如何用 C 語言畫小豬佩奇

來自專欄 Milo的編程

我們曾在《用 C 語言畫光（一）：基礎》中，使用到帶符號距離場（signed distance field, SDF）表示圓形：

沿用這個方法表示形狀，但這次我們想利用 ASCII 字元|/=畫出形狀的外框，並填充內部，類似這樣：

===== //.....\||.......|| \.....// =====

SDF 的梯度（gradient）代表 SDF 變化最大的方向，可用這個方向去決定用哪一個字元。

我們通過差分求 SDF 的梯度近似值，然後用 atan2() 求出梯度的角度：

用 C 語言簡單實現，在 畫布中畫一個半徑 0.8 並帶有 0.1 寛度外框的圓形：

#include <math.h>#include <stdio.h>#define T doubleT f(T x, T y) { return sqrt(x * x + y * y) - 0.8f;}char outline(T x, T y) { T delta = 0.001; if (fabs(f(x, y)) < 0.05) { T dx = f(x + delta, y) - f(x - delta, y); T dy = f(x, y + delta) - f(x, y - delta); return "|/=\|/=\|"[(int)((atan2(dy, dx) / 6.2831853072 + 0.5) * 8 + 0.5)]; } else if (f(x, y) < 0) return .; else return ;}int main() { for (T y = -1; y < 1; y += 0.05, putchar(
)) for (T x = -1; x < 1; x += 0.025) putchar(outline(x, y));}

然後，我們就可以畫多個圓形，把它們適當地旋轉和縮放，用構造實體幾何比它們組合起來，那麼用19行代碼就可以畫出小豬佩奇了：

// ASCII Peppa Pig by Milo Yip#include <math.h>#include <stdio.h>#include <stdlib.h>#define T doubleT c(T x,T y,T r){return sqrt(x*x+y*y)-r;}T u(T x,T y,T t){return x*cos(t)+y*sin(t);}T v(T x,T y,T t){return y*cos(t)-x*sin(t);}T fa(T x,T y){return fmin(c(x,y,0.5),c(x*0.47+0.15,y+0.25,0.3));}T no(T x,T y){return c(x*1.2+0.97,y+0.25,0.2);}T nh(T x,T y){return fmin(c(x+0.9,y+0.25,0.03),c(x+0.75,y+0.25,0.03));}T ea(T x,T y){return fmin(c(x*1.7+0.3,y+0.7,0.15),c(u(x,y,0.25)*1.7,v(x,y,0.25)+0.65,0.15));}T ey(T x,T y){return fmin(c(x+0.4,y+0.35,0.1),c(x+0.15,y+0.35,0.1));}T pu(T x,T y){return fmin(c(x+0.38,y+0.33,0.03),c(x+0.13,y+0.33,0.03));}T fr(T x,T y){return c(x*1.1-0.3,y+0.1,0.15);}T mo(T x,T y){return fmax(c(x+0.15,y-0.05,0.2),-c(x+0.15,y,0.25));}T o(T x,T y,T(*f)(T,T),T i){T r=f(x,y);return fabs(r)<0.02?(atan2(f(x,y+1e-3)-r,f(x+1e-3,y)-r)+0.3)*1.273+6.5:r<0?i:0;}T s(T x,T y,T(*f)(T,T),T i){return f(x,y)<0?i:0;}T f(T x,T y){return o(x,y,no,1)?fmax(o(x,y,no,1),s(x,y,nh,12)):fmax(o(x,y,fa,1),fmax(o(x,y,ey,11),fmax(o(x,y,ea,1),fmax(o(x,y,mo,1),fmax(s(x,y,fr,13),s(x,y,pu,12))))));}int main(int a,char**b){for(T y=-1,s=a>1?strtod(b[1],0):1;y<0.6;y+=0.05/s,putchar(
))for(T x=-1;x<0.6;x+=0.025/s)putchar(" .|/=\|/=\| @!"[(int)f(u(x,y,0.3),v(x,y,0.3))]);}

2倍：

4 倍：

8 倍：

今天也是精緻的豬豬女孩～

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