plane.h

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#pragma once
#include "vde/core/point.h"
 
namespace vde::core {
 
template <typename T>
class Plane {
public:
    Plane() = default;
 
    Plane(const Point3D& point, const Vector3D& normal)
        : normal_(normal.normalized()), d_(-normal_.dot(point)) {}
 
    Plane(const Point3D& a, const Point3D& b, const Point3D& c)
        : Plane(a, (b - a).cross(c - a)) {}
 
    [[nodiscard]] const Vector3D& normal() const { return normal_; }
 
    [[nodiscard]] T d() const { return d_; }
 
    [[nodiscard]] T signed_distance(const Point3D& p) const { return normal_.dot(p) + d_; }
 
    [[nodiscard]] T distance(const Point3D& p) const { return std::abs(signed_distance(p)); }
 
    [[nodiscard]] Point3D project(const Point3D& p) const {
        return p - normal_ * signed_distance(p);
    }
 
private:
    Vector3D normal_{0,0,1};
    T d_{0};
};
 
using Plane3D = Plane<double>;
 
}  // namespace vde::core