8 extern int Factorial(int n);
9 extern int BinomialCoeff(int n, int k);
10 extern Real Bernstein(int k, int n, const Real & u);
12 inline std::pair<Real,Real> SolveQuadratic(const Real & a, const Real & b, const Real & c)
14 Real x0((b + Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
15 Real x1((b - Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
16 return std::pair<Real,Real>(x0,x1);
19 /** A _cubic_ bezier. **/
26 Bezier() = default; // Needed so we can fread/fwrite this struct... for now.
27 Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2, Real _x3, Real _y3) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3)
32 Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x2), y3(_y2) {}
34 std::string Str() const
37 s << "Bezier{" << Float(x0) << "," << Float(y0) << " -> " << Float(x1) << "," << Float(y1) << " -> " << Float(x2) << "," << Float(y2) << " -> " << Float(x3) << "," << Float(y3) << "}";
42 * Construct absolute control points using relative control points to a bounding rectangle
43 * ie: If cpy is relative to bounds rectangle, this will be absolute
45 Bezier(const Bezier & cpy, const Rect & t = Rect(0,0,1,1)) : x0(cpy.x0), y0(cpy.y0), x1(cpy.x1), y1(cpy.y1), x2(cpy.x2),y2(cpy.y2), x3(cpy.x3), y3(cpy.y3)
65 Rect SolveBounds() const;
67 /** Convert absolute control points to control points relative to bounds
68 * (This basically does the opposite of the Copy constructor)
69 * ie: If this is absolute, the returned Bezier will be relative to the bounds rectangle
71 Bezier CopyInverse(const Rect & bounds) const
73 // x' <- (x - x0)/w etc
74 // special cases when w or h = 0
75 // (So can't just use the Copy constructor on the inverse of bounds)
76 // Rect inverse = {-bounds.x/bounds.w, -bounds.y/bounds.h, Real(1)/bounds.w, Real(1)/bounds.h};
87 result.x0 = (x0 - bounds.x)/bounds.w;
88 result.x1 = (x1 - bounds.x)/bounds.w;
89 result.x2 = (x2 - bounds.x)/bounds.w;
90 result.x3 = (x3 - bounds.x)/bounds.w;
102 result.y0 = (y0 - bounds.y)/bounds.h;
103 result.y1 = (y1 - bounds.y)/bounds.h;
104 result.y2 = (y2 - bounds.y)/bounds.h;
105 result.y3 = (y3 - bounds.y)/bounds.h;
111 /** Evaluate the Bezier at parametric parameter u, puts resultant point in (x,y) **/
112 void Evaluate(Real & x, Real & y, const Real & u) const
115 for (unsigned i = 0; i < 4; ++i)
116 coeff[i] = Bernstein(i,3,u);
117 x = x0*coeff[0] + x1*coeff[1] + x2*coeff[2] + x3*coeff[3];
118 y = y0*coeff[0] + y1*coeff[1] + y2*coeff[2] + y3*coeff[3];