work in progress for shape operations
A experimental/Intersection
A experimental/Intersection/Intersections.h
A experimental/Intersection/DataTypes.cpp
A experimental/Intersection/QuadraticReduceOrder.cpp
A experimental/Intersection/IntersectionUtilities.cpp
A experimental/Intersection/CubicIntersection_Tests.h
A experimental/Intersection/LineParameteters_Test.cpp
A experimental/Intersection/ReduceOrder.cpp
A experimental/Intersection/QuadraticIntersection.cpp
A experimental/Intersection/Extrema.h
A experimental/Intersection/CubicIntersection_TestData.h
A experimental/Intersection/QuadraticParameterization_Test.cpp
A experimental/Intersection/TestUtilities.cpp
A experimental/Intersection/CubicRoots.cpp
A experimental/Intersection/QuadraticParameterization.cpp
A experimental/Intersection/QuadraticSubDivide.cpp
A experimental/Intersection/LineIntersection_Test.cpp
A experimental/Intersection/LineIntersection.cpp
A experimental/Intersection/CubicParameterizationCode.cpp
A experimental/Intersection/LineParameters.h
A experimental/Intersection/CubicIntersection.h
A experimental/Intersection/CubeRoot.cpp
A experimental/Intersection/SkAntiEdge.h
A experimental/Intersection/ConvexHull_Test.cpp
A experimental/Intersection/CubicBezierClip_Test.cpp
A experimental/Intersection/CubicIntersection_Tests.cpp
A experimental/Intersection/CubicBezierClip.cpp
A experimental/Intersection/CubicIntersectionT.cpp
A experimental/Intersection/Inline_Tests.cpp
A experimental/Intersection/ReduceOrder_Test.cpp
A experimental/Intersection/QuadraticIntersection_TestData.h
A experimental/Intersection/DataTypes.h
A experimental/Intersection/Extrema.cpp
A experimental/Intersection/EdgeApp.cpp
A experimental/Intersection/CubicIntersection_TestData.cpp
A experimental/Intersection/IntersectionUtilities.h
A experimental/Intersection/CubicReduceOrder.cpp
A experimental/Intersection/CubicCoincidence.cpp
A experimental/Intersection/CubicIntersection_Test.cpp
A experimental/Intersection/CubicIntersection.cpp
A experimental/Intersection/QuadraticUtilities.h
A experimental/Intersection/SkAntiEdge.cpp
A experimental/Intersection/TestUtilities.h
A experimental/Intersection/CubicParameterization_Test.cpp
A experimental/Intersection/LineIntersection.h
A experimental/Intersection/CubicSubDivide.cpp
A experimental/Intersection/CubicParameterization.cpp
A experimental/Intersection/QuadraticBezierClip_Test.cpp
A experimental/Intersection/QuadraticBezierClip.cpp
A experimental/Intersection/BezierClip_Test.cpp
A experimental/Intersection/ConvexHull.cpp
A experimental/Intersection/BezierClip.cpp
A experimental/Intersection/QuadraticIntersection_TestData.cpp
git-svn-id: http://skia.googlecode.com/svn/trunk@3005 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/experimental/Intersection/CubicSubDivide.cpp b/experimental/Intersection/CubicSubDivide.cpp
new file mode 100644
index 0000000..b8202fe
--- /dev/null
+++ b/experimental/Intersection/CubicSubDivide.cpp
@@ -0,0 +1,103 @@
+#include "CubicIntersection.h"
+#include "IntersectionUtilities.h"
+
+/*
+ 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
+ 23_ = B*1/3 + C*2/3
+ _34 = C*2/3 + D*1/3
+ 34_ = C*1/3 + D*2/3
+ _123 = (A*2/3 + B*1/3)*2/3 + (B*2/3 + C*1/3)*1/3 = A*4/9 + B*4/9 + C*1/9
+ 123_ = (A*1/3 + B*2/3)*1/3 + (B*1/3 + C*2/3)*2/3 = A*1/9 + B*4/9 + C*4/9
+ _234 = (B*2/3 + C*1/3)*2/3 + (C*2/3 + D*1/3)*1/3 = B*4/9 + C*4/9 + D*1/9
+ 234_ = (B*1/3 + C*2/3)*1/3 + (C*1/3 + D*2/3)*2/3 = B*1/9 + C*4/9 + D*4/9
+ _1234 = (A*4/9 + B*4/9 + C*1/9)*2/3 + (B*4/9 + C*4/9 + D*1/9)*1/3
+ = A*8/27 + B*12/27 + C*6/27 + D*1/27
+ = E
+ 1234_ = (A*1/9 + B*4/9 + C*4/9)*1/3 + (B*1/9 + C*4/9 + D*4/9)*2/3
+ = A*1/27 + B*6/27 + C*12/27 + D*8/27
+ = 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
+ N*2 - M = C*18
+ 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);
+ double bc = interp(src[2], src[4], t);
+ double cd = interp(src[4], src[6], t);
+ double abc = interp(ab, bc, t);
+ double bcd = interp(bc, cd, t);
+ 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);
+ double ex = interp_cubic_coords(&src[0].x, (t1*2+t2)/3);
+ double ey = interp_cubic_coords(&src[0].y, (t1*2+t2)/3);
+ double fx = interp_cubic_coords(&src[0].x, (t1+t2*2)/3);
+ double fy = interp_cubic_coords(&src[0].y, (t1+t2*2)/3);
+ double dx = dst[3].x = interp_cubic_coords(&src[0].x, t2);
+ double dy = dst[3].y = interp_cubic_coords(&src[0].y, t2);
+ double mx = ex * 27 - ax * 8 - dx;
+ double my = ey * 27 - ay * 8 - dy;
+ double nx = fx * 27 - ax - dx * 8;
+ double ny = fy * 27 - ay - dy * 8;
+ /* bx = */ dst[1].x = (mx * 2 - nx) / 18;
+ /* by = */ dst[1].y = (my * 2 - ny) / 18;
+ /* cx = */ dst[2].x = (nx * 2 - mx) / 18;
+ /* cy = */ dst[2].y = (ny * 2 - my) / 18;
+}
+
+/* classic one t subdivision */
+static void interp_cubic_coords(const double* src, double* dst, double t)
+{
+ double ab = interp(src[0], src[2], t);
+ double bc = interp(src[2], src[4], t);
+ double cd = interp(src[4], src[6], t);
+ double abc = interp(ab, bc, t);
+ double bcd = interp(bc, cd, t);
+ double abcd = interp(abc, bcd, t);
+
+ dst[0] = src[0];
+ dst[2] = ab;
+ dst[4] = abc;
+ dst[6] = abcd;
+ dst[8] = bcd;
+ dst[10] = cd;
+ dst[12] = src[6];
+}
+
+void chop_at(const Cubic& src, CubicPair& dst, double t)
+{
+ interp_cubic_coords(&src[0].x, &dst.pts[0].x, t);
+ interp_cubic_coords(&src[0].y, &dst.pts[0].y, t);
+}