本文转自知乎：/question/7195 Milo Yip大神的回答
#include <stdio.h>int main() {for (float y = 1.5f; y > -1.5f; y -= 0.1f) {for (float x = -1.5f; x < 1.5f; x += 0.05f) {float a = x * x + y * y - 1;putchar(a * a * a - x * x * y * y * y <= 0.0f ? '*' : ' ');}putchar('\n');}}
再来个有花纹的。（这其实是该函数的Level set）
#include <stdio.h>int main() {for (float y = 1.5f; y > -1.5f; y -= 0.1f) {for (float x = -1.5f; x < 1.5f; x += 0.05f) {float z = x * x + y * y - 1;float f = z * z * z - x * x * y * y * y;putchar(f <= 0.0f ? ".:-=+*#%@"[(int)(f * -8.0f)] : ' ');}putchar('\n');}}
简单使用迭代法求解，用Finite difference求法矢量，用wrapped diffuse着色。
#include <stdio.h>#include <math.h>float f(float x, float y, float z) {float a = x * x + 9.0f / 4.0f * y * y + z * z - 1;return a * a * a - x * x * z * z * z - 9.0f / 80.0f * y * y * z * z * z;}float h(float x, float z) {for (float y = 1.0f; y >= 0.0f; y -= 0.001f)if (f(x, y, z) <= 0.0f)return y;return 0.0f;}int main() {for (float z = 1.5f; z > -1.5f; z -= 0.05f) {for (float x = -1.5f; x < 1.5f; x += 0.025f) {float v = f(x, 0.0f, z);if (v <= 0.0f) {float y0 = h(x, z);float ny = 0.01f;float nx = h(x + ny, z) - y0;float nz = h(x, z + ny) - y0;float nd = 1.0f / sqrtf(nx * nx + ny * ny + nz * nz);float d = (nx + ny - nz) * nd * 0.5f + 0.5f;putchar(".:-=+*#%@"[(int)(d * 5.0f)]);}elseputchar(' ');}putchar('\n');}}
「3D」版，简单使用迭代法求解，用Finite difference求法矢量，用wrapped diffuse着色。
#include <stdio.h>#include <math.h>float f(float x, float y, float z) {float a = x * x + 9.0f / 4.0f * y * y + z * z - 1;return a * a * a - x * x * z * z * z - 9.0f / 80.0f * y * y * z * z * z;}float h(float x, float z) {for (float y = 1.0f; y >= 0.0f; y -= 0.001f)if (f(x, y, z) <= 0.0f)return y;return 0.0f;}int main() {for (float z = 1.5f; z > -1.5f; z -= 0.05f) {for (float x = -1.5f; x < 1.5f; x += 0.025f) {float v = f(x, 0.0f, z);if (v <= 0.0f) {float y0 = h(x, z);float ny = 0.01f;float nx = h(x + ny, z) - y0;float nz = h(x, z + ny) - y0;float nd = 1.0f / sqrtf(nx * nx + ny * ny + nz * nz);float d = (nx + ny - nz) * nd * 0.5f + 0.5f;putchar(".:-=+*#%@"[(int)(d * 5.0f)]);}elseputchar(' ');}putchar('\n');}}
把「3D版」输出至PPM文件，可以用Photoshop打开。另外降低了ny的值导致有超有趣的pattern，就保留下来吧。
#ifdef _MSC_VER#define _CRT_SECURE_NO_WARNINGS#endif#include <stdio.h>#include <math.h>float f(float x, float y, float z) {float a = x * x + 9.0f / 4.0f * y * y + z * z - 1;return a * a * a - x * x * z * z * z - 9.0f / 80.0f * y * y * z * z * z;}float h(float x, float z) {for (float y = 1.0f; y >= 0.0f; y -= 0.001f)if (f(x, y, z) <= 0.0f)return y;return 0.0f;}int main() {FILE* fp = fopen("heart.ppm", "w");int sw = 512, sh = 512;fprintf(fp, "P3\n%d %d\n255\n", sw, sh);for (int sy = 0; sy < sh; sy++) {float z = 1.5f - sy * 3.0f / sh;for (int sx = 0; sx < sw; sx++) {float x = sx * 3.0f / sw - 1.5f;float v = f(x, 0.0f, z);int r = 0;if (v <= 0.0f) {float y0 = h(x, z);float ny = 0.001f;float nx = h(x + ny, z) - y0;float nz = h(x, z + ny) - y0;float nd = 1.0f / sqrtf(nx * nx + ny * ny + nz * nz);float d = (nx + ny - nz) / sqrtf(3) * nd * 0.5f + 0.5f;r = (int)(d * 255.0f);}fprintf(fp, "%d 0 0 ", r);}fputc('\n', fp);}fclose(fp);}原文出处：/question/7195
