Real x2; Real y2;
Real x3; Real y3;
- typedef enum {LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type;
+ 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)
+ 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)
{
- //TODO: classify the curve
- type = SERPENTINE;
+
}
+ 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)
+ Real a1 = (x1-x0)*3;
+ Real a2 = (x0- x1*2 +x2)*3;
+ Real a3 = (x3 - x0 + (x1 - x2)*3);
+
+ Real b1 = (y1-y0)*3;
+ Real b2 = (y0- y1*2 +y2)*3;
+ Real b3 = (y3 - y0 + (y1 - y2)*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 (fabs(d1+d2+d3) < 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 (fabs(delta1+delta2+delta3) < 1e-6)
+ {
+ type = QUADRATIC;
+
+ //Debug("QUADRATIC %s", Str().c_str());
+ return type;
+ }
+
+ Real discriminant = d1*d3*4 -d2*d2;
+ if (fabs(discriminant) < 1e-6)
+ {
+ type = CUSP;
+ //Debug("CUSP %s", Str().c_str());
+ }
+ else if (discriminant > 0)
+ {
+ type = SERPENTINE;
+ //Debug("SERPENTINE %s", Str().c_str());
+ }
+ else
+ {
+ type = LOOP;
+ //Debug("LOOP %s", Str().c_str());
+ }
+ //Debug("disc %.30f", discriminant);
+ return type;
+ }
+
+
std::string Str() const
{
std::stringstream s;