extern int Factorial(int n);
extern int BinomialCoeff(int n, int k);
extern Real Bernstein(int k, int n, const Real & u);
+
+ 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
+
+ // delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2
+ /*
+ 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);
+ */
+ // 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
+
+ ////HACK: We know any roots we care about will be between 0 and 1, so...
+ Real maxi(100);
+ Real prevRes(d);
+ std::vector<Real> roots;
+ 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) || (y < Real(0) && prevRes > Real(0)) || (y > Real(0) && prevRes < Real(0)))
+ {
+ roots.push_back(x);
+ }
+ }
+ return roots;
+
+ }
+
/** A _cubic_ bezier. **/
struct Bezier
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, 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, 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) {}
s << "Bezier{" << Float(x0) << "," << Float(y0) << " -> " << Float(x1) << "," << Float(y1) << " -> " << Float(x2) << "," << Float(y2) << " -> " << Float(x3) << "," << Float(y3) << "}";
return s.str();
}
+
+ /**
+ * 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)
{
x0 *= t.w;
y3 += t.y;
}
- Rect ToRect() {return Rect(x0,y0,x3-x0,y3-y0);}
+ Rect SolveBounds() const;
+
+ Bezier ToAbsolute(const Rect & bounds) const
+ {
+ return Bezier(*this, bounds);
+ }
+
+ /** Convert absolute control points to control points relative to bounds
+ * (This basically does the opposite of the Copy constructor)
+ * ie: If this is absolute, the returned Bezier will be relative to the bounds rectangle
+ */
+ Bezier ToRelative(const Rect & bounds) const
+ {
+ // x' <- (x - x0)/w etc
+ // special cases when w or h = 0
+ // (So can't just use the Copy constructor on the inverse of bounds)
+ // Rect inverse = {-bounds.x/bounds.w, -bounds.y/bounds.h, Real(1)/bounds.w, Real(1)/bounds.h};
+ Bezier result;
+ if (bounds.w == 0)
+ {
+ result.x0 = 0;
+ result.x1 = 0;
+ result.x2 = 0;
+ result.x3 = 0;
+ }
+ else
+ {
+ result.x0 = (x0 - bounds.x)/bounds.w;
+ result.x1 = (x1 - bounds.x)/bounds.w;
+ result.x2 = (x2 - bounds.x)/bounds.w;
+ result.x3 = (x3 - bounds.x)/bounds.w;
+ }
+
+ if (bounds.h == 0)
+ {
+ result.y0 = 0;
+ result.y1 = 0;
+ result.y2 = 0;
+ result.y3 = 0;
+ }
+ else
+ {
+ result.y0 = (y0 - bounds.y)/bounds.h;
+ result.y1 = (y1 - bounds.y)/bounds.h;
+ result.y2 = (y2 - bounds.y)/bounds.h;
+ result.y3 = (y3 - bounds.y)/bounds.h;
+ }
+ return result;
+ }
+
/** Evaluate the Bezier at parametric parameter u, puts resultant point in (x,y) **/
- void Evaluate(Real & x, Real & y, const Real & u)
+ void Evaluate(Real & x, Real & y, const Real & u) const
{
Real coeff[4];
for (unsigned i = 0; i < 4; ++i)
git.ucc.asn.au / ipdf / code.git / blobdiff
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