+
+ }
+
+ Type GetType()
+ {
+ if (type != Bezier::UNKNOWN)
+ return type;
+ // From Loop-Blinn 2005, with w0 == w1 == w2 == w3 = 1
+ // Transformed control points: (a0 = x0, b0 = y0)
+ BReal a1 = (x1-x0)*BReal(3);
+ BReal a2 = (x0- x1*BReal(2) +x2)*BReal(3);
+ BReal a3 = (x3 - x0 + (x1 - x2)*BReal(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)
+ BReal d1 = a2*b3 - a3*b2;
+ BReal d2 = a3*b1 - a1*b3;
+ BReal d3 = a1*b2 - a2*b1;
+
+ if (Abs(d1+d2+d3) < BReal(1e-6))
+ {
+ type = LINE;
+ //Debug("LINE %s", Str().c_str());
+ return type;
+ }
+
+ BReal delta1 = -(d1*d1);
+ BReal delta2 = d1*d2;
+ BReal delta3 = d1*d3 -(d2*d2);
+ if (Abs(delta1+delta2+delta3) < BReal(1e-6))
+ {
+ type = QUADRATIC;
+
+ //Debug("QUADRATIC %s", Str().c_str());
+ return type;
+ }
+
+ 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 > BReal(0))
+ {
+ type = SERPENTINE;
+ //Debug("SERPENTINE %s", Str().c_str());
+ }
+ else
+ {
+ type = LOOP;
+ //Debug("LOOP %s", Str().c_str());
+ }
+ //Debug("disc %.30f", discriminant);
+ return type;