1.方程

(1)心形線的經典隱函數方程為：

(2)參數方程（更平滑的心形）：

(3)極坐標心形線

(4)參數方程（3D心形）

(5)隱函數3D心形

2.?MATLAB代碼

clc;close all;clear all;warning off;%清除變量
rand('seed', 100);
randn('seed', 100);%% 繪制各種心形曲線% (1)隱函數繪制心形線
figure;
fimplicit(@(x,y) (x.^2 + y.^2 - 1).^3 - x.^2 .* y.^3, ...[-1.5, 1.5, -1, 1.5], 'LineWidth', 2, 'Color', 'r');
axis equal;
title('2D Heart Curve (Implicit Equation)');
grid on;% (2)參數方程繪制心形
t = linspace(0, 2*pi, 1000);
x = 16 * sin(t).^3;
y = 13 * cos(t) - 5 * cos(2*t) - 2 * cos(3*t) - cos(4*t);figure;
fill(x, y, 'r', 'EdgeColor', 'none');  % 填充紅色
axis equal; 
title('Parametric Heart Curve');%  (3)極坐標心形線
theta = linspace(0, 2*pi, 1000);
r = 1 - cos(theta);figure;
polarplot(theta, r, 'r', 'LineWidth', 2);
title('Polar Heart (Cardioid)');% (4)3D蘋果曲面
[u, v] = meshgrid(linspace(0, 2*pi, 50), linspace(0, 2*pi, 50));
x = (1 - cos(u)) .* sin(u) .* cos(v);
y = (1 - cos(u)) .* sin(u) .* sin(v);
z = (1 - cos(u)) .* cos(u);figure;
surf(x, y, z, 'FaceColor', 'r', 'EdgeColor', 'none');
axis equal; view(3); 
title('3D Heart Surface');
light; lighting gouraud;  % 添加光照效果% (5)隱函數繪制3D心形
figure;
fimplicit3(@(x,y,z) (2*x.^2 + y.^2 + z.^2 - 1).^3 - 0.1*x.^2.*z.^3 - y.^2.*z.^3, ...[-1.5, 1.5, -1.5, 1.5, -1, 1], 'FaceColor', 'r', 'EdgeColor', 'none');
axis equal; view(3);
title('3D Implicit Heart');

3.程序結果