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);
+ }
- /** A _cubic_ bezier. I really want to make them an arbitrary size but that might upset David. **/
+ /** 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)
+
+ /**
+ * 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;
+ 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 SolveBounds() const;
+
+ Bezier ToAbsolute(const Rect & bounds) const
{
- x1 = x0 + (x1-x0)*t.w;
- y1 = y0 + (y1-y0)*t.h;
- x2 = x0 + (x2-x0)*t.w;
- y2 = y0 + (y2-y0)*t.h;
+ 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;
+ }
- Rect ToRect() {return Rect(x0,y0,x2-x0,y2-y0);}
+ 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[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];
}
};
git.ucc.asn.au / ipdf / code.git / blobdiff
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