shape ops work in progress
add quartic solution for intersecting quadratics

git-svn-id: http://skia.googlecode.com/svn/trunk@5541 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/experimental/Intersection/QuarticRoot_Test.cpp b/experimental/Intersection/QuarticRoot_Test.cpp
new file mode 100644
index 0000000..2fe3e72
--- /dev/null
+++ b/experimental/Intersection/QuarticRoot_Test.cpp
@@ -0,0 +1,148 @@
+#include <assert.h>
+#include <math.h>
+#include "CubicUtilities.h"
+#include "Intersection_Tests.h"
+
+namespace QuarticRootTest {
+
+#include "QuarticRoot.cpp"
+
+}
+
+double mulA[] = {-3, -1, 1, 3};
+size_t mulACount = sizeof(mulA) / sizeof(mulA[0]);
+double rootB[] = {-9, -6, -3, -1, 0, 1, 3, 6, 9};
+size_t rootBCount = sizeof(rootB) / sizeof(rootB[0]);
+double rootC[] = {-8, -6, -2, -1, 0, 1, 2, 6, 8};
+size_t rootCCount = sizeof(rootC) / sizeof(rootC[0]);
+double rootD[] = {-7, -4, -1, 0, 1, 2, 5};
+size_t rootDCount = sizeof(rootD) / sizeof(rootD[0]);
+double rootE[] = {-5, -1, 0, 1, 7};
+size_t rootECount = sizeof(rootE) / sizeof(rootE[0]);
+
+static void quadraticTest() {
+    // (x - a)(x - b) == x^2 - (a + b)x + ab
+    for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
+        for (size_t bIndex = 0; bIndex < rootBCount; ++bIndex) {
+            for (size_t cIndex = 0; cIndex < rootCCount; ++cIndex) {
+                const double A = mulA[aIndex];
+                const double B = rootB[bIndex];
+                const double C = rootC[cIndex];
+                const double b = A * (B + C);
+                const double c = A * B * C;
+                double roots[2];
+                const int rootCount = QuarticRootTest::quadraticRootsX(A, b, c, roots);
+                const int expected = 1 + (B != C);
+                assert(rootCount == expected);
+                assert(approximately_equal(roots[0], -B)
+                        || approximately_equal(roots[0], -C));
+                if (B != C) {
+                    assert(!approximately_equal(roots[0], roots[1]));
+                    assert(approximately_equal(roots[1], -B)
+                            || approximately_equal(roots[1], -C));
+                }
+            }
+        }
+    }
+}
+
+static void cubicTest() {
+    // (x - a)(x - b)(x - c) == x^3 - (a + b + c)x^2 + (ab + bc + ac)x - abc
+    for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
+        for (size_t bIndex = 0; bIndex < rootBCount; ++bIndex) {
+            for (size_t cIndex = 0; cIndex < rootCCount; ++cIndex) {
+                for (size_t dIndex = 0; dIndex < rootDCount; ++dIndex) {
+                    const double A = mulA[aIndex];
+                    const double B = rootB[bIndex];
+                    const double C = rootC[cIndex];
+                    const double D = rootD[dIndex];
+                    const double b = A * (B + C + D);
+                    const double c = A * (B * C + C * D + B * D);
+                    const double d = A * B * C * D;
+                    double roots[3];
+                    const int rootCount = QuarticRootTest::cubicRootsX(A, b, c, d, roots);
+                    const int expected = 1 + (B != C) + (B != D && C != D);
+                    assert(rootCount == expected);
+                    assert(approximately_equal(roots[0], -B)
+                            || approximately_equal(roots[0], -C)
+                            || approximately_equal(roots[0], -D));
+                    if (expected > 1) {
+                        assert(!approximately_equal(roots[0], roots[1]));
+                        assert(approximately_equal(roots[1], -B)
+                                || approximately_equal(roots[1], -C)
+                                || approximately_equal(roots[1], -D));
+                        if (expected > 2) {
+                            assert(!approximately_equal(roots[0], roots[2])
+                                    && !approximately_equal(roots[1], roots[2]));
+                            assert(approximately_equal(roots[2], -B)
+                                    || approximately_equal(roots[2], -C)
+                                    || approximately_equal(roots[2], -D));
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+static void quarticTest() {
+    // (x - a)(x - b)(x - c)(x - d) == x^4 - (a + b + c + d)x^3
+    //   + (ab + bc + cd + ac + bd + cd)x^2 - (abc + bcd + abd + acd) * x + abcd
+    for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
+        for (size_t bIndex = 0; bIndex < rootBCount; ++bIndex) {
+            for (size_t cIndex = 0; cIndex < rootCCount; ++cIndex) {
+                for (size_t dIndex = 0; dIndex < rootDCount; ++dIndex) {
+                    for (size_t eIndex = 0; eIndex < rootECount; ++eIndex) {
+                        const double A = mulA[aIndex];
+                        const double B = rootB[bIndex];
+                        const double C = rootC[cIndex];
+                        const double D = rootD[dIndex];
+                        const double E = rootE[eIndex];
+                        const double b = A * (B + C + D + E);
+                        const double c = A * (B * C + C * D + B * D + B * E + C * E + D * E);
+                        const double d = A * (B * C * D + B * C * E + B * D * E + C * D * E);
+                        const double e = A * B * C * D * E;
+                        double roots[4];
+                        const int rootCount = QuarticRootTest::quarticRoots(A, b, c, d, e, roots);
+                        const int expected = 1 + (B != C) + (B != D && C != D) + (B != E && C != E && D != E);
+                        assert(rootCount == expected);
+                        assert(approximately_equal(roots[0], -B)
+                                || approximately_equal(roots[0], -C)
+                                || approximately_equal(roots[0], -D)
+                                || approximately_equal(roots[0], -E));
+                        if (expected > 1) {
+                            assert(!approximately_equal(roots[0], roots[1]));
+                            assert(approximately_equal(roots[1], -B)
+                                    || approximately_equal(roots[1], -C)
+                                    || approximately_equal(roots[1], -D)
+                                    || approximately_equal(roots[1], -E));
+                            if (expected > 2) {
+                                assert(!approximately_equal(roots[0], roots[2])
+                                        && !approximately_equal(roots[1], roots[2]));
+                                assert(approximately_equal(roots[2], -B)
+                                        || approximately_equal(roots[2], -C)
+                                        || approximately_equal(roots[2], -D)
+                                        || approximately_equal(roots[2], -E));
+                                if (expected > 3) {
+                                    assert(!approximately_equal(roots[0], roots[3])
+                                            && !approximately_equal(roots[1], roots[3])
+                                            && !approximately_equal(roots[2], roots[3]));
+                                    assert(approximately_equal(roots[3], -B)
+                                            || approximately_equal(roots[3], -C)
+                                            || approximately_equal(roots[3], -D)
+                                            || approximately_equal(roots[3], -E));
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+void QuarticRoot_Test() {
+    quadraticTest();
+    cubicTest();
+    quarticTest();
+}