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| // https://www.arndt-bruenner.de/mathe/10/parabeltangente.htm#:~:text=Somit%20ergibt%20sich%20f%C3%BCr%20die%20Tangente%20an%20die,jeden%20Punkt%20x%20durch%202ax%20%2B%20b%20gegeben.
#include <iostream>
#include <string>
#include <vector>
#include <iterator>
#include <initializer_list>
class Point
{
private:
float mX, mY;
public:
Point() :
mX{ 0 },
mY{ 0 }
{}
Point(float x, float y) :
mX{ x },
mY{ y }
{}
Point(Point const& p) :
mX{ p.mX },
mY{ p.mY }
{}
Point& operator=(Point const& rhs) {
mX = rhs.mX;
mY = rhs.mY;
return *this;
}
float x() const
{
return mX;
}
float y() const
{
return mY;
}
void set_x(float xx)
{
mX = xx;
}
void set_y(float yy)
{
mY = yy;
}
friend std::ostream&
operator<<(std::ostream& os, Point const& p) {
return os << "x = " << p.mX << " y = " << p.mY;
}
};
class Kurve : public Point {
public:
std::vector<Point> kur;
public:
Kurve(std::initializer_list<Point> liste) : kur{ liste } {}
Kurve(Point p) {
kur.push_back(p);
}
std::vector<Point>& get_kur() {
return kur;
}
};
class Segment
{
private:
Point mA, mB;
public:
Segment(Point A, Point B) :
mA{ A }, mB{ B }
{}
float A() const // Coefficient A: y = Ax + B
{
return (mA.y() - mB.y()) / (mA.x() - mB.x());
// source: https://calculis.net/droite
// A completer
}
float B() const // Coefficient B: y = Ax + B
{
return mA.y() - A() * mA.x();
// source: https://calculis.net/droite
// A completer
}
Point intersection(Segment const& other)
{
float x = (other.B() - B()) / (A() - other.A());
// source: https://calculis.net/intersection
// A completer
// A completer
return Point{ x , A() * x + B() };
}
std::string equation() const
{
return "y = " + std::to_string(A()) + "x + " + std::to_string(B());
}
};
int main() {
Point poiA(0, 0);
Point poiB(2, pow(2, 2));
Kurve parabole({ 0,0 });
for (float i = 0; i < 100; i++)
parabole.kur.push_back({ i * 0.1f,pow(i * 0.1f,2.0f) });
float xQ, yQ;
std::cout << "Veuillez calculer le point à partir duquel la tangente est calculée sur la parabole: " << std::endl;
std::cout << "S’il vous plaît x: ";
std::cin >> xQ;
std::cout << std::endl;
std::cout << "S’il vous plaît y: ";
std::cin >> yQ;
std::cout << std::endl;
Kurve parabole_Bsp_1({ 0.0f,0.0f });
for (float i = -30.0f; i < 100; i++) {
parabole_Bsp_1.kur.push_back({ i * 0.1f, -3 * pow(i * 0.1f,2.0f) + 2*i*0.1f + 1 });
}
// Calculer la tangente , Point Q connu Q(-1,-1), La tangente a une forme y = Ax + B , Parabole f(x) = -3x^2 + 2x +1
// Point de contact T(xT,yT) , yT = A*xT + B, A est tangente de l’angle de la tangente A = f'(x) = -6x + 2
// Parabel yT = -3xT^2 + 2xT +1 ; Tangente yT = (-6xT +2) xT + B
// https://www.youtube.com/watch?v=ql_w5paclOs
// f(x)Tangente = f(x)Parabel
// -3x^2 +2x + 1 = AxO + B = (-6x + 2) * xQ + B
// -3 * x^2 + 2 * x * xQ + 1 = -6 * x^2 + 2x + B
// 3 * x^2 - 6 * xQ * x + 2 * xQ - yQ + 1 = 0
float a = 3;
float b = -6 * xQ;
float c = 2 * xQ - yQ + 1;
float xT1 = ((-1) * b + std::sqrt(pow(b, 2.0f) - 4 * a * c)) / (2 * a);
float xT2 = ((-1) * b - std::sqrt(pow(b, 2.0f) - 4 * a * c)) / (2 * a);
float A1 = -6.0f * xT1 + 2;
float A2 = -6.0f * xT2 + 2;
float B1 = yQ - A1 * xQ;
float B2 = yQ - A2 * xQ;
float yT1 = A1 * xT1 + B1;
float yT2 = A2 * xT2 + B2;
Point Q(xQ, yQ);
Point T1(xT1, yT1);
Point T2(xT2, yT2);
Segment tangente1(Q, T1);
std::cout << tangente1.equation() << std::endl;
Segment tangente2(Q, T2);
std::cout << tangente2.equation() << std::endl;
std::cout << "Le point de contact de la tangente1 et de la parabole est "
<< "T1(" << xT1 << ", " << yT1 << ")" << std::endl;
std::cout << "Le point de contact de la tangente1 et de la parabole est "
<< "T2(" << xT2 << ", " << yT2 << ")" << std::endl;
auto it = parabole_Bsp_1.kur.begin();
while (it != parabole_Bsp_1.kur.end()) {
std::cout << "parabole(x, y) " << *it++ << std::endl;
}
std::cout << "Hiperbole " << std::endl;
Kurve hiperbole({ 0,0 });
for (float i = 0; i < 100; i++)
hiperbole.kur.push_back({ i * 0.1f,pow(i * 0.1f,.5f) });
auto it_h = hiperbole.kur.begin();
while (it_h != hiperbole.kur.end()) {
std::cout << *it_h++ << std::endl;
}
Point pA(3.5f, 4.0f);
Point pB(-4.0f, 2.0f);
Point pC(2.0f, -2.0f);
Point pD(-2.0f, 5.0f);
std::cout << "Point d'intersection des deux lignes droites: " << std::endl;
Segment Line1(pA, pB);
std::cout << Line1.equation() << std::endl;
Segment Line2(pC, pD);
std::cout << Line2.equation() << std::endl;
std::cout << Line1.intersection(Line2); // Point d'intersection des deux lignes droites |
