share derivative code with extrema logic, remove some dead code.
git-svn-id: http://skia.googlecode.com/svn/trunk@9050 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/src/core/SkGeometry.cpp b/src/core/SkGeometry.cpp
index 8bf68d9..2004578 100644
--- a/src/core/SkGeometry.cpp
+++ b/src/core/SkGeometry.cpp
@@ -1398,15 +1398,7 @@
// coeff[1] for t
// coeff[2] for constant term
//
-#if 0
-static void rat_numer_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) {
- coeff[0] = src[0] + src[4] - 2 * src[2] * w;
- coeff[1] = 2 * (src[2] * w - src[0]);
- coeff[0] = src[0];
-}
-#endif
-
-static SkScalar rat_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) {
+static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) {
SkASSERT(src);
SkASSERT(t >= 0 && t <= SK_Scalar1);
@@ -1426,23 +1418,35 @@
// F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w)
//
-// {t^2 (2 P0 - 2 P2 - 2 P0 w + 2 P2 w), t (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w), -2 P0 w + 2 P1 w}
+// t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w)
+// t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w)
+// t^0 : -2 P0 w + 2 P1 w
+//
+// We disregard magnitude, so we can freely ignore the denominator of F', and
+// divide the numerator by 2
//
// coeff[0] for t^2
-// coeff[1] for t
-// coeff[2] for constant term
+// coeff[1] for t^1
+// coeff[2] for t^0
//
-static void rat_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) {
- SkScalar diff40 = src[4] - src[0];
- SkScalar diff20 = 2 * w * (src[2] - src[0]);
- coeff[0] = 2 * (w * diff40 - diff40);
- coeff[1] = 2 * (diff40 - diff20);
- coeff[2] = diff20;
+static void conic_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) {
+ const SkScalar P20 = src[4] - src[0];
+ const SkScalar P10 = src[2] - src[0];
+ const SkScalar wP10 = w * P10;
+ coeff[0] = w * P20 - P20;
+ coeff[1] = P20 - 2 * wP10;
+ coeff[2] = wP10;
}
-static bool rat_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) {
+static SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) {
SkScalar coeff[3];
- rat_deriv_coeff(src, w, coeff);
+ conic_deriv_coeff(coord, w, coeff);
+ return t * (t * coeff[0] + coeff[1]) + coeff[2];
+}
+
+static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) {
+ SkScalar coeff[3];
+ conic_deriv_coeff(src, w, coeff);
SkScalar tValues[2];
int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues);
@@ -1483,47 +1487,12 @@
dst[2].set(src[2].fX * 1, src[2].fY * 1, 1);
}
-/* Derivative of conic : just the numerator, as the denom has no P values
- and can be ignored if we want to return a "normalized" tangent vector.
-
- 2 (P2 t (1 + t (-1 + w)) - P0 (-1 + t) (t (-1 + w) - w) + P1 (1 - 2 t) w)
-
- -- grouping by powers of t yields --
-
- t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w)
- t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w)
- t^0 : -2 P0 w + 2 P1 w
-
- We can trivially divide everything by 2 to simplify
-*/
-static SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) {
- // At^2 + Bt + C == t * (t * A + B) + C
-
- const SkScalar P0 = coord[0];
- const SkScalar P1 = coord[2];
- const SkScalar P2 = coord[4];
- const SkScalar P20 = P2 - P0;
- const SkScalar P10 = P1 - P0;
- const SkScalar wP10 = w * P10;
- // 2 P0 - 2 P2 - 2 P0 w + 2 P2 w
- // 2 * (P0 - P2 - P0w + P2w)
- SkScalar A = w * P20 - P20;
- // -2 P0 + 2 P2 + 4 P0 w - 4 P1 w
- // 2 * (P2 - P0 + 2 * w (P0 - P1))
- // 2 * (w * (P0 - P1) + P2 - P0)
- SkScalar B = P20 - 2 * wP10;
- // -2 P0 w + 2 P1 w
- SkScalar C = wP10;
-
- return t * (t * A + B) + C;
-}
-
void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const {
SkASSERT(t >= 0 && t <= SK_Scalar1);
if (pt) {
- pt->set(rat_eval_pos(&fPts[0].fX, fW, t),
- rat_eval_pos(&fPts[0].fY, fW, t));
+ pt->set(conic_eval_pos(&fPts[0].fX, fW, t),
+ conic_eval_pos(&fPts[0].fY, fW, t));
}
if (tangent) {
tangent->set(conic_eval_tan(&fPts[0].fX, fW, t),
@@ -1559,7 +1528,7 @@
}
static SkScalar subdivide_w_value(SkScalar w) {
- return SkScalarSqrt((1 + w) * SK_ScalarHalf);
+ return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf);
}
void SkConic::chop(SkConic dst[2]) const {
@@ -1637,11 +1606,11 @@
}
bool SkConic::findXExtrema(SkScalar* t) const {
- return rat_find_extrema(&fPts[0].fX, fW, t);
+ return conic_find_extrema(&fPts[0].fX, fW, t);
}
bool SkConic::findYExtrema(SkScalar* t) const {
- return rat_find_extrema(&fPts[0].fY, fW, t);
+ return conic_find_extrema(&fPts[0].fY, fW, t);
}
bool SkConic::chopAtXExtrema(SkConic dst[2]) const {