发几幅由计算机生成的图像,以展示算法之美.并提供生成图像的算法代码.代码中,一部分是由C++实现,另一部分是由一种我定义的脚本语言实现.
相关软件见:Why数学图像生成工具.
(1)树
1 void CPixelIFSTree::BuildPixelsMap()
2 {
3 float m[5][7];
4
5 //‘IFS码赋值
6 m[0][0] = 0.195f; m[0][1] =-0.488f; m[0][2] = 0.344f; m[0][3] = 0.433f; m[0][4] = 0.4431f; m[0][5] = 0.2452f; m[0][6] = 0.25f;
7 m[1][0] = 0.462f; m[1][1] = 0.414f; m[1][2] =-0.252f; m[1][3] = 0.361f; m[1][4] = 0.2511f; m[1][5] = 0.5692f; m[1][6] = 0.25f;
8 m[2][0] =-0.058f; m[2][1] =-0.07f; m[2][2] = 0.453f; m[2][3] =-0.111f; m[2][4] = 0.5976f; m[2][5] = 0.0969f; m[2][6] = 0.25f;
9 m[3][0] =-0.035f; m[3][1] = 0.07f; m[3][2] =-0.469f; m[3][3] =-0.022f; m[3][4] = 0.4884f; m[3][5] = 0.5069f; m[3][6] = 0.2f;
10 m[4][0] =-0.637f; m[4][1] = 0.0f; m[4][2] = 0.0f; m[4][3] = 0.501f; m[4][4] = 0.8562f; m[4][5] = 0.2513f; m[4][6] = 0.05f;
11
12 float a, b, c, d, e, f; //‘仿射变幻中的系数
13
14 float x = 0.0f;
15 float y = 0.0f;
16 float t;
17
18 for (int i = 0; i < 100000000; i++)
19 {
20 float R = (float)rand()/RAND_MAX;
21
22 if (R <= m[0][6])
23 {
24 a = m[0][0]; b = m[0][1]; c = m[0][2]; d = m[0][3]; e = m[0][4]; f = m[0][5];
25 }
26 else if (R <= m[0][6] + m[1][6])
27 {
28 a = m[1][0]; b = m[1][1]; c = m[1][2]; d = m[1][3]; e = m[1][4]; f = m[1][5];
29 }
30 else if (R <= m[0][6] + m[1][6] + m[2][6])
31 {
32 a = m[2][0]; b = m[2][1]; c = m[2][2]; d = m[2][3]; e = m[2][4]; f = m[2][5];
33 }
34 else if (R <= m[0][6] + m[1][6] + m[2][6] + m[3][6])
35 {
36 a = m[3][0]; b = m[3][1]; c = m[3][2]; d = m[3][3]; e = m[3][4]; f = m[3][5];
37 }
38 else
39 {
40 a = m[4][0]; b = m[4][1]; c = m[4][2]; d = m[4][3]; e = m[4][4]; f = m[4][5];
41 }
42
43 t = a*x + b*y + e;
44 y = c*x + d*y + f;
45 x = t;
46
47 int ix = ((int)(x*1024.0f))&0x3ff;
48 int iy = 1024 - ((int)(y*1024.0f))&0x3ff;
49 m_pixels_map[iy][ix]+=1;
50 }
51
52 if (!m_pixels_map[0][0])
53 {
54 m_pixels_map[0][0] = 1;
55 }
56 }
57
58 unsigned int CPixelIFSTree::CalculatePixel(unsigned int x, unsigned int y)
59 {
60 if (!m_pixels_map[0][0])
61 {
62 BuildPixelsMap();
63 }
64
65 float fr = logf((float)m_pixels_map[y][x])*32.0f;
66 unsigned int r = FLOAT_255_TO_BYTE(fr);
67 float fg = logf((float)m_pixels_map[y][x]*1.2f)*56.0f;
68 unsigned int g = FLOAT_255_TO_BYTE(fg);
69
70 unsigned b = m_pixels_map[y][x] & 0xff;
71
72 return MAKE_RGB(r,g,b);
73 }
(2)晕
这是由Sin函数生成的图像,让人看着眼花
pixels = W:1024 H:1024 x = from (-8*PI) to (8*PI) W y = from (-8*PI) to (8*PI) H r = sin(x+y) g = sin(x-y) b = sin(x*y) r = r*0.5 + 0.5 g = g*0.5 + 0.5 b = b*0.5 + 0.5
(3)格
这是由Tan函数生成的图像,密集恐惧症者可以拿它来练胆.
pixels = W:1024 H:1024 x = from 0 to 1023 W y = from 0 to 1023 H r = tan(x*y) g = r*0.5 b = r*0.2
(4)JuliaSets
1 unsigned int CPixelJuliaSets3::CalculatePixel(unsigned int x, unsigned int y)
2 {
3 int K=100;
4 int m=500;
5 float xs = -1.5f;
6 float xl = 1.5f;
7 float ys = -1.5f;
8 float yl = 1.5f;
9 float p = 0.32f;
10 float q = 0.043f;
11 float xb = (xl - xs) / m_width;
12 float yb = (yl - ys) / m_height;
13
14 float x0=xs+x*xb;
15 float y0=ys+y*yb;
16 int k=0;
17 int H;
18 loop1:
19 float xk=x0*x0-y0*y0+p;
20 float yk=2*x0*y0+q;
21 k=k+1;
22 float r=xk*xk+yk*yk;
23 x0=xk;
24 y0=yk;
25 if(r>m)
26 {
27 H=k;
28 goto loop2;
29 }
30 if(k==K)
31 {
32 H=int(r*10);
33 goto loop2;
34 }
35 if(r<=m && k<K)
36 {
37 goto loop1;
38 }
39 loop2:
40
41 float fr = logf((float)H)*256.0f;
42 unsigned int br = (unsigned char)fr;
43
44 float fg = logf((float)H)*128.0f;
45 unsigned int bg = (unsigned char)fg;
46
47 unsigned int bb = (H*100)&0xff;
48
49 return MAKE_RGB(br,bg,bb);
50 }
(5)Mandlbrot
1 unsigned int CPixelMandlbrot1::CalculatePixel(unsigned int x, unsigned int y)
2 {
3 int K=100;
4 int m=500;
5 float pl=0.9f;
6 float ps=-2.3f;
7 float ql=1.2f;
8 float qs=-1.2f;
9
10 float p=(pl-ps)/m_width;
11 float q=(ql-qs)/m_height;
12
13 float p0=ps+x*p;
14 float q0=qs+y*q;
15 int k=0;
16 float x0=0.0f;
17 float y0=0.0f;
18 int H;
19
20 float xk;
21 float yk;
22 float r;
23
24 loop1:
25 xk=x0*x0-y0*y0+p0;
26 yk=2*x0*y0+q0;
27 k=k+1;
28 r=xk*xk+yk*yk;
29 x0=xk;
30 y0=yk;
31 if(r>m)
32 {
33 H=k;
34 goto loop2;
35 }
36 if(k==K)
37 {
38 H=int(r*1);
39 goto loop2;
40 }
41 if(r<=m && k<K)
42 {
43 goto loop1;
44 }
45
46 loop2:
47 float fr = logf((float)H)*256.0f;
48 unsigned int br = (unsigned char)fr;
49
50 float fg = logf((float)H)*128.0f;
51 unsigned int bg = (unsigned char)fg;
52
53 unsigned int bb = (H*100)&0xff;
54
55 return MAKE_RGB(br,bg,bb);
56 }
(6)棋盘
pixels = W:1024 H:1024 u = from 0 to 16 W v = from 0 to 16 H m = floor(u%2) n = floor(v%2) r = if(xor_bool(m,n), 0.0, 1.0) g = r b = r
时间： 2024-08-27 21:06:12