Careful, you may have to shade your eyes

[ipdf/code.git] / src / bezier.h

diff --git a/src/bezier.h b/src/bezier.h
index 9dd38c0..7ff4f87 100644 (file)
--- a/src/bezier.h
+++ b/src/bezier.h
@@ -13,65 +13,9 @@ namespace IPDF
        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)
-       {
-               Real x0((-b + Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
-               Real x1((-b - Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
-               return std::pair<Real,Real>(x0,x1);
-       }
-
-       inline std::vector<Real> SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d)
-       {
-               // 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);
-               
-               Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f (Discriminant: %f)", a,b,c,d, discriminant);
-               // discriminant > 0 => 3 distinct, real roots.
-               // discriminant = 0 => a multiple root (1 or 2 real roots)
-               // discriminant < 0 => 1 real root, 2 complex conjugate roots
-
-               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;
+       extern std::vector<Real> SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min = 0, const Real & max = 1);
 
-
-               Real C = pow((delta1 + Sqrt((delta1 * delta1) - 4 * (delta0 * delta0 * delta0)) ) / Real(2), 1/3);
-
-               if (false && discriminant < 0)
-               {
-                       Real real_root = (Real(-1) / (Real(3) * a)) * (b + C + delta0 / C);
-
-                       roots.push_back(real_root);
-
-                       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 = 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))))
-                       {
-                               Debug("Found root of %fx^3 + %fx^2 + %fx + %f at %f (%f)", a, b, c, d, x, y);
-                               roots.push_back(x);
-                       }
-                       prevRes = y;
-               }
-               return roots;
-                       
-       }
+       extern std::vector<Real> SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d, const Real & min = 0, const Real & max = 1, const Real & delta = 1e-4);
 
        /** A _cubic_ bezier. **/
        struct Bezier
@@ -327,6 +271,21 @@ namespace IPDF
                        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];
                }
+               std::vector<Vec2> Evaluate(const std::vector<Real> & u) const;
+               
+               std::vector<Real> SolveXParam(const Real & x) const;
+               std::vector<Real> SolveYParam(const Real & x) const;
+               
+               // Get points with same X
+               inline std::vector<Vec2> SolveX(const Real & x) const
+               {
+                       return Evaluate(SolveXParam(x));
+               }
+               // Get points with same Y
+               inline std::vector<Vec2> SolveY(const Real & y) const
+               {
+                       return Evaluate(SolveYParam(y));
+               }
                
                bool operator==(const Bezier & equ) const
                {