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→Assignment 1: Julia Set
{| class="wikitable mw-collapsible mw-collapsed"
! Julia.cpp
/**
* Mandelbrot.cpp
* Vincent Terpstra
* Feb 18 / 2019
* Functions to display a Mandlebrot set
*/
#include <iostream>
#include <math.h>
#include "Bitmap.h"
#define MAXCYCLES 1000
#define ITER 1
#define PI 3.14159
void calcJulia(int* array, int width, int height, float jR, float jI);
void createBMP(int* array, int width, int height);
int main(int size, const char ** args) {
int height = (size > 1) ? atoi(args[1]) : 1000;
int width = height / 2 * 3;
int * array = new int[height * width];
float jI = -0.4f;
float jR = 0.6f;
float angle = 2.0f / ITER * PI;
float cosA = cos(angle);
float sinA = sin(angle);
for(int i = 0; i < ITER; i++){
calcJulia(array, width, height, jI, jR);
createBMP(array, width, height);
//rotate the Julia point
float tmp = jI;
jI = cosA * jI - sinA * jR;
jR = cosA * jR + sinA * tmp;
}
delete[] array;
return 0;
}
/**
* calcDepth
* finds the escape value of the Julia set
* inputs sR, sI: starting position on the map
* jR, jI: values of the julia set
* exits when |s| > 2 or reached MAXCYCLES
* return the
*/
int calcDepth(float sR, float sI, const float jR, const float jI){
int cycle = 0;
while(sR * sR + sI * sI <= 4 && ++cycle < MAXCYCLES){
// s(next) = s * s + j
float tmp = sR;
sR = sR * sR - sI * sI + jR;
sI = 2 * tmp * sI + jI;
}
return cycle;
}
/**
* calcJulia
* Function to calculate the values from (-1.5, 1.5),(-1, 1) in the Julia set
* saves the values onto the array
*/
void calcJulia(int * array, int width, int height, const float jR, const float jI){
float delta = 2 / (float)height;
float x, y = -1;
for(int i = 0; i < height; i++){
x = -1.5f;
for(int j = 0; j < width; j++){
*array++ = calcDepth(x, y, jR, jI);
x+=delta;
}
y += delta;
}
}
struct Pix {
float val;
int r, g, b;
Pix(float val, int r, int g, int b) :
val(val), r(r), g(g), b(b) {}
};
bool lerp(float clr, Pix& first, Pix& second, Bitmap & map);
/**
* createBMP
* maps the values in the array to a .bmp file
* linear interpolates between color values
*/
void createBMP(int * array, int width, int height){
static int idx = 0;
char name[] = "julia000.bmp";
name[5] = (idx / 100) + '0';
name[6] = ((idx / 10) % 10) + '0';
name[7] = (idx % 10) + '0';
Bitmap map (name, width, height);
//idx++;
const int pix = width * height;
struct Pix
clr0(0, 20, 20, 30),
clr1(10, 20, 10, 100),
clr2(180, 20, 170, 205),
clr3(MAXCYCLES, 0, 0, 0);
const int * pMax = array + width * height;
while(array < pMax){
float clr = *array++;
bool draw =
lerp(clr, clr0, clr1, map) ||
lerp(clr, clr1, clr2, map) ||
lerp(clr, clr2, clr3, map);
}
}
/**
* Function to linearly interpolate color values and draw to the Bitmap
*/
bool lerp(float clr, Pix& first, Pix& second, Bitmap & map){
if(clr <= second.val){
float diff = (clr - first.val) / (second.val - first.val);
map << first.b + diff * (second.b - first.b);
map << first.g + diff * (second.g - first.g);
map << first.r + diff * (second.r - first.r);
return true;
}
return false;
}
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