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<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);
+ 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);
/** A _cubic_ bezier. **/
struct Bezier
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, 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), type(UNKNOWN)
+ //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)
{
}
return type;
// From Loop-Blinn 2005, with w0 == w1 == w2 == w3 = 1
// Transformed control points: (a0 = x0, b0 = y0)
- Real a1 = (x1-x0)*3;
- Real a2 = (x0- x1*2 +x2)*3;
- Real a3 = (x3 - x0 + (x1 - x2)*3);
+ Real a1 = (x1-x0)*Real(3);
+ Real a2 = (x0- x1*Real(2) +x2)*Real(3);
+ Real a3 = (x3 - x0 + (x1 - x2)*Real(3));
- Real b1 = (y1-y0)*3;
- Real b2 = (y0- y1*2 +y2)*3;
- Real b3 = (y3 - y0 + (y1 - y2)*3);
+ Real b1 = (y1-y0)*Real(3);
+ Real b2 = (y0- y1*Real(2) +y2)*Real(3);
+ Real b3 = (y3 - y0 + (y1 - y2)*Real(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;
- if (Abs(d1+d2+d3) < 1e-6)
+ if (Abs(d1+d2+d3) < Real(1e-6))
{
type = LINE;
//Debug("LINE %s", Str().c_str());
Real delta1 = -(d1*d1);
Real delta2 = d1*d2;
Real delta3 = d1*d3 -(d2*d2);
- if (Abs(delta1+delta2+delta3) < 1e-6)
+ if (Abs(delta1+delta2+delta3) < Real(1e-6))
{
type = QUADRATIC;
return type;
}
- Real discriminant = d1*d3*4 -d2*d2;
- if (Abs(discriminant) < 1e-6)
+ Real discriminant = d1*d3*Real(4) -d2*d2;
+ if (Abs(discriminant) < Real(1e-6))
{
type = CUSP;
//Debug("CUSP %s", Str().c_str());
}
- else if (discriminant > 0)
+ else if (discriminant > Real(0))
{
type = SERPENTINE;
//Debug("SERPENTINE %s", Str().c_str());
// (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)
+ if (bounds.w == Real(0))
{
result.x0 = 0;
result.x1 = 0;
result.x3 = (x3 - bounds.x)/bounds.w;
}
- if (bounds.h == 0)
+ if (bounds.h == Real(0))
{
result.y0 = 0;
result.y1 = 0;
// Find its roots.
std::vector<Real> 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);
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());
// Find its roots.
std::vector<Real> 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);
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());
// Merge and sort.
x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end());
{
Real t1 = *it;
if (t1 == t0) continue;
- Debug(" -- t0: %f to t1: %f: %f", Double(t0), Double(t1), (t1 + t0)/Real(2));
+ 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)));
if (r.PointIn(ptx, pty))