extern int BinomialCoeff(int n, int k);
extern Real Bernstein(int k, int n, const Real & u);
- /** A _quadratic_ bezier. **/
+ /** A _cubic_ bezier. **/
struct Bezier
{
Real x0; Real y0;
Real x1; Real y1;
Real x2; Real y2;
+ Real x3; Real y3;
Bezier() = default; // Needed so we can fread/fwrite this struct... for now.
- 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) {}
+ 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) {}
+
+ 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) {}
+
std::string Str() const
{
std::stringstream s;
- s << "Bezier{" << Float(x0) << "," << Float(y0) << " -> " << Float(x1) << "," << Float(y1) << " -> " << Float(x2) << "," << Float(y2) << "}";
+ s << "Bezier{" << Float(x0) << "," << Float(y0) << " -> " << Float(x1) << "," << Float(y1) << " -> " << Float(x2) << "," << Float(y2) << " -> " << Float(x3) << "," << Float(y3) << "}";
return s.str();
}
- Bezier(const Bezier & cpy, const Rect & t = Rect(0,0,1,1)) : x0(cpy.x0+t.x), y0(cpy.y0+t.y), x1(cpy.x1+t.x), y1(cpy.y1+t.y), x2(cpy.x2+t.x),y2(cpy.y2+t.y)
+ 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)
{
- x1 = x0 + (x1-x0)*t.w;
- y1 = y0 + (y1-y0)*t.h;
- x2 = x0 + (x2-x0)*t.w;
- y2 = y0 + (y2-y0)*t.h;
+ x0 *= t.w;
+ y0 *= t.h;
+ x1 *= t.w;
+ y1 *= t.h;
+ x2 *= t.w;
+ y2 *= t.h;
+ x3 *= t.w;
+ y3 *= t.h;
+ x0 += t.x;
+ y0 += t.y;
+ x1 += t.x;
+ y1 += t.y;
+ x2 += t.x;
+ y2 += t.y;
+ x3 += t.x;
+ y3 += t.y;
}
- Rect ToRect() {return Rect(x0,y0,x2-x0,y2-y0);}
+ Rect ToRect() {return Rect(x0,y0,x3-x0,y3-y0);}
/** Evaluate the Bezier at parametric parameter u, puts resultant point in (x,y) **/
void Evaluate(Real & x, Real & y, const Real & u)
{
- Real coeff[3];
- for (unsigned i = 0; i < 3; ++i)
- coeff[i] = Bernstein(i,2,u);
- x = x0*coeff[0] + x1*coeff[1] + x2*coeff[2];
- y = y0*coeff[0] + y1*coeff[1] + y2*coeff[2];
+ Real coeff[4];
+ for (unsigned i = 0; i < 4; ++i)
+ coeff[i] = Bernstein(i,3,u);
+ x = x0*coeff[0] + x1*coeff[1] + x2*coeff[2] + x3*coeff[3];
+ y = y0*coeff[0] + y1*coeff[1] + y2*coeff[2] + y3*coeff[3];
}
};