原理

思路：
面积和：
abc == obc+aoc+abo,应该有更简洁的方法，但是这个方法思路更简单

代码实现:

注意二维向量的叉乘后，是垂直于平面的向量，相当于z为0三维向量叉乘，所以只有z维度有值，xy=0.
float值不要直接==，考虑作差或者用库函数。

#include <string>
#include <math.h>

using namespace std;

struct Vec {
    float x_;
    float y_;

    Vec() {}

    float dot(const Vec &other) {
        return sqrt(x_ * x_ + y_ * y_);
    }

    float cross_norm(const Vec &other) {
        // Vec3d {y0*z1-z0-y1, -(x0*z1-z0*x1), x0*y1-x1*y0}
        float Vec3d_z = x_ * other.y_ - y_ * other.x_;
        return fabs(Vec3d_z);
    }
};

struct Point {
    float x_;
    float y_;

    Point() {}

    Point(const float &x, const float &y) : x_(x), y_(y) {}

    Vec operator-(const Point &other) const {
        Vec res;
        res.x_ = x_ - other.x_;
        res.y_ = y_ - other.y_;
        return res;
    }
};

struct Triangle {
    Point A_;
    Point B_;
    Point C_;

    Triangle(const Point &A, const Point &B, const Point &C) : A_(A), B_(B), C_(C) {}

    float get_area() const {
        Vec a = A_ - B_;
        Vec b = A_ - C_;
        return a.cross_norm(b) / 2;
    }
};

float get_area(const Triangle &tmp) {
    return tmp.get_area();
}


int main() {
    Point A(0.0, 0.0);
    Point B(1.0, 2.0);
    Point C(2.0, 1.0);
    Point O(1.5, 1.49);

    float area_ABC = get_area(Triangle(A, B, C));
    float area_OBC = get_area(Triangle(O, B, C));
    float area_AOC = get_area(Triangle(A, O, C));
    float area_ABO = get_area(Triangle(A, B, O));

    bool in_tri = fabs(area_ABC - (area_OBC + area_AOC + area_ABO)) < 0.0001; // notify : cannot float A == float B

    if (in_tri)
        printf("Point in Triangle");
    else
        printf("Point Not in Triangle");

    return 0;
}