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Points and Lines

Line get_line (const Point& p) const function
Returns the Line l corresponding to the line from *this to p. l.position will be *this, and l.direction will be p - *this. See Line Reference.

real slope (Point p, [char m = 'x', [char n = 'y']]) const function
Returns a real number representing the slope of the trace of the line defined by *this and p on the plane indicated by the arguments m and n. 
          Point p0(3, 4, 5);
          Point p1(2, 7, 12);
          real r = p0.slope(p1, 'x', 'y');
          => r == -3
          r = p0.slope(p1, 'x', 'z');
          => r == -7
          r = p0.slope(p1, 'z', 'y');
          => r == 0.428571

bool_real is_on_segment (Point p0, Point p1) Function
bool_real is_on_segment (const Point& p0, const Point& p1) const function
These functions return a bool_real, where the bool part is true, if the Point lies on the line segment between p0 and p1, otherwise false. If the Point lies on the line segment, the real part is a value r such that 0 <= r <= 1 indicating how far the Point is along the way from p0 to p1. For example, if the Point is half of the way from p0 to p1, r will be .5. If the Point does not lie on the line segment, but on the line passing through p0 and p1, r will be <0 or >1.

If the Point doesn't lie on the line passing through p0 and p1, r will be INVALID_REAL. 

          Point p0(-1, -2, 1);
          Point p1(3, 2, 5);
          Point p2(p0.mediate(p1, .75));
          Point p3(p0.mediate(p1, 1.5));
          Point p4(p2);
          p4.shift(-2, 1, -1);
          bool_real br = p2.is_on_segment(p0, p1);
          cout << br.first;
          -| 1
          cout << br.second;
          -| 0.75
          bool_real br = p3.is_on_segment(p0, p1);
          cout << br.first;
          -| 0
          cout << br.second;
          -| 1.5
          bool_real br = p4.is_on_segment(p0, p1);
          cout << br.first;
          -| 0
          cout << br.second;
          -| 3.40282e+38
          cout << (br.second == INVALID_REAL)
          -| 1


[Figure 91. Not displayed.]

Fig. 91.

bool_real is_on_line (const Point& p0, const Point& p1) const function
Returns a bool_real where the bool part is true, if the Point lies on the line passing through p0 and p1, otherwise false. If the Point lies on the line, the real part is a value r indicating how how far the Point is along the way from p0 to p1, otherwise INVALID_REAL. The following values of r are possible for a call to P.is_on_line(A, B), where the Point P lies on the line AB: 
          P == A ---> r== 0.
          
          P == B ---> r== 1.
          
          P lies on the opposite side of A from B ---> r < 0.
          
          P lies between A and B ---> 0 <  r < 1.
          
          P lies on the opposite side of A from B ---> r > 1
          
          Point A(-1, -2);
          Point B(2, 3);
          Point C(B.mediate(A, 1.25));
          bool_real br = C.is_on_line(A, B);
          Point D(A.mediate(B));
          br = D.is_on_line(A, B);
          Point E(A.mediate(B, 1.25));
          br = E.is_on_line(A, B);
          Point F(D);
          F.shift(-1, 1);
          br = F.is_on_line(A, B);


[Figure 92. Not displayed.]

Fig. 92.

Point mediate (Point p, [const real r = .5]) const function
Returns a Point r of the way from *this to p. 
          Point p0(-1, 0, -1);
          Point p1(10, 0, 10);
          Point p2(5, 5, 5);
          Point p3 = p0.mediate(p1, 1.5);
          p3.show("p3:");
          -| p3: (15.5, 0, 15.5)
          Point p4 = p0.mediate(p2, 1/3.0);
          p4.show("p4:");
          -| p4: (1, 1.66667, 1)


[Figure 93. Not displayed.]

Fig. 93.