| Index: experimental/Intersection/CubicSubDivide.cpp |
| =================================================================== |
| --- experimental/Intersection/CubicSubDivide.cpp (revision 5253) |
| +++ experimental/Intersection/CubicSubDivide.cpp (working copy) |
| @@ -3,21 +3,21 @@ |
| /* |
| Given a cubic c, t1, and t2, find a small cubic segment. |
| - |
| + |
| The new cubic is defined as points A, B, C, and D, where |
| s1 = 1 - t1 |
| s2 = 1 - t2 |
| A = c[0]*s1*s1*s1 + 3*c[1]*s1*s1*t1 + 3*c[2]*s1*t1*t1 + c[3]*t1*t1*t1 |
| D = c[0]*s2*s2*s2 + 3*c[1]*s2*s2*t2 + 3*c[2]*s2*t2*t2 + c[3]*t2*t2*t2 |
| - |
| + |
| We don't have B or C. So We define two equations to isolate them. |
| First, compute two reference T values 1/3 and 2/3 from t1 to t2: |
| - |
| + |
| c(at (2*t1 + t2)/3) == E |
| c(at (t1 + 2*t2)/3) == F |
| - |
| + |
| Next, compute where those values must be if we know the values of B and C: |
| - |
| + |
| _12 = A*2/3 + B*1/3 |
| 12_ = A*1/3 + B*2/3 |
| _23 = B*2/3 + C*1/3 |
| @@ -36,9 +36,9 @@ |
| = F |
| E*27 = A*8 + B*12 + C*6 + D |
| F*27 = A + B*6 + C*12 + D*8 |
| - |
| + |
| Group the known values on one side: |
| - |
| + |
| M = E*27 - A*8 - D = B*12 + C* 6 |
| N = F*27 - A - D*8 = B* 6 + C*12 |
| M*2 - N = B*18 |
| @@ -46,7 +46,7 @@ |
| B = (M*2 - N)/18 |
| C = (N*2 - M)/18 |
| */ |
| - |
| + |
| static double interp_cubic_coords(const double* src, double t) |
| { |
| double ab = interp(src[0], src[2], t); |
| @@ -57,7 +57,7 @@ |
| double abcd = interp(abc, bcd, t); |
| return abcd; |
| } |
| - |
| + |
| void sub_divide(const Cubic& src, double t1, double t2, Cubic& dst) { |
| double ax = dst[0].x = interp_cubic_coords(&src[0].x, t1); |
| double ay = dst[0].y = interp_cubic_coords(&src[0].y, t1); |
| Property changes on: experimental/Intersection/CubicSubDivide.cpp |
| ___________________________________________________________________ |
| Added: svn:eol-style |
| + LF |
