Result of running tools/sanitize_source_files.py (which was added in https://codereview.appspot.com/6465078/)
This CL is part II of IV (I broke down the 1280 files into 4 CLs).
Review URL: https://codereview.appspot.com/6474054
git-svn-id: http://skia.googlecode.com/svn/trunk@5263 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/experimental/Intersection/CubicParameterization.cpp b/experimental/Intersection/CubicParameterization.cpp
index bb75771..7656c66 100644
--- a/experimental/Intersection/CubicParameterization.cpp
+++ b/experimental/Intersection/CubicParameterization.cpp
@@ -3,7 +3,7 @@
/* from http://tom.cs.byu.edu/~tom/papers/cvgip84.pdf 4.1
*
- * This paper proves that Syvester's method can compute the implicit form of
+ * This paper proves that Syvester's method can compute the implicit form of
* the quadratic from the parameterzied form.
*
* Given x = a*t*t*t + b*t*t + c*t + d (the parameterized form)
@@ -28,30 +28,30 @@
*
* Resultant[a*t^3 + b*t^2 + c*t + d - x, e*t^3 + f*t^2 + g*t + h - y, t]
*
- * -d^3 e^3 + c d^2 e^2 f - b d^2 e f^2 + a d^2 f^3 - c^2 d e^2 g +
- * 2 b d^2 e^2 g + b c d e f g - 3 a d^2 e f g - a c d f^2 g -
- * b^2 d e g^2 + 2 a c d e g^2 + a b d f g^2 - a^2 d g^3 + c^3 e^2 h -
- * 3 b c d e^2 h + 3 a d^2 e^2 h - b c^2 e f h + 2 b^2 d e f h +
- * a c d e f h + a c^2 f^2 h - 2 a b d f^2 h + b^2 c e g h -
- * 2 a c^2 e g h - a b d e g h - a b c f g h + 3 a^2 d f g h +
- * a^2 c g^2 h - b^3 e h^2 + 3 a b c e h^2 - 3 a^2 d e h^2 +
- * a b^2 f h^2 - 2 a^2 c f h^2 - a^2 b g h^2 + a^3 h^3 + 3 d^2 e^3 x -
- * 2 c d e^2 f x + 2 b d e f^2 x - 2 a d f^3 x + c^2 e^2 g x -
- * 4 b d e^2 g x - b c e f g x + 6 a d e f g x + a c f^2 g x +
- * b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x +
- * 3 b c e^2 h x - 6 a d e^2 h x - 2 b^2 e f h x - a c e f h x +
- * 2 a b f^2 h x + a b e g h x - 3 a^2 f g h x + 3 a^2 e h^2 x -
- * 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 +
- * 2 b e^2 g x^2 - 3 a e f g x^2 + 3 a e^2 h x^2 + e^3 x^3 -
- * c^3 e^2 y + 3 b c d e^2 y - 3 a d^2 e^2 y + b c^2 e f y -
- * 2 b^2 d e f y - a c d e f y - a c^2 f^2 y + 2 a b d f^2 y -
- * b^2 c e g y + 2 a c^2 e g y + a b d e g y + a b c f g y -
- * 3 a^2 d f g y - a^2 c g^2 y + 2 b^3 e h y - 6 a b c e h y +
- * 6 a^2 d e h y - 2 a b^2 f h y + 4 a^2 c f h y + 2 a^2 b g h y -
- * 3 a^3 h^2 y - 3 b c e^2 x y + 6 a d e^2 x y + 2 b^2 e f x y +
- * a c e f x y - 2 a b f^2 x y - a b e g x y + 3 a^2 f g x y -
- * 6 a^2 e h x y - 3 a e^2 x^2 y - b^3 e y^2 + 3 a b c e y^2 -
- * 3 a^2 d e y^2 + a b^2 f y^2 - 2 a^2 c f y^2 - a^2 b g y^2 +
+ * -d^3 e^3 + c d^2 e^2 f - b d^2 e f^2 + a d^2 f^3 - c^2 d e^2 g +
+ * 2 b d^2 e^2 g + b c d e f g - 3 a d^2 e f g - a c d f^2 g -
+ * b^2 d e g^2 + 2 a c d e g^2 + a b d f g^2 - a^2 d g^3 + c^3 e^2 h -
+ * 3 b c d e^2 h + 3 a d^2 e^2 h - b c^2 e f h + 2 b^2 d e f h +
+ * a c d e f h + a c^2 f^2 h - 2 a b d f^2 h + b^2 c e g h -
+ * 2 a c^2 e g h - a b d e g h - a b c f g h + 3 a^2 d f g h +
+ * a^2 c g^2 h - b^3 e h^2 + 3 a b c e h^2 - 3 a^2 d e h^2 +
+ * a b^2 f h^2 - 2 a^2 c f h^2 - a^2 b g h^2 + a^3 h^3 + 3 d^2 e^3 x -
+ * 2 c d e^2 f x + 2 b d e f^2 x - 2 a d f^3 x + c^2 e^2 g x -
+ * 4 b d e^2 g x - b c e f g x + 6 a d e f g x + a c f^2 g x +
+ * b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x +
+ * 3 b c e^2 h x - 6 a d e^2 h x - 2 b^2 e f h x - a c e f h x +
+ * 2 a b f^2 h x + a b e g h x - 3 a^2 f g h x + 3 a^2 e h^2 x -
+ * 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 +
+ * 2 b e^2 g x^2 - 3 a e f g x^2 + 3 a e^2 h x^2 + e^3 x^3 -
+ * c^3 e^2 y + 3 b c d e^2 y - 3 a d^2 e^2 y + b c^2 e f y -
+ * 2 b^2 d e f y - a c d e f y - a c^2 f^2 y + 2 a b d f^2 y -
+ * b^2 c e g y + 2 a c^2 e g y + a b d e g y + a b c f g y -
+ * 3 a^2 d f g y - a^2 c g^2 y + 2 b^3 e h y - 6 a b c e h y +
+ * 6 a^2 d e h y - 2 a b^2 f h y + 4 a^2 c f h y + 2 a^2 b g h y -
+ * 3 a^3 h^2 y - 3 b c e^2 x y + 6 a d e^2 x y + 2 b^2 e f x y +
+ * a c e f x y - 2 a b f^2 x y - a b e g x y + 3 a^2 f g x y -
+ * 6 a^2 e h x y - 3 a e^2 x^2 y - b^3 e y^2 + 3 a b c e y^2 -
+ * 3 a^2 d e y^2 + a b^2 f y^2 - 2 a^2 c f y^2 - a^2 b g y^2 +
* 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3
*/
@@ -75,7 +75,7 @@
// FIXME: factoring version unwritten
// static bool straight_forward = true;
-/* from CubicParameterizationCode.cpp output:
+/* from CubicParameterizationCode.cpp output:
* double A = e * e * e;
* double B = -3 * a * e * e;
* double C = 3 * a * a * e;
@@ -96,7 +96,7 @@
// start of generated code
static double calc_xx(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
-3 * d * e * e * e
+ c * e * e * f
- b * e * f * f
@@ -108,7 +108,7 @@
static double calc_xy(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
-3 * b * c * e * e
+ 6 * a * d * e * e
+ 2 * b * b * e * f
@@ -121,7 +121,7 @@
static double calc_yy(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
-b * b * b * e
+ 3 * a * b * c * e
- 3 * a * a * d * e
@@ -133,7 +133,7 @@
static double calc_x(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
3 * d * d * e * e * e
- 2 * c * d * e * e * f
+ 2 * b * d * e * f * f
@@ -159,7 +159,7 @@
static double calc_y(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
-c * c * c * e * e
+ 3 * b * c * d * e * e
- 3 * a * d * d * e * e
@@ -185,7 +185,7 @@
static double calc_c(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
-d * d * d * e * e * e
+ c * d * d * e * e * f
- b * d * d * e * f * f
@@ -231,65 +231,65 @@
*/
static double calc_c(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
-d*d*d*e*e*e - 3*d*d*(3*c*e*e*f + 3*b*e*(-3*f*f + 2*e*g) + a*(9*f*f*f - 9*e*f*g + e*e*h)) -
- h*(27*c*c*c*e*e - 27*c*c*(3*b*e*f - 3*a*f*f + 2*a*e*g) +
- h*(-27*b*b*b*e + 27*a*b*b*f - 9*a*a*b*g + a*a*a*h) +
- 9*c*(9*b*b*e*g + a*b*(-9*f*g + 3*e*h) + a*a*(3*g*g - 2*f*h))) +
- 3*d*(9*c*c*e*e*g + 9*b*b*e*(3*g*g - 2*f*h) + 3*a*b*(-9*f*g*g + 6*f*f*h + e*g*h) +
+ return
+d*d*d*e*e*e - 3*d*d*(3*c*e*e*f + 3*b*e*(-3*f*f + 2*e*g) + a*(9*f*f*f - 9*e*f*g + e*e*h)) -
+ h*(27*c*c*c*e*e - 27*c*c*(3*b*e*f - 3*a*f*f + 2*a*e*g) +
+ h*(-27*b*b*b*e + 27*a*b*b*f - 9*a*a*b*g + a*a*a*h) +
+ 9*c*(9*b*b*e*g + a*b*(-9*f*g + 3*e*h) + a*a*(3*g*g - 2*f*h))) +
+ 3*d*(9*c*c*e*e*g + 9*b*b*e*(3*g*g - 2*f*h) + 3*a*b*(-9*f*g*g + 6*f*f*h + e*g*h) +
a*a*(9*g*g*g - 9*f*g*h + e*h*h) + 3*c*(3*b*e*(-3*f*g + e*h) + a*(9*f*f*g - 6*e*g*g - e*f*h)))
;
}
-// - Power(e - 3*f + 3*g - h,3)*Power(x,3)
+// - Power(e - 3*f + 3*g - h,3)*Power(x,3)
static double calc_xxx(double e3f3gh) {
return -e3f3gh * e3f3gh * e3f3gh;
}
static double calc_y(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
-+ 3*(6*b*d*d*e*e - d*d*d*e*e + 18*b*b*d*e*f - 18*b*d*d*e*f -
- 9*b*d*d*f*f - 54*b*b*d*e*g + 12*b*d*d*e*g - 27*b*b*d*g*g - 18*b*b*b*e*h + 18*b*b*d*e*h +
- 18*b*b*d*f*h + a*a*a*h*h - 9*b*b*b*h*h + 9*c*c*c*e*(e + 2*h) +
- a*a*(-3*b*h*(2*g + h) + d*(-27*g*g + 9*g*h - h*(2*e + h) + 9*f*(g + h))) +
- a*(9*b*b*h*(2*f + h) - 3*b*d*(6*f*f - 6*f*(3*g - 2*h) + g*(-9*g + h) + e*(g + h)) +
- d*d*(e*e + 9*f*(3*f - g) + e*(-9*f - 9*g + 2*h))) -
- 9*c*c*(d*e*(e + 2*g) + 3*b*(f*h + e*(f + h)) + a*(-3*f*f - 6*f*h + 2*(g*h + e*(g + h)))) +
- 3*c*(d*d*e*(e + 2*f) + a*a*(3*g*g + 6*g*h - 2*h*(2*f + h)) + 9*b*b*(g*h + e*(g + h)) +
- a*d*(-9*f*f - 18*f*g + 6*g*g + f*h + e*(f + 12*g + h)) +
- b*(d*(-3*e*e + 9*f*g + e*(9*f + 9*g - 6*h)) + 3*a*(h*(2*e - 3*g + h) - 3*f*(g + h))))) // *y
+ return
++ 3*(6*b*d*d*e*e - d*d*d*e*e + 18*b*b*d*e*f - 18*b*d*d*e*f -
+ 9*b*d*d*f*f - 54*b*b*d*e*g + 12*b*d*d*e*g - 27*b*b*d*g*g - 18*b*b*b*e*h + 18*b*b*d*e*h +
+ 18*b*b*d*f*h + a*a*a*h*h - 9*b*b*b*h*h + 9*c*c*c*e*(e + 2*h) +
+ a*a*(-3*b*h*(2*g + h) + d*(-27*g*g + 9*g*h - h*(2*e + h) + 9*f*(g + h))) +
+ a*(9*b*b*h*(2*f + h) - 3*b*d*(6*f*f - 6*f*(3*g - 2*h) + g*(-9*g + h) + e*(g + h)) +
+ d*d*(e*e + 9*f*(3*f - g) + e*(-9*f - 9*g + 2*h))) -
+ 9*c*c*(d*e*(e + 2*g) + 3*b*(f*h + e*(f + h)) + a*(-3*f*f - 6*f*h + 2*(g*h + e*(g + h)))) +
+ 3*c*(d*d*e*(e + 2*f) + a*a*(3*g*g + 6*g*h - 2*h*(2*f + h)) + 9*b*b*(g*h + e*(g + h)) +
+ a*d*(-9*f*f - 18*f*g + 6*g*g + f*h + e*(f + 12*g + h)) +
+ b*(d*(-3*e*e + 9*f*g + e*(9*f + 9*g - 6*h)) + 3*a*(h*(2*e - 3*g + h) - 3*f*(g + h))))) // *y
;
}
static double calc_yy(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
-- 3*(18*c*c*c*e - 18*c*c*d*e + 6*c*d*d*e - d*d*d*e + 3*c*d*d*f - 9*c*c*d*g + a*a*a*h + 9*c*c*c*h -
- 9*b*b*b*(e + 2*h) - a*a*(d*(e - 9*f + 18*g - 7*h) + 3*c*(2*f - 6*g + h)) +
- a*(-9*c*c*(2*e - 6*f + 2*g - h) + d*d*(-7*e + 18*f - 9*g + h) + 3*c*d*(7*e - 17*f + 3*g + h)) +
- 9*b*b*(3*c*(e + g + h) + a*(f + 2*h) - d*(e - 2*(f - 3*g + h))) -
- 3*b*(-(d*d*(e - 6*f + 2*g)) - 3*c*d*(e + 3*f + 3*g - h) + 9*c*c*(e + f + h) + a*a*(g + 2*h) +
- a*(c*(-3*e + 9*f + 9*g + 3*h) + d*(e + 3*f - 17*g + 7*h)))) // *Power(y,2)
+ return
+- 3*(18*c*c*c*e - 18*c*c*d*e + 6*c*d*d*e - d*d*d*e + 3*c*d*d*f - 9*c*c*d*g + a*a*a*h + 9*c*c*c*h -
+ 9*b*b*b*(e + 2*h) - a*a*(d*(e - 9*f + 18*g - 7*h) + 3*c*(2*f - 6*g + h)) +
+ a*(-9*c*c*(2*e - 6*f + 2*g - h) + d*d*(-7*e + 18*f - 9*g + h) + 3*c*d*(7*e - 17*f + 3*g + h)) +
+ 9*b*b*(3*c*(e + g + h) + a*(f + 2*h) - d*(e - 2*(f - 3*g + h))) -
+ 3*b*(-(d*d*(e - 6*f + 2*g)) - 3*c*d*(e + 3*f + 3*g - h) + 9*c*c*(e + f + h) + a*a*(g + 2*h) +
+ a*(c*(-3*e + 9*f + 9*g + 3*h) + d*(e + 3*f - 17*g + 7*h)))) // *Power(y,2)
;
}
-// + Power(a - 3*b + 3*c - d,3)*Power(y,3)
+// + Power(a - 3*b + 3*c - d,3)*Power(y,3)
static double calc_yyy(double a3b3cd) {
return a3b3cd * a3b3cd * a3b3cd;
}
static double calc_xx(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
// + Power(x,2)*
-(-3*(-9*b*e*f*f + 9*a*f*f*f + 6*b*e*e*g - 9*a*e*f*g + 27*b*e*f*g - 27*a*f*f*g + 18*a*e*g*g - 54*b*e*g*g +
- 27*a*f*g*g + 27*b*f*g*g - 18*a*g*g*g + a*e*e*h - 9*b*e*e*h + 3*a*e*f*h + 9*b*e*f*h + 9*a*f*f*h -
- 18*b*f*f*h - 21*a*e*g*h + 51*b*e*g*h - 9*a*f*g*h - 27*b*f*g*h + 18*a*g*g*h + 7*a*e*h*h - 18*b*e*h*h - 3*a*f*h*h +
- 18*b*f*h*h - 6*a*g*h*h - 3*b*g*h*h + a*h*h*h +
- 3*c*(-9*f*f*(g - 2*h) + 3*g*g*h - f*h*(9*g + 2*h) + e*e*(f - 6*g + 6*h) +
- e*(9*f*g + 6*g*g - 17*f*h - 3*g*h + 3*h*h)) -
- d*(e*e*e + e*e*(-6*f - 3*g + 7*h) - 9*(2*f - g)*(f*f + g*g - f*(g + h)) +
+(-3*(-9*b*e*f*f + 9*a*f*f*f + 6*b*e*e*g - 9*a*e*f*g + 27*b*e*f*g - 27*a*f*f*g + 18*a*e*g*g - 54*b*e*g*g +
+ 27*a*f*g*g + 27*b*f*g*g - 18*a*g*g*g + a*e*e*h - 9*b*e*e*h + 3*a*e*f*h + 9*b*e*f*h + 9*a*f*f*h -
+ 18*b*f*f*h - 21*a*e*g*h + 51*b*e*g*h - 9*a*f*g*h - 27*b*f*g*h + 18*a*g*g*h + 7*a*e*h*h - 18*b*e*h*h - 3*a*f*h*h +
+ 18*b*f*h*h - 6*a*g*h*h - 3*b*g*h*h + a*h*h*h +
+ 3*c*(-9*f*f*(g - 2*h) + 3*g*g*h - f*h*(9*g + 2*h) + e*e*(f - 6*g + 6*h) +
+ e*(9*f*g + 6*g*g - 17*f*h - 3*g*h + 3*h*h)) -
+ d*(e*e*e + e*e*(-6*f - 3*g + 7*h) - 9*(2*f - g)*(f*f + g*g - f*(g + h)) +
e*(18*f*f + 9*g*g + 3*g*h + h*h - 3*f*(3*g + 7*h)))) )
;
}
@@ -301,35 +301,35 @@
static double calc_x(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
// + x*
-(-3*(27*b*b*e*g*g - 27*a*b*f*g*g + 9*a*a*g*g*g - 18*b*b*e*f*h + 18*a*b*f*f*h + 3*a*b*e*g*h -
- 27*b*b*e*g*h - 9*a*a*f*g*h + 27*a*b*f*g*h - 9*a*a*g*g*h + a*a*e*h*h - 9*a*b*e*h*h +
- 27*b*b*e*h*h + 6*a*a*f*h*h - 18*a*b*f*h*h - 9*b*b*f*h*h + 3*a*a*g*h*h +
- 6*a*b*g*h*h - a*a*h*h*h + 9*c*c*(e*e*(g - 3*h) - 3*f*f*h + e*(3*f + 2*g)*h) +
- d*d*(e*e*e - 9*f*f*f + 9*e*f*(f + g) - e*e*(3*f + 6*g + h)) +
- d*(-3*c*(-9*f*f*g + e*e*(2*f - 6*g - 3*h) + e*(9*f*g + 6*g*g + f*h)) +
- a*(-18*f*f*f - 18*e*g*g + 18*g*g*g - 2*e*e*h + 3*e*g*h + 2*e*h*h + 9*f*f*(3*g + 2*h) +
- 3*f*(6*e*g - 9*g*g - e*h - 6*g*h)) - 3*b*(9*f*g*g + e*e*(4*g - 3*h) - 6*f*f*h -
- e*(6*f*f + g*(18*g + h) - 3*f*(3*g + 4*h)))) +
- 3*c*(3*b*(e*e*h + 3*f*g*h - e*(3*f*g - 6*f*h + 6*g*h + h*h)) +
+(-3*(27*b*b*e*g*g - 27*a*b*f*g*g + 9*a*a*g*g*g - 18*b*b*e*f*h + 18*a*b*f*f*h + 3*a*b*e*g*h -
+ 27*b*b*e*g*h - 9*a*a*f*g*h + 27*a*b*f*g*h - 9*a*a*g*g*h + a*a*e*h*h - 9*a*b*e*h*h +
+ 27*b*b*e*h*h + 6*a*a*f*h*h - 18*a*b*f*h*h - 9*b*b*f*h*h + 3*a*a*g*h*h +
+ 6*a*b*g*h*h - a*a*h*h*h + 9*c*c*(e*e*(g - 3*h) - 3*f*f*h + e*(3*f + 2*g)*h) +
+ d*d*(e*e*e - 9*f*f*f + 9*e*f*(f + g) - e*e*(3*f + 6*g + h)) +
+ d*(-3*c*(-9*f*f*g + e*e*(2*f - 6*g - 3*h) + e*(9*f*g + 6*g*g + f*h)) +
+ a*(-18*f*f*f - 18*e*g*g + 18*g*g*g - 2*e*e*h + 3*e*g*h + 2*e*h*h + 9*f*f*(3*g + 2*h) +
+ 3*f*(6*e*g - 9*g*g - e*h - 6*g*h)) - 3*b*(9*f*g*g + e*e*(4*g - 3*h) - 6*f*f*h -
+ e*(6*f*f + g*(18*g + h) - 3*f*(3*g + 4*h)))) +
+ 3*c*(3*b*(e*e*h + 3*f*g*h - e*(3*f*g - 6*f*h + 6*g*h + h*h)) +
a*(9*f*f*(g - 2*h) + f*h*(-e + 9*g + 4*h) - 3*(2*g*g*h + e*(2*g*g - 4*g*h + h*h))))) )
;
}
-
+
static double calc_xy(double a, double b, double c, double d,
double e, double f, double g, double h) {
- return
+ return
// + x*3*
-(-2*a*d*e*e - 7*d*d*e*e + 15*a*d*e*f + 21*d*d*e*f - 9*a*d*f*f - 18*d*d*f*f - 15*a*d*e*g -
- 3*d*d*e*g - 9*a*a*f*g + 9*d*d*f*g + 18*a*a*g*g + 9*a*d*g*g + 2*a*a*e*h - 2*d*d*e*h +
- 3*a*a*f*h + 15*a*d*f*h - 21*a*a*g*h - 15*a*d*g*h + 7*a*a*h*h + 2*a*d*h*h -
- 9*c*c*(2*e*e + 3*f*f + 3*f*h - 2*g*h + e*(-3*f - 4*g + h)) +
- 9*b*b*(3*g*g - 3*g*h + 2*h*(-2*f + h) + e*(-2*f + 3*g + h)) +
- 3*b*(3*c*(e*e + 3*e*(f - 3*g) + (9*f - 3*g - h)*h) + a*(6*f*f + e*g - 9*f*g - 9*g*g - 5*e*h + 9*f*h + 14*g*h - 7*h*h) +
- d*(-e*e + 12*f*f - 27*f*g + e*(-9*f + 20*g - 5*h) + g*(9*g + h))) +
- 3*c*(a*(-(e*f) - 9*f*f + 27*f*g - 12*g*g + 5*e*h - 20*f*h + 9*g*h + h*h) +
- d*(7*e*e + 9*f*f + 9*f*g - 6*g*g - f*h + e*(-14*f - 9*g + 5*h)))) // *y
+(-2*a*d*e*e - 7*d*d*e*e + 15*a*d*e*f + 21*d*d*e*f - 9*a*d*f*f - 18*d*d*f*f - 15*a*d*e*g -
+ 3*d*d*e*g - 9*a*a*f*g + 9*d*d*f*g + 18*a*a*g*g + 9*a*d*g*g + 2*a*a*e*h - 2*d*d*e*h +
+ 3*a*a*f*h + 15*a*d*f*h - 21*a*a*g*h - 15*a*d*g*h + 7*a*a*h*h + 2*a*d*h*h -
+ 9*c*c*(2*e*e + 3*f*f + 3*f*h - 2*g*h + e*(-3*f - 4*g + h)) +
+ 9*b*b*(3*g*g - 3*g*h + 2*h*(-2*f + h) + e*(-2*f + 3*g + h)) +
+ 3*b*(3*c*(e*e + 3*e*(f - 3*g) + (9*f - 3*g - h)*h) + a*(6*f*f + e*g - 9*f*g - 9*g*g - 5*e*h + 9*f*h + 14*g*h - 7*h*h) +
+ d*(-e*e + 12*f*f - 27*f*g + e*(-9*f + 20*g - 5*h) + g*(9*g + h))) +
+ 3*c*(a*(-(e*f) - 9*f*f + 27*f*g - 12*g*g + 5*e*h - 20*f*h + 9*g*h + h*h) +
+ d*(7*e*e + 9*f*f + 9*f*g - 6*g*g - f*h + e*(-14*f - 9*g + 5*h)))) // *y
;
}
@@ -358,7 +358,7 @@
c = 3*C - 3*D
d = D
*/
-
+
/* http://www.algorithmist.net/bezier3.html
p = 3 * A
q = 3 * B
@@ -369,9 +369,9 @@
d = D - A + q - r
B(t) = a + t * (b + t * (c + t * d))
-
+
so
-
+
B(t) = a + t*b + t*t*(c + t*d)
= a + t*b + t*t*c + t*t*t*d
*/