triangle.h

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#pragma once
#include "vde/core/point.h"
#include <array>
 
namespace vde::core {
 
template <typename T>
class Triangle {
public:
    Triangle() = default;
 
    Triangle(const Point3D& v0, const Point3D& v1, const Point3D& v2)
        : v_{v0, v1, v2} {}
 
    [[nodiscard]] const Point3D& v(int i) const { return v_[i]; }
 
    [[nodiscard]] const std::array<Point3D, 3>& vertices() const { return v_; }
 
    [[nodiscard]] Vector3D normal() const {
        return (v_[1] - v_[0]).cross(v_[2] - v_[0]).normalized();
    }
 
    [[nodiscard]] T area() const {
        return (v_[1] - v_[0]).cross(v_[2] - v_[0]).norm() * 0.5;
    }
 
    [[nodiscard]] Point3D centroid() const {
        return (v_[0] + v_[1] + v_[2]) / 3.0;
    }
 
    [[nodiscard]] bool contains(const Point3D& p) const {
        Vector3D v0 = v_[2] - v_[0], v1 = v_[1] - v_[0], v2 = p - v_[0];
        T d00 = v0.dot(v0), d01 = v0.dot(v1), d11 = v1.dot(v1);
        T d20 = v2.dot(v0), d21 = v2.dot(v1);
        T denom = d00 * d11 - d01 * d01;
        T v = (d11 * d20 - d01 * d21) / denom;
        T w = (d00 * d21 - d01 * d20) / denom;
        return v >= 0 && w >= 0 && v + w <= 1;
    }
 
private:
    std::array<Point3D, 3> v_{};
};
 
using Triangle3D = Triangle<double>;
using Triangle3f = Triangle<float>;
 
}  // namespace vde::core