#include <vector>
#include <algorithm>
-
-#include "real.h"
#include "rect.h"
+#include "real.h"
+
+
+
namespace IPDF
{
+ typedef Real BReal;
+ typedef TRect<BReal> BRect;
+
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);
+ extern BReal Bernstein(int k, int n, const BReal & u);
+ extern std::pair<BReal,BReal> BezierTurningPoints(const BReal & p0, const BReal & p1, const BReal & p2, const BReal & p3);
- extern std::vector<Real> SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min = 0, const Real & max = 1);
+ extern std::vector<BReal> SolveQuadratic(const BReal & a, const BReal & b, const BReal & c, const BReal & min = 0, const BReal & max = 1);
- 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-9);
+ extern std::vector<BReal> SolveCubic(const BReal & a, const BReal & b, const BReal & c, const BReal & d, const BReal & min = 0, const BReal & max = 1, const BReal & delta = 1e-9);
/** A _cubic_ bezier. **/
struct Bezier
{
- Real x0; Real y0;
- Real x1; Real y1;
- Real x2; Real y2;
- Real x3; Real y3;
+ BReal x0; BReal y0;
+ BReal x1; BReal y1;
+ BReal x2; BReal y2;
+ BReal x3; BReal y3;
typedef enum {UNKNOWN, LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type;
Type type;
//Bezier() = default; // Needed so we can fread/fwrite this struct... for now.
- Bezier(Real _x0=0, Real _y0=0, Real _x1=0, Real _y1=0, Real _x2=0, Real _y2=0, Real _x3=0, Real _y3=0) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3), type(UNKNOWN)
+ Bezier(BReal _x0=0, BReal _y0=0, BReal _x1=0, BReal _y1=0, BReal _x2=0, BReal _y2=0, BReal _x3=0, BReal _y3=0) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3), type(UNKNOWN)
{
}
return type;
// From Loop-Blinn 2005, with w0 == w1 == w2 == w3 = 1
// Transformed control points: (a0 = x0, b0 = y0)
- Real a1 = (x1-x0)*Real(3);
- Real a2 = (x0- x1*Real(2) +x2)*Real(3);
- Real a3 = (x3 - x0 + (x1 - x2)*Real(3));
+ BReal a1 = (x1-x0)*BReal(3);
+ BReal a2 = (x0- x1*BReal(2) +x2)*BReal(3);
+ BReal a3 = (x3 - x0 + (x1 - x2)*BReal(3));
- Real b1 = (y1-y0)*Real(3);
- Real b2 = (y0- y1*Real(2) +y2)*Real(3);
- Real b3 = (y3 - y0 + (y1 - y2)*Real(3));
+ BReal b1 = (y1-y0)*BReal(3);
+ BReal b2 = (y0- y1*BReal(2) +y2)*BReal(3);
+ BReal b3 = (y3 - y0 + (y1 - y2)*BReal(3));
// d vector (d0 = 0 since all w = 1)
- Real d1 = a2*b3 - a3*b2;
- Real d2 = a3*b1 - a1*b3;
- Real d3 = a1*b2 - a2*b1;
+ BReal d1 = a2*b3 - a3*b2;
+ BReal d2 = a3*b1 - a1*b3;
+ BReal d3 = a1*b2 - a2*b1;
- if (Abs(d1+d2+d3) < Real(1e-6))
+ if (Abs(d1+d2+d3) < BReal(1e-6))
{
type = LINE;
//Debug("LINE %s", Str().c_str());
return type;
}
- Real delta1 = -(d1*d1);
- Real delta2 = d1*d2;
- Real delta3 = d1*d3 -(d2*d2);
- if (Abs(delta1+delta2+delta3) < Real(1e-6))
+ BReal delta1 = -(d1*d1);
+ BReal delta2 = d1*d2;
+ BReal delta3 = d1*d3 -(d2*d2);
+ if (Abs(delta1+delta2+delta3) < BReal(1e-6))
{
type = QUADRATIC;
return type;
}
- Real discriminant = d1*d3*Real(4) -d2*d2;
- if (Abs(discriminant) < Real(1e-6))
+ BReal discriminant = d1*d3*BReal(4) -d2*d2;
+ if (Abs(discriminant) < BReal(1e-6))
{
type = CUSP;
//Debug("CUSP %s", Str().c_str());
}
- else if (discriminant > Real(0))
+ else if (discriminant > BReal(0))
{
type = SERPENTINE;
//Debug("SERPENTINE %s", Str().c_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), type(cpy.type)
+ Bezier(const Bezier & cpy, const BRect & t = BRect(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;
y3 += t.y;
}
- Rect SolveBounds() const;
+ BRect 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;
+ std::pair<BReal,BReal> GetTop() const;
+ std::pair<BReal,BReal> GetBottom() const;
+ std::pair<BReal,BReal> GetLeft() const;
+ std::pair<BReal,BReal> GetRight() const;
- Bezier ToAbsolute(const Rect & bounds) const
+ Bezier ToAbsolute(const BRect & bounds) const
{
return Bezier(*this, 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
+ Bezier ToRelative(const BRect & 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};
+ // BRect inverse = {-bounds.x/bounds.w, -bounds.y/bounds.h, BReal(1)/bounds.w, BReal(1)/bounds.h};
Bezier result;
- if (bounds.w == Real(0))
+ if (bounds.w == 0)
{
result.x0 = 0;
result.x1 = 0;
result.x3 = (x3 - bounds.x)/bounds.w;
}
- if (bounds.h == Real(0))
+ if (bounds.h == 0)
{
result.y0 = 0;
result.y1 = 0;
}
// Performs one round of De Casteljau subdivision and returns the [t,1] part.
- Bezier DeCasteljauSubdivideLeft(const Real& t)
+ Bezier DeCasteljauSubdivideLeft(const BReal& t)
{
- Real one_minus_t = Real(1) - t;
+ BReal one_minus_t = BReal(1) - t;
// X Coordinates
- Real x01 = x1*t + x0*one_minus_t;
- Real x12 = x2*t + x1*one_minus_t;
- Real x23 = x3*t + x2*one_minus_t;
+ BReal x01 = x1*t + x0*one_minus_t;
+ BReal x12 = x2*t + x1*one_minus_t;
+ BReal x23 = x3*t + x2*one_minus_t;
- Real x012 = x12*t + x01*one_minus_t;
- Real x123 = x23*t + x12*one_minus_t;
+ BReal x012 = x12*t + x01*one_minus_t;
+ BReal x123 = x23*t + x12*one_minus_t;
- Real x0123 = x123*t + x012*one_minus_t;
+ BReal x0123 = x123*t + x012*one_minus_t;
// Y Coordinates
- Real y01 = y1*t + y0*one_minus_t;
- Real y12 = y2*t + y1*one_minus_t;
- Real y23 = y3*t + y2*one_minus_t;
+ BReal y01 = y1*t + y0*one_minus_t;
+ BReal y12 = y2*t + y1*one_minus_t;
+ BReal y23 = y3*t + y2*one_minus_t;
- Real y012 = y12*t + y01*one_minus_t;
- Real y123 = y23*t + y12*one_minus_t;
+ BReal y012 = y12*t + y01*one_minus_t;
+ BReal y123 = y23*t + y12*one_minus_t;
- Real y0123 = y123*t + y012*one_minus_t;
+ BReal 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 [t,1] part.
- Bezier DeCasteljauSubdivideRight(const Real& t)
+ Bezier DeCasteljauSubdivideRight(const BReal& t)
{
- Real one_minus_t = Real(1) - t;
+ BReal one_minus_t = BReal(1) - t;
// X Coordinates
- Real x01 = x1*t + x0*one_minus_t;
- Real x12 = x2*t + x1*one_minus_t;
- Real x23 = x3*t + x2*one_minus_t;
+ BReal x01 = x1*t + x0*one_minus_t;
+ BReal x12 = x2*t + x1*one_minus_t;
+ BReal x23 = x3*t + x2*one_minus_t;
- Real x012 = x12*t + x01*one_minus_t;
- Real x123 = x23*t + x12*one_minus_t;
+ BReal x012 = x12*t + x01*one_minus_t;
+ BReal x123 = x23*t + x12*one_minus_t;
- Real x0123 = x123*t + x012*one_minus_t;
+ BReal x0123 = x123*t + x012*one_minus_t;
// Y Coordinates
- Real y01 = y1*t + y0*one_minus_t;
- Real y12 = y2*t + y1*one_minus_t;
- Real y23 = y3*t + y2*one_minus_t;
+ BReal y01 = y1*t + y0*one_minus_t;
+ BReal y12 = y2*t + y1*one_minus_t;
+ BReal y23 = y3*t + y2*one_minus_t;
- Real y012 = y12*t + y01*one_minus_t;
- Real y123 = y23*t + y12*one_minus_t;
+ BReal y012 = y12*t + y01*one_minus_t;
+ BReal y123 = y23*t + y12*one_minus_t;
- Real y0123 = y123*t + y012*one_minus_t;
+ BReal 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)
+ Bezier ReParametrise(const BReal& t0, const BReal& t1)
{
- Debug("Reparametrise: %f -> %f",Double(t0),Double(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", Double(new_t0));
+ BReal new_t0 = t0 / t1;
+ //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());
+ //Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str());
return new_bezier;
}
- std::vector<Bezier> ClipToRectangle(const Rect& r)
+ std::vector<Bezier> ClipToRectangle(const BRect & r)
{
// Find points of intersection with the rectangle.
- Debug("Clipping Bezier to Rect %s", r.Str().c_str());
+ Debug("Clipping Bezier to BRect %s", r.Str().c_str());
// Find its roots.
- std::vector<Real> x_intersection = SolveXParam(r.x);
- Debug("Found %d intersections on left edge", x_intersection.size());
+ std::vector<BReal> x_intersection = SolveXParam(r.x);
+ //Debug("Found %d intersections on left edge", x_intersection.size());
// And for the other side.
- std::vector<Real> x_intersection_pt2 = SolveXParam(r.x + r.w);
+ std::vector<BReal> x_intersection_pt2 = SolveXParam(r.x + r.w);
x_intersection.insert(x_intersection.end(), x_intersection_pt2.begin(), x_intersection_pt2.end());
- Debug("Found %d intersections on right edge (total x: %d)", x_intersection_pt2.size(), x_intersection.size());
+ //Debug("Found %d intersections on right edge (total x: %d)", x_intersection_pt2.size(), x_intersection.size());
// Find its roots.
- std::vector<Real> y_intersection = SolveYParam(r.y);
- Debug("Found %d intersections on top edge", y_intersection.size());
+ std::vector<BReal> y_intersection = SolveYParam(r.y);
+ //Debug("Found %d intersections on top edge", y_intersection.size());
- std::vector<Real> y_intersection_pt2 = SolveYParam(r.y+r.h);
+ std::vector<BReal> y_intersection_pt2 = SolveYParam(r.y+r.h);
y_intersection.insert(y_intersection.end(), y_intersection_pt2.begin(), y_intersection_pt2.end());
- Debug("Found %d intersections on bottom edge (total y: %d)", y_intersection_pt2.size(), y_intersection.size());
+ //Debug("Found %d intersections on bottom edge (total y: %d)", y_intersection_pt2.size(), y_intersection.size());
// Merge and sort.
x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end());
- x_intersection.push_back(Real(0));
- x_intersection.push_back(Real(1));
+ x_intersection.push_back(BReal(0));
+ x_intersection.push_back(BReal(1));
std::sort(x_intersection.begin(), x_intersection.end());
- Debug("Found %d intersections.\n", x_intersection.size());
- for(auto t : x_intersection)
+ //Debug("Found %d intersections.\n", x_intersection.size());
+ /*for(auto t : x_intersection)
{
- Real ptx, pty;
+ BReal 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)
all_beziers.push_back(*this);
return all_beziers;
}
- Real t0 = *(x_intersection.begin());
+ BReal t0 = *(x_intersection.begin());
for (auto it = x_intersection.begin()+1; it != x_intersection.end(); ++it)
{
- Real t1 = *it;
+ BReal t1 = *it;
if (t1 == t0) continue;
- Debug(" -- t0: %f to t1: %f: %f", Double(t0), Double(t1), Double((t1 + t0)/Real(2)));
- Real ptx, pty;
- Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
+ //Debug(" -- t0: %f to t1: %f: %f", Double(t0), Double(t1), Double((t1 + t0)/BReal(2)));
+ BReal ptx, pty;
+ Evaluate(ptx, pty, ((t1 + t0) / BReal(2)));
if (r.PointIn(ptx, pty))
{
- Debug("Adding segment: (point at %f, %f)", Double(ptx), Double(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)", Double(ptx), Double(pty));
+ //Debug("Segment removed (point at %f, %f)", Double(ptx), Double(pty));
}
t0 = t1;
}
}
/** Evaluate the Bezier at parametric parameter u, puts resultant point in (x,y) **/
- void Evaluate(Real & x, Real & y, const Real & u) const
+ void Evaluate(BReal & x, BReal & y, const BReal & u) const
{
- Real coeff[4];
+ BReal 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];
}
- std::vector<Vec2> Evaluate(const std::vector<Real> & u) const;
+ std::vector<Vec2> Evaluate(const std::vector<BReal> & u) const;
- std::vector<Real> SolveXParam(const Real & x) const;
- std::vector<Real> SolveYParam(const Real & x) const;
+ std::vector<BReal> SolveXParam(const BReal & x) const;
+ std::vector<BReal> SolveYParam(const BReal & x) const;
// Get points with same X
- inline std::vector<Vec2> SolveX(const Real & x) const
+ inline std::vector<Vec2> SolveX(const BReal & x) const
{
return Evaluate(SolveXParam(x));
}
// Get points with same Y
- inline std::vector<Vec2> SolveY(const Real & y) const
+ inline std::vector<Vec2> SolveY(const BReal & y) const
{
return Evaluate(SolveYParam(y));
}
git.ucc.asn.au / ipdf / code.git / blobdiff
UCC git Repository :: git.ucc.asn.au