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/CubeRoot.cpp b/experimental/Intersection/CubeRoot.cpp
new file mode 100644
index 0000000..e188b34
--- /dev/null
+++ b/experimental/Intersection/CubeRoot.cpp
@@ -0,0 +1,387 @@
+// http://metamerist.com/cbrt/CubeRoot.cpp
+//
+
+#include <math.h>
+#include "CubicIntersection.h"
+
+#define TEST_ALTERNATIVES 0
+#if TEST_ALTERNATIVES
+typedef float (*cuberootfnf) (float);
+typedef double (*cuberootfnd) (double);
+
+// estimate bits of precision (32-bit float case)
+inline int bits_of_precision(float a, float b)
+{
+ const double kd = 1.0 / log(2.0);
+
+ if (a==b)
+ return 23;
+
+ const double kdmin = pow(2.0, -23.0);
+
+ double d = fabs(a-b);
+ if (d < kdmin)
+ return 23;
+
+ return int(-log(d)*kd);
+}
+
+// estiamte bits of precision (64-bit double case)
+inline int bits_of_precision(double a, double b)
+{
+ const double kd = 1.0 / log(2.0);
+
+ if (a==b)
+ return 52;
+
+ const double kdmin = pow(2.0, -52.0);
+
+ double d = fabs(a-b);
+ if (d < kdmin)
+ return 52;
+
+ return int(-log(d)*kd);
+}
+
+// cube root via x^(1/3)
+static float pow_cbrtf(float x)
+{
+ return (float) pow(x, 1.0f/3.0f);
+}
+
+// cube root via x^(1/3)
+static double pow_cbrtd(double x)
+{
+ return pow(x, 1.0/3.0);
+}
+
+// cube root approximation using bit hack for 32-bit float
+static float cbrt_5f(float f)
+{
+ unsigned int* p = (unsigned int *) &f;
+ *p = *p/3 + 709921077;
+ return f;
+}
+#endif
+
+// cube root approximation using bit hack for 64-bit float
+// adapted from Kahan's cbrt
+static double cbrt_5d(double d)
+{
+ const unsigned int B1 = 715094163;
+ double t = 0.0;
+ unsigned int* pt = (unsigned int*) &t;
+ unsigned int* px = (unsigned int*) &d;
+ pt[1]=px[1]/3+B1;
+ return t;
+}
+
+#if TEST_ALTERNATIVES
+// cube root approximation using bit hack for 64-bit float
+// adapted from Kahan's cbrt
+#if 0
+static double quint_5d(double d)
+{
+ return sqrt(sqrt(d));
+
+ const unsigned int B1 = 71509416*5/3;
+ double t = 0.0;
+ unsigned int* pt = (unsigned int*) &t;
+ unsigned int* px = (unsigned int*) &d;
+ pt[1]=px[1]/5+B1;
+ return t;
+}
+#endif
+
+// iterative cube root approximation using Halley's method (float)
+static float cbrta_halleyf(const float a, const float R)
+{
+ const float a3 = a*a*a;
+ const float b= a * (a3 + R + R) / (a3 + a3 + R);
+ return b;
+}
+#endif
+
+// iterative cube root approximation using Halley's method (double)
+static double cbrta_halleyd(const double a, const double R)
+{
+ const double a3 = a*a*a;
+ const double b= a * (a3 + R + R) / (a3 + a3 + R);
+ return b;
+}
+
+#if TEST_ALTERNATIVES
+// iterative cube root approximation using Newton's method (float)
+static float cbrta_newtonf(const float a, const float x)
+{
+// return (1.0 / 3.0) * ((a + a) + x / (a * a));
+ return a - (1.0f / 3.0f) * (a - x / (a*a));
+}
+
+// iterative cube root approximation using Newton's method (double)
+static double cbrta_newtond(const double a, const double x)
+{
+ return (1.0/3.0) * (x / (a*a) + 2*a);
+}
+
+// cube root approximation using 1 iteration of Halley's method (double)
+static double halley_cbrt1d(double d)
+{
+ double a = cbrt_5d(d);
+ return cbrta_halleyd(a, d);
+}
+
+// cube root approximation using 1 iteration of Halley's method (float)
+static float halley_cbrt1f(float d)
+{
+ float a = cbrt_5f(d);
+ return cbrta_halleyf(a, d);
+}
+
+// cube root approximation using 2 iterations of Halley's method (double)
+static double halley_cbrt2d(double d)
+{
+ double a = cbrt_5d(d);
+ a = cbrta_halleyd(a, d);
+ return cbrta_halleyd(a, d);
+}
+#endif
+
+// cube root approximation using 3 iterations of Halley's method (double)
+static double halley_cbrt3d(double d)
+{
+ double a = cbrt_5d(d);
+ a = cbrta_halleyd(a, d);
+ a = cbrta_halleyd(a, d);
+ return cbrta_halleyd(a, d);
+}
+
+#if TEST_ALTERNATIVES
+// cube root approximation using 2 iterations of Halley's method (float)
+static float halley_cbrt2f(float d)
+{
+ float a = cbrt_5f(d);
+ a = cbrta_halleyf(a, d);
+ return cbrta_halleyf(a, d);
+}
+
+// cube root approximation using 1 iteration of Newton's method (double)
+static double newton_cbrt1d(double d)
+{
+ double a = cbrt_5d(d);
+ return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 2 iterations of Newton's method (double)
+static double newton_cbrt2d(double d)
+{
+ double a = cbrt_5d(d);
+ a = cbrta_newtond(a, d);
+ return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 3 iterations of Newton's method (double)
+static double newton_cbrt3d(double d)
+{
+ double a = cbrt_5d(d);
+ a = cbrta_newtond(a, d);
+ a = cbrta_newtond(a, d);
+ return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 4 iterations of Newton's method (double)
+static double newton_cbrt4d(double d)
+{
+ double a = cbrt_5d(d);
+ a = cbrta_newtond(a, d);
+ a = cbrta_newtond(a, d);
+ a = cbrta_newtond(a, d);
+ return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 2 iterations of Newton's method (float)
+static float newton_cbrt1f(float d)
+{
+ float a = cbrt_5f(d);
+ return cbrta_newtonf(a, d);
+}
+
+// cube root approximation using 2 iterations of Newton's method (float)
+static float newton_cbrt2f(float d)
+{
+ float a = cbrt_5f(d);
+ a = cbrta_newtonf(a, d);
+ return cbrta_newtonf(a, d);
+}
+
+// cube root approximation using 3 iterations of Newton's method (float)
+static float newton_cbrt3f(float d)
+{
+ float a = cbrt_5f(d);
+ a = cbrta_newtonf(a, d);
+ a = cbrta_newtonf(a, d);
+ return cbrta_newtonf(a, d);
+}
+
+// cube root approximation using 4 iterations of Newton's method (float)
+static float newton_cbrt4f(float d)
+{
+ float a = cbrt_5f(d);
+ a = cbrta_newtonf(a, d);
+ a = cbrta_newtonf(a, d);
+ a = cbrta_newtonf(a, d);
+ return cbrta_newtonf(a, d);
+}
+
+static double TestCubeRootf(const char* szName, cuberootfnf cbrt, double rA, double rB, int rN)
+{
+ const int N = rN;
+
+ float dd = float((rB-rA) / N);
+
+ // calculate 1M numbers
+ int i=0;
+ float d = (float) rA;
+
+ double s = 0.0;
+
+ for(d=(float) rA, i=0; i<N; i++, d += dd)
+ {
+ s += cbrt(d);
+ }
+
+ double bits = 0.0;
+ double worstx=0.0;
+ double worsty=0.0;
+ int minbits=64;
+
+ for(d=(float) rA, i=0; i<N; i++, d += dd)
+ {
+ float a = cbrt((float) d);
+ float b = (float) pow((double) d, 1.0/3.0);
+
+ int bc = bits_of_precision(a, b);
+ bits += bc;
+
+ if (b > 1.0e-6)
+ {
+ if (bc < minbits)
+ {
+ minbits = bc;
+ worstx = d;
+ worsty = a;
+ }
+ }
+ }
+
+ bits /= N;
+
+ printf(" %3d mbp %6.3f abp\n", minbits, bits);
+
+ return s;
+}
+
+
+static double TestCubeRootd(const char* szName, cuberootfnd cbrt, double rA, double rB, int rN)
+{
+ const int N = rN;
+
+ double dd = (rB-rA) / N;
+
+ int i=0;
+
+ double s = 0.0;
+ double d = 0.0;
+
+ for(d=rA, i=0; i<N; i++, d += dd)
+ {
+ s += cbrt(d);
+ }
+
+
+ double bits = 0.0;
+ double worstx = 0.0;
+ double worsty = 0.0;
+ int minbits = 64;
+ for(d=rA, i=0; i<N; i++, d += dd)
+ {
+ double a = cbrt(d);
+ double b = pow(d, 1.0/3.0);
+
+ int bc = bits_of_precision(a, b); // min(53, count_matching_bitsd(a, b) - 12);
+ bits += bc;
+
+ if (b > 1.0e-6)
+ {
+ if (bc < minbits)
+ {
+ bits_of_precision(a, b);
+ minbits = bc;
+ worstx = d;
+ worsty = a;
+ }
+ }
+ }
+
+ bits /= N;
+
+ printf(" %3d mbp %6.3f abp\n", minbits, bits);
+
+ return s;
+}
+
+static int _tmain()
+{
+ // a million uniform steps through the range from 0.0 to 1.0
+ // (doing uniform steps in the log scale would be better)
+ double a = 0.0;
+ double b = 1.0;
+ int n = 1000000;
+
+ printf("32-bit float tests\n");
+ printf("----------------------------------------\n");
+ TestCubeRootf("cbrt_5f", cbrt_5f, a, b, n);
+ TestCubeRootf("pow", pow_cbrtf, a, b, n);
+ TestCubeRootf("halley x 1", halley_cbrt1f, a, b, n);
+ TestCubeRootf("halley x 2", halley_cbrt2f, a, b, n);
+ TestCubeRootf("newton x 1", newton_cbrt1f, a, b, n);
+ TestCubeRootf("newton x 2", newton_cbrt2f, a, b, n);
+ TestCubeRootf("newton x 3", newton_cbrt3f, a, b, n);
+ TestCubeRootf("newton x 4", newton_cbrt4f, a, b, n);
+ printf("\n\n");
+
+ printf("64-bit double tests\n");
+ printf("----------------------------------------\n");
+ TestCubeRootd("cbrt_5d", cbrt_5d, a, b, n);
+ TestCubeRootd("pow", pow_cbrtd, a, b, n);
+ TestCubeRootd("halley x 1", halley_cbrt1d, a, b, n);
+ TestCubeRootd("halley x 2", halley_cbrt2d, a, b, n);
+ TestCubeRootd("halley x 3", halley_cbrt3d, a, b, n);
+ TestCubeRootd("newton x 1", newton_cbrt1d, a, b, n);
+ TestCubeRootd("newton x 2", newton_cbrt2d, a, b, n);
+ TestCubeRootd("newton x 3", newton_cbrt3d, a, b, n);
+ TestCubeRootd("newton x 4", newton_cbrt4d, a, b, n);
+ printf("\n\n");
+
+ return 0;
+}
+#endif
+
+double cube_root(double x) {
+ return halley_cbrt3d(x);
+}
+
+#if TEST_ALTERNATIVES
+// http://bytes.com/topic/c/answers/754588-tips-find-cube-root-program-using-c
+/* cube root */
+int icbrt(int n) {
+ int t=0, x=(n+2)/3; /* works for n=0 and n>=1 */
+ for(; t!=x;) {
+ int x3=x*x*x;
+ t=x;
+ x*=(2*n + x3);
+ x/=(2*x3 + n);
+ }
+ return x ; /* always(?) equal to floor(n^(1/3)) */
+}
+#endif