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/QuadraticIntersection.cpp b/experimental/Intersection/QuadraticIntersection.cpp
new file mode 100644
index 0000000..9a92c69
--- /dev/null
+++ b/experimental/Intersection/QuadraticIntersection.cpp
@@ -0,0 +1,188 @@
+#include "CubicIntersection.h"
+#include "Intersections.h"
+#include "IntersectionUtilities.h"
+#include "LineIntersection.h"
+
+class QuadraticIntersections : public Intersections {
+public:
+
+QuadraticIntersections(const Quadratic& q1, const Quadratic& q2, Intersections& i)
+ : quad1(q1)
+ , quad2(q2)
+ , intersections(i)
+ , depth(0)
+ , splits(0) {
+}
+
+bool intersect() {
+ double minT1, minT2, maxT1, maxT2;
+ if (!bezier_clip(quad2, quad1, minT1, maxT1)) {
+ return false;
+ }
+ if (!bezier_clip(quad1, quad2, minT2, maxT2)) {
+ return false;
+ }
+ int split;
+ if (maxT1 - minT1 < maxT2 - minT2) {
+ intersections.swap();
+ minT2 = 0;
+ maxT2 = 1;
+ split = maxT1 - minT1 > tClipLimit;
+ } else {
+ minT1 = 0;
+ maxT1 = 1;
+ split = (maxT2 - minT2 > tClipLimit) << 1;
+ }
+ return chop(minT1, maxT1, minT2, maxT2, split);
+}
+
+protected:
+
+bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
+ Quadratic smaller, larger;
+ // FIXME: carry last subdivide and reduceOrder result with quad
+ sub_divide(quad1, minT1, maxT1, intersections.swapped() ? larger : smaller);
+ sub_divide(quad2, minT2, maxT2, intersections.swapped() ? smaller : larger);
+ Quadratic smallResult;
+ if (reduceOrder(smaller, smallResult) <= 2) {
+ Quadratic largeResult;
+ if (reduceOrder(larger, largeResult) <= 2) {
+ _Point pt;
+ const _Line& smallLine = (const _Line&) smallResult;
+ const _Line& largeLine = (const _Line&) largeResult;
+ if (!lineIntersect(smallLine, largeLine, &pt)) {
+ return false;
+ }
+ double smallT = t_at(smallLine, pt);
+ double largeT = t_at(largeLine, pt);
+ if (intersections.swapped()) {
+ smallT = interp(minT2, maxT2, smallT);
+ largeT = interp(minT1, maxT1, largeT);
+ } else {
+ smallT = interp(minT1, maxT1, smallT);
+ largeT = interp(minT2, maxT2, largeT);
+ }
+ intersections.add(smallT, largeT);
+ return true;
+ }
+ }
+ double minT, maxT;
+ if (!bezier_clip(smaller, larger, minT, maxT)) {
+ if (minT == maxT) {
+ if (intersections.swapped()) {
+ minT1 = (minT1 + maxT1) / 2;
+ minT2 = interp(minT2, maxT2, minT);
+ } else {
+ minT1 = interp(minT1, maxT1, minT);
+ minT2 = (minT2 + maxT2) / 2;
+ }
+ intersections.add(minT1, minT2);
+ return true;
+ }
+ return false;
+ }
+
+ int split;
+ if (intersections.swapped()) {
+ double newMinT1 = interp(minT1, maxT1, minT);
+ double newMaxT1 = interp(minT1, maxT1, maxT);
+ split = (newMaxT1 - newMinT1 > (maxT1 - minT1) * tClipLimit) << 1;
+ printf("%s d=%d s=%d new1=(%g,%g) old1=(%g,%g) split=%d\n", __FUNCTION__, depth,
+ splits, newMinT1, newMaxT1, minT1, maxT1, split);
+ minT1 = newMinT1;
+ maxT1 = newMaxT1;
+ } else {
+ double newMinT2 = interp(minT2, maxT2, minT);
+ double newMaxT2 = interp(minT2, maxT2, maxT);
+ split = newMaxT2 - newMinT2 > (maxT2 - minT2) * tClipLimit;
+ printf("%s d=%d s=%d new2=(%g,%g) old2=(%g,%g) split=%d\n", __FUNCTION__, depth,
+ splits, newMinT2, newMaxT2, minT2, maxT2, split);
+ minT2 = newMinT2;
+ maxT2 = newMaxT2;
+ }
+ return chop(minT1, maxT1, minT2, maxT2, split);
+}
+
+bool chop(double minT1, double maxT1, double minT2, double maxT2, int split) {
+ ++depth;
+ intersections.swap();
+ if (split) {
+ ++splits;
+ if (split & 2) {
+ double middle1 = (maxT1 + minT1) / 2;
+ intersect(minT1, middle1, minT2, maxT2);
+ intersect(middle1, maxT1, minT2, maxT2);
+ } else {
+ double middle2 = (maxT2 + minT2) / 2;
+ intersect(minT1, maxT1, minT2, middle2);
+ intersect(minT1, maxT1, middle2, maxT2);
+ }
+ --splits;
+ intersections.swap();
+ --depth;
+ return intersections.intersected();
+ }
+ bool result = intersect(minT1, maxT1, minT2, maxT2);
+ intersections.swap();
+ --depth;
+ return result;
+}
+
+private:
+
+static const double tClipLimit = 0.8; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf see Multiple intersections
+const Quadratic& quad1;
+const Quadratic& quad2;
+Intersections& intersections;
+int depth;
+int splits;
+};
+
+bool intersectStart(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
+ QuadraticIntersections q(q1, q2, i);
+ return q.intersect();
+}
+
+
+// Another approach is to start with the implicit form of one curve and solve
+// by substituting in the parametric form of the other.
+// The downside of this approach is that early rejects are difficult to come by.
+// http://planetmath.org/encyclopedia/GaloisTheoreticDerivationOfTheQuarticFormula.html#step
+/*
+given x^4 + ax^3 + bx^2 + cx + d
+the resolvent cubic is x^3 - 2bx^2 + (b^2 + ac - 4d)x + (c^2 + a^2d - abc)
+use the cubic formula (CubicRoots.cpp) to find the radical expressions t1, t2, and t3.
+
+(x - r1 r2) (x - r3 r4) = x^2 - (t2 + t3 - t1) / 2 x + d
+s = r1*r2 = ((t2 + t3 - t1) + sqrt((t2 + t3 - t1)^2 - 16*d)) / 4
+t = r3*r4 = ((t2 + t3 - t1) - sqrt((t2 + t3 - t1)^2 - 16*d)) / 4
+
+u = r1+r2 = (-a + sqrt(a^2 - 4*t1)) / 2
+v = r3+r4 = (-a - sqrt(a^2 - 4*t1)) / 2
+
+r1 = (u + sqrt(u^2 - 4*s)) / 2
+r2 = (u - sqrt(u^2 - 4*s)) / 2
+r3 = (v + sqrt(v^2 - 4*t)) / 2
+r4 = (v - sqrt(v^2 - 4*t)) / 2
+*/
+
+
+/* square root of complex number
+http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
+Algebraic formula
+When the number is expressed using Cartesian coordinates the following formula
+ can be used for the principal square root:[5][6]
+
+sqrt(x + iy) = sqrt((r + x) / 2) +/- i*sqrt((r - x) / 2)
+
+where the sign of the imaginary part of the root is taken to be same as the sign
+ of the imaginary part of the original number, and
+
+r = abs(x + iy) = sqrt(x^2 + y^2)
+
+is the absolute value or modulus of the original number. The real part of the
+principal value is always non-negative.
+The other square root is simply –1 times the principal square root; in other
+words, the two square roots of a number sum to 0.
+ */
+
\ No newline at end of file