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

1 files changed, 63 insertions, 0 deletions

diff --git a/experimental/Intersection/QuadraticSubDivide.cpp b/experimental/Intersection/QuadraticSubDivide.cpp
new file mode 100644
index 0000000000..947f7d8355
--- /dev/null
+++ b/experimental/Intersection/QuadraticSubDivide.cpp
@@ -0,0 +1,63 @@
+#include "CubicIntersection.h"
+#include "IntersectionUtilities.h"
+
+/*
+Given a quadratic q, t1, and t2, find a small quadratic segment.
+
+The new quadratic is defined by A, B, and C, where
+ A = c[0]*(1 - t1)*(1 - t1) + 2*c[1]*t1*(1 - t1) + c[2]*t1*t1
+ C = c[3]*(1 - t1)*(1 - t1) + 2*c[2]*t1*(1 - t1) + c[1]*t1*t1
+
+To find B, compute the point halfway between t1 and t2:
+
+q(at (t1 + t2)/2) == D
+
+Next, compute where D must be if we know the value of B:
+
+_12 = A/2 + B/2
+12_ = B/2 + C/2
+123 = A/4 + B/2 + C/4
+    = D
+    
+Group the known values on one side:
+
+B   = D*2 - A/2 - C/2
+*/
+
+static double interp_quad_coords(const double* src, double t)
+{
+    double ab = interp(src[0], src[2], t);
+    double bc = interp(src[2], src[4], t);
+    double abc = interp(ab, bc, t);
+    return abc;
+}
+
+void sub_divide(const Quadratic& src, double t1, double t2, Quadratic& dst) {
+    double ax = dst[0].x = interp_quad_coords(&src[0].x, t1);
+    double ay = dst[0].y = interp_quad_coords(&src[0].y, t1);
+    double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2);
+    double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2);
+    double cx = dst[2].x = interp_quad_coords(&src[0].x, t2);
+    double cy = dst[2].y = interp_quad_coords(&src[0].y, t2);
+    /* bx = */ dst[1].x = 2*dx - (ax + cx)/2;
+    /* by = */ dst[1].y = 2*dy - (ay + cy)/2;
+}
+
+/* classic one t subdivision */
+static void interp_quad_coords(const double* src, double* dst, double t)
+{
+    double ab = interp(src[0], src[2], t);
+    double bc = interp(src[2], src[4], t);
+
+    dst[0] = src[0];
+    dst[2] = ab;
+    dst[4] = interp(ab, bc, t);
+    dst[6] = bc;
+    dst[8] = src[4];
+}
+
+void chop_at(const Quadratic& src, QuadraticPair& dst, double t)
+{
+    interp_quad_coords(&src[0].x, &dst.pts[0].x, t);
+    interp_quad_coords(&src[0].y, &dst.pts[0].y, t);
+}