}
- const Type & GetType()
+ Type GetType()
{
if (type != Bezier::UNKNOWN)
return type;
Real d2 = a3*b1 - a1*b3;
Real d3 = a1*b2 - a2*b1;
- if (d1 == d2 && d2 == d3 && d3 == 0)
+ if (Abs(d1+d2+d3) < 1e-6)
{
type = LINE;
//Debug("LINE %s", Str().c_str());
return type;
}
- Real delta1 = -d1*d1;
+ Real delta1 = -(d1*d1);
Real delta2 = d1*d2;
- Real delta3 = d1*d3 -d2*d2;
- if (delta1 == delta2 && delta2 == delta3 && delta3 == 0)
+ Real delta3 = d1*d3 -(d2*d2);
+ if (Abs(delta1+delta2+delta3) < 1e-6)
{
type = QUADRATIC;
}
Real discriminant = d1*d3*4 -d2*d2;
- if (discriminant == 0)
+ if (Abs(discriminant) < 1e-6)
{
type = CUSP;
//Debug("CUSP %s", Str().c_str());
type = LOOP;
//Debug("LOOP %s", Str().c_str());
}
+ //Debug("disc %.30f", discriminant);
return type;
}
* 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), type(UNKNOWN)
+ 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;
}
// Performs one round of De Casteljau subdivision and returns the [t,1] part.
- Bezier DeCasteljauSubdivideRight(const Real& t)
+ Bezier DeCasteljauSubdivideLeft(const Real& t)
{
Real one_minus_t = Real(1) - t;
// X Coordinates
- Real x01 = x0*t + x1*one_minus_t;
- Real x12 = x1*t + x2*one_minus_t;
- Real x23 = x2*t + x3*one_minus_t;
+ Real x01 = x1*t + x0*one_minus_t;
+ Real x12 = x2*t + x1*one_minus_t;
+ Real x23 = x3*t + x2*one_minus_t;
- Real x012 = x01*t + x12*one_minus_t;
- Real x123 = x12*t + x23*one_minus_t;
+ Real x012 = x12*t + x01*one_minus_t;
+ Real x123 = x23*t + x12*one_minus_t;
- Real x0123 = x012*t + x123*one_minus_t;
+ Real x0123 = x123*t + x012*one_minus_t;
// Y Coordinates
- Real y01 = y0*t + y1*one_minus_t;
- Real y12 = y1*t + y2*one_minus_t;
- Real y23 = y2*t + y3*one_minus_t;
+ Real y01 = y1*t + y0*one_minus_t;
+ Real y12 = y2*t + y1*one_minus_t;
+ Real y23 = y3*t + y2*one_minus_t;
- Real y012 = y01*t + y12*one_minus_t;
- Real y123 = y12*t + y23*one_minus_t;
+ Real y012 = y12*t + y01*one_minus_t;
+ Real y123 = y23*t + y12*one_minus_t;
- Real y0123 = y012*t + y123*one_minus_t;
+ Real y0123 = y123*t + y012*one_minus_t;
return Bezier(x0, y0, x01, y01, x012, y012, x0123, y0123);
}
- // Performs one round of De Casteljau subdivision and returns the [0,t] part.
- Bezier DeCasteljauSubdivideLeft(const Real& t)
+ // Performs one round of De Casteljau subdivision and returns the [t,1] part.
+ Bezier DeCasteljauSubdivideRight(const Real& t)
{
Real one_minus_t = Real(1) - t;
// X Coordinates
- Real x01 = x0*t + x1*one_minus_t;
- Real x12 = x1*t + x2*one_minus_t;
- Real x23 = x2*t + x3*one_minus_t;
+ Real x01 = x1*t + x0*one_minus_t;
+ Real x12 = x2*t + x1*one_minus_t;
+ Real x23 = x3*t + x2*one_minus_t;
- Real x012 = x01*t + x12*one_minus_t;
- Real x123 = x12*t + x23*one_minus_t;
+ Real x012 = x12*t + x01*one_minus_t;
+ Real x123 = x23*t + x12*one_minus_t;
- Real x0123 = x012*t + x123*one_minus_t;
+ Real x0123 = x123*t + x012*one_minus_t;
// Y Coordinates
- Real y01 = y0*t + y1*one_minus_t;
- Real y12 = y1*t + y2*one_minus_t;
- Real y23 = y2*t + y3*one_minus_t;
+ Real y01 = y1*t + y0*one_minus_t;
+ Real y12 = y2*t + y1*one_minus_t;
+ Real y23 = y3*t + y2*one_minus_t;
- Real y012 = y01*t + y12*one_minus_t;
- Real y123 = y12*t + y23*one_minus_t;
+ Real y012 = y12*t + y01*one_minus_t;
+ Real y123 = y23*t + y12*one_minus_t;
- Real y0123 = y012*t + y123*one_minus_t;
+ Real y0123 = y123*t + y012*one_minus_t;
return Bezier(x0123, y0123, x123, y123, x23, y23, x3, y3);
}
Bezier ReParametrise(const Real& t0, const Real& t1)
{
- Debug("Reparametrise: %f -> %f",t0,t1);
+ Debug("Reparametrise: %f -> %f",Double(t0),Double(t1));
Bezier new_bezier;
// Subdivide to get from [0,t1]
new_bezier = DeCasteljauSubdivideLeft(t1);
// Convert t0 from [0,1] range to [0, t1]
Real new_t0 = t0 / t1;
- Debug("New t0 = %f", new_t0);
+ Debug("New t0 = %f", Double(new_t0));
new_bezier = new_bezier.DeCasteljauSubdivideRight(new_t0);
Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str());
// Find points of intersection with the rectangle.
Debug("Clipping Bezier to Rect %s", r.Str().c_str());
- // Convert bezier coefficients -> cubic coefficients
- Real xd = x0 - r.x;
- Real xc = Real(3)*(x1 - x0);
- Real xb = Real(3)*(x2 - x1) - xc;
- Real xa = x3 - x0 - xc - xb;
// Find its roots.
- std::vector<Real> x_intersection = SolveCubic(xa, xb, xc, xd);
+ std::vector<Real> x_intersection = SolveXParam(r.x);
// And for the other side.
- xd = x0 - r.x - r.w;
- std::vector<Real> x_intersection_pt2 = SolveCubic(xa, xb, xc, xd);
+ std::vector<Real> x_intersection_pt2 = SolveXParam(r.x + r.w);
x_intersection.insert(x_intersection.end(), x_intersection_pt2.begin(), x_intersection_pt2.end());
- // Similarly for y-coordinates.
- // Convert bezier coefficients -> cubic coefficients
- Real yd = y0 - r.y;
- Real yc = Real(3)*(y1 - y0);
- Real yb = Real(3)*(y2 - y1) - yc;
- Real ya = y3 - y0 - yc - yb;
-
// Find its roots.
- std::vector<Real> y_intersection = SolveCubic(ya, yb, yc, yd);
+ std::vector<Real> y_intersection = SolveYParam(r.y);
- // And for the other side.
- yd = y0 - r.y - r.h;
-
- std::vector<Real> y_intersection_pt2 = SolveCubic(ya, yb, yc, yd);
+ std::vector<Real> y_intersection_pt2 = SolveYParam(r.y+r.h);
y_intersection.insert(y_intersection.end(), y_intersection_pt2.begin(), y_intersection_pt2.end());
// Merge and sort.
std::sort(x_intersection.begin(), x_intersection.end());
Debug("Found %d intersections.\n", x_intersection.size());
+ for(auto t : x_intersection)
+ {
+ Real ptx, pty;
+ Evaluate(ptx, pty, t);
+ Debug("Root: t = %f, (%f,%f)", Double(t), Double(ptx), Double(pty));
+ }
std::vector<Bezier> all_beziers;
if (x_intersection.size() <= 2)
{
Real t1 = *it;
if (t1 == t0) continue;
- Debug(" -- t0: %f to t1: %f", t0, t1);
+ Debug(" -- t0: %f to t1: %f: %f", Double(t0), Double(t1), (t1 + t0)/Real(2));
Real ptx, pty;
Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
- if (true || r.PointIn(ptx, pty))
+ if (r.PointIn(ptx, pty))
{
+ Debug("Adding segment: (point at %f, %f)", Double(ptx), Double(pty));
all_beziers.push_back(this->ReParametrise(t0, t1));
}
else
{
- Debug("Segment removed (point at %f, %f)", ptx, pty);
+ Debug("Segment removed (point at %f, %f)", Double(ptx), Double(pty));
}
t0 = t1;
}
git.ucc.asn.au / ipdf / code.git / blobdiff
UCC git Repository :: git.ucc.asn.au