double real_hi, double imag_lo,
 static void *pixel_row(void *void_args)
 {
     ThreadArgs *args = (ThreadArgs*)void_args;
+    int iterations;
+    double real_step = (args->real_hi - args->real_lo) / (0.5 + (args->width - 1));
     for (int x = 0; x < args->width; x++)
     {
         double a = map_range((double)x, 0, args->width, args->real_lo, args->real_hi);
-        Color color = args->palette[mandelbrot_in_set(a, args->imag)];
-        args->row[x * PIXELS_CHANELS] = color.rgb.r;
-        args->row[x * PIXELS_CHANELS + 1] = color.rgb.g;
-        args->row[x * PIXELS_CHANELS + 2] = color.rgb.b;
+        if (SAMPLES == 1)
+            iterations = mandelbrot_in_set(a, args->imag);
+        else
+        {
+            iterations = mandelbrot_in_set_super_sampled(
+                a, args->imag, real_step, args->imag_step);
+        }
+
+        /* double logBase = 1.0 / log(2.0); */
+        /* double logHalfBase = log(0.5) * logBase; */
+        /* int color_index = (int)(5 + iterations - logHalfBase */
+        /*                   - log(log(a * a + args->imag * args->imag)) * logBase); */
+        Color color = args->palette[iterations];
+        int row_index = x * PIXELS_CHANELS;
+        args->row[row_index] = color.rgb.r;
+        args->row[row_index + 1] = color.rgb.g;
+        args->row[row_index + 2] = color.rgb.b;
     }
     free(args);
     return NULL;