C语言基于海伦公式半角正切实现三角形坐标计算面积周长及角度

问题分析与修复方案 #

核心错误梳理 #

1. 公式参数混用：海伦半角正切公式要求输入半周长s，你的注释和代码中错误替换为了面积P，这是计算结果异常的核心原因。
2. 定义域越界风险来源：
   • 输入三点共线时，面积为0，且半周长减边长的结果为0，会出现除以0、根号入参为0/负数的问题
   • 浮点计算误差可能导致半周长减边长的结果出现极小负数，触发sqrt函数非法入参报错

修复要点 #

• 半角正切公式的参数换回半周长s
• 新增三点共线校验：面积小于1e-6（浮点误差阈值）时直接提示无法构成三角形，终止计算
• 根号内的运算结果加钳位逻辑，所有可能出现负数/0的参数都限制为不小于1e-12，避免非法运算

修正后代码 #

#include <stdio.h>
#include <math.h>

#define PI  (4. * atan(1))
#define EPS 1e-12
#define TRIANGLE_EPS 1e-6

int main() {
    float xa, ya, xb, yb, xc, yc, s, area, a, b, c, x, y, z, alphadeg, alpharad, betadeg, betarad, gammadeg, gammarad;

    printf("Insert the first point's coordinates (a space should be between the X and Y coordinate):\n"); 
    scanf("%f %f", &xa, &ya);
    
    printf("Insert the second point's coordinates (a space should be between the X and Y coordinate):\n");
    scanf("%f %f", &xb, &yb);
    
    printf("Insert the third point's coordinates (a space should be between the X and Y coordinate):\n");
    scanf("%f %f", &xc, &yc);
    
    // 计算三边长度
    a = sqrt(pow(xa - xb, 2) + pow(ya - yb, 2));
    b = sqrt(pow(xa - xc, 2) + pow(ya - yc, 2));
    c = sqrt(pow(xb - xc, 2) + pow(yb - yc, 2));

    printf("Distance between point 1 and 2: %f\n", a);
    printf("Distance between point 1 and 3: %f\n", b);
    printf("Distance between point 2 and 3: %f\n", c);
    
    // 半周长
    s = (a + b + c) / 2;
    // 面积
    area = sqrt(s * fmax(s - a, EPS) * fmax(s - b, EPS) * fmax(s - c, EPS));

    // 校验是否能构成三角形
    if (area < TRIANGLE_EPS) {
        printf("Input points are collinear, cannot form a triangle\n");
        return 0;
    }

    printf("The area of your triangle is %f\n", area);
    printf("The perimeter of your triangle is %f\n", a + b + c);
 
    // 半角正切计算，参数使用半周长s，加钳位避免非法入参
    x = sqrt((fmax(s - b, EPS) * fmax(s - c, EPS)) / (s * fmax(s - a, EPS)));
    y = sqrt((fmax(s - a, EPS) * fmax(s - c, EPS)) / (s * fmax(s - b, EPS)));
    z = sqrt((fmax(s - a, EPS) * fmax(s - b, EPS)) / (s * fmax(s - c, EPS)));

    alpharad = 2 * atan(x);
    betarad = 2 * atan(y);
    gammarad = 2 * atan(z);

    alphadeg = alpharad * 180.0 / PI;
    betadeg = betarad * 180.0 / PI;
    gammadeg = gammarad * 180.0 / PI;

    printf("The value of the alpha angle is %0.3f degrees\n", alphadeg);
    printf("The value of the beta angle is %0.3f degrees\n", betadeg);
    printf("The value of the gamma angle is %0.3f degrees\n", gammadeg);

    printf("Sum of angles in radians: %f = %f\n", PI, alpharad + betarad + gammarad);
    
    return 0;
}

关键修改说明 #

1. 将面积变量名从P改为area，避免和半周长混淆，半角公式全部使用半周长s计算，符合数学定义
2. 用fmax函数对所有参与根号、除法运算的参数做钳位，保证不会出现负数和除以0的问题，彻底解决定义域越界
3. 新增三点共线校验，提前拦截非法输入
4. 优化了角度转换逻辑，复用弧度计算结果转换为角度，可读性更高

内容的提问来源于stack exchange，提问作者Dylikk