extern int Factorial(int n);
extern int BinomialCoeff(int n, int k);
extern Real Bernstein(int k, int n, const Real & u);
+ extern std::pair<Real,Real> BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3);
inline std::pair<Real,Real> SolveQuadratic(const Real & a, const Real & b, const Real & c)
{
// This is going to be a big one...
// See http://en.wikipedia.org/wiki/Cubic_function#General_formula_for_roots
+ std::vector<Real> roots;
// delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2
+#if 0
Real discriminant = Real(18) * a * b * c * d - Real(4) * (b * b * b) * d
+ (b * b) * (c * c) - Real(4) * a * (c * c * c)
- Real(27) * (a * a) * (d * d);
Real delta0 = (b*b) - Real(3) * a * c;
Real delta1 = Real(2) * (b * b * b) - Real(9) * a * b * c + Real(27) * (a * a) * d;
- std::vector<Real> roots;
Real C = pow((delta1 + Sqrt((delta1 * delta1) - 4 * (delta0 * delta0 * delta0)) ) / Real(2), 1/3);
return roots;
}
-
+#endif
////HACK: We know any roots we care about will be between 0 and 1, so...
Real maxi(100);
Real prevRes(d);
- for(int i = -1; i <= 100; ++i)
+ for(int i = 0; i <= 100; ++i)
{
Real x(i);
x /= maxi;
Real y = a*(x*x*x) + b*(x*x) + c*x + d;
- if ( ((y < Real(0)) && (prevRes > Real(0))) || ((y > Real(0)) && (prevRes < Real(0))))
+ if (((y < Real(0)) && (prevRes > Real(0))) || ((y > Real(0)) && (prevRes < Real(0))))
{
Debug("Found root of %fx^3 + %fx^2 + %fx + %f at %f (%f)", a, b, c, d, x, y);
roots.push_back(x);
Real x1; Real y1;
Real x2; Real y2;
Real x3; Real y3;
+
+ typedef enum {LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type;
+ Type type;
+
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, Real _x3, Real _y3) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3)
{
-
+ //TODO: classify the curve
+ type = SERPENTINE;
}
- 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;
* Construct absolute control points using relative control points to a bounding rectangle
* ie: If cpy is relative to bounds rectangle, this will be absolute
*/
- 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)
+ 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), type(cpy.type)
{
x0 *= t.w;
y0 *= t.h;
Rect SolveBounds() const;
+ std::pair<Real,Real> GetTop() const;
+ std::pair<Real,Real> GetBottom() const;
+ std::pair<Real,Real> GetLeft() const;
+ std::pair<Real,Real> GetRight() const;
+
Bezier ToAbsolute(const Rect & bounds) const
{
return Bezier(*this, bounds);
Debug("Found %d intersections.\n", x_intersection.size());
std::vector<Bezier> all_beziers;
- if (x_intersection.empty())
+ if (x_intersection.size() <= 2)
{
all_beziers.push_back(*this);
return all_beziers;
Debug(" -- t0: %f to t1: %f", t0, t1);
Real ptx, pty;
Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
- if (r.PointIn(ptx, pty))
+ if (true || r.PointIn(ptx, pty))
{
all_beziers.push_back(this->ReParametrise(t0, t1));
}
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];
}
+
+ bool operator==(const Bezier & equ) const
+ {
+ return (x0 == equ.x0 && y0 == equ.y0
+ && x1 == equ.x1 && y1 == equ.y1
+ && x2 == equ.x2 && y2 == equ.y2
+ && x3 == equ.x3 && y3 == equ.y3);
+ }
+ bool operator!=(const Bezier & equ) const {return !this->operator==(equ);}
};