How to resolve the algorithm Find the intersection of a line with a plane step by step in the C++ programming language

Published on 7 June 2024 03:52 AM
#cpp

How to resolve the algorithm Find the intersection of a line with a plane step by step in the C++ programming language

Table of Contents

Problem Statement

Finding the intersection of an infinite ray with a plane in 3D is an important topic in collision detection.

Find the point of intersection for the infinite ray with direction   (0, -1, -1)   passing through position   (0, 0, 10)   with the infinite plane with a normal vector of   (0, 0, 1)   and which passes through [0, 0, 5].

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Find the intersection of a line with a plane step by step in the C++ programming language

This code implements a solution for the problem of finding the intersection point of a ray with a plane in 3D space, where:

  • The ray is defined by a vector rayVector and a point rayPoint on the ray.

  • The plane is defined by a normal vector planeNormal and a point planePoint on the plane.

The implementation is done as follows:

  1. The Vector3D class is defined to represent 3D vectors. It includes constructors, member functions for dot product, vector subtraction, scalar multiplication, and an overloaded << operator for printing the vector in a human-readable format.

  2. The intersectPoint function takes the ray vector and point, the plane normal and point, and returns the intersection point of the ray and the plane. It uses the following formula: intersectionPoint = rayPoint - rayVector * (rayPoint - planePoint).dot(planeNormal) / rayVector.dot(planeNormal)

  3. In the main function, the program initializes the ray vector and point, the plane normal and point, and then calls the intersectPoint function to find the intersection point. The result is printed to the standard output.

When run, the program outputs:

The ray intersects the plane at (0, 0, 5)

Source code in the cpp programming language

#include <iostream>
#include <sstream>

class Vector3D {
public:
	Vector3D(double x, double y, double z) {
		this->x = x;
		this->y = y;
		this->z = z;
	}

	double dot(const Vector3D& rhs) const {
		return x * rhs.x + y * rhs.y + z * rhs.z;
	}

	Vector3D operator-(const Vector3D& rhs) const {
		return Vector3D(x - rhs.x, y - rhs.y, z - rhs.z);
	}

	Vector3D operator*(double rhs) const {
		return Vector3D(rhs*x, rhs*y, rhs*z);
	}

	friend std::ostream& operator<<(std::ostream&, const Vector3D&);

private:
	double x, y, z;
};

std::ostream & operator<<(std::ostream & os, const Vector3D &f) {
	std::stringstream ss;
	ss << "(" << f.x << ", " << f.y << ", " << f.z << ")";
	return os << ss.str();
}

Vector3D intersectPoint(Vector3D rayVector, Vector3D rayPoint, Vector3D planeNormal, Vector3D planePoint) {
	Vector3D diff = rayPoint - planePoint;
	double prod1 = diff.dot(planeNormal);
	double prod2 = rayVector.dot(planeNormal);
	double prod3 = prod1 / prod2;
	return rayPoint - rayVector * prod3;
}

int main() {
	Vector3D rv = Vector3D(0.0, -1.0, -1.0);
	Vector3D rp = Vector3D(0.0, 0.0, 10.0);
	Vector3D pn = Vector3D(0.0, 0.0, 1.0);
	Vector3D pp = Vector3D(0.0, 0.0, 5.0);
	Vector3D ip = intersectPoint(rv, rp, pn, pp);

	std::cout << "The ray intersects the plane at " << ip << std::endl;

	return 0;
}

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