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add extrema for conics

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git-svn-id: http://skia.googlecode.com/svn/trunk@8712 2bbb7eff-a529-9590-31e7-b0007b416f81
This commit is contained in:
mike@reedtribe.org 2013-04-17 01:21:01 +00:00
parent 17a2c919d0
commit 0c5c3867bd
2 changed files with 92 additions and 31 deletions
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5
include/core/SkGeometry.h
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@ -222,6 +222,11 @@ struct SkRationalQuad {
int computeQuadPOW2(SkScalar tol) const;
int chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;
bool findXExtrema(SkScalar* t) const;
bool findYExtrema(SkScalar* t) const;
bool chopAtXExtrema(SkRationalQuad dst[2]) const;
bool chopAtYExtrema(SkRationalQuad dst[2]) const;
};
#endif

112
src/core/SkGeometry.cpp
View File

@ -1383,7 +1383,30 @@ int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,
///////////////////////////////////////////////////////////////////////////////
static SkScalar eval_ratquad(const SkScalar src[], SkScalar w, SkScalar t) {
// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w)
// ------------------------------------------
// ((1 - t)^2 + t^2 + 2 (1 - t) t w)
//
// = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0}
// ------------------------------------------------
// {t^2 (2 - 2 w), t (-2 + 2 w), 1}
//
// Take the parametric specification for the conic (either X or Y) and return
// in coeff[] the coefficients for the simple quadratic polynomial
// coeff[0] for t^2
// 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) {
SkASSERT(src);
SkASSERT(t >= 0 && t <= SK_Scalar1);
@ -1401,42 +1424,36 @@ static SkScalar eval_ratquad(const SkScalar src[], SkScalar w, SkScalar t) {
return SkScalarDiv(numer, denom);
}
#if 0
// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w)
// ------------------------------------------
// ((1 - t)^2 + t^2 + 2 (1 - t) t w)
//
// = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0}
// ------------------------------------------------
// {t^2 (2 - 2 w), t (-2 + 2 w), 1}
//
// 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}
//
// Take the parametric specification for the conic (either X or Y) and return
// in coeff[] the coefficients for the simple quadratic polynomial
// coeff[0] for t^2
// coeff[1] for t
// coeff[2] for constant term
//
static void conic_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];
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;
}
// coeff[0] for t^2
// coeff[1] for t
// coeff[2] for constant term
//
static void conic_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) {
coeff[0] = 2 * (src[0] - src[2] + w * (src[4] - src[0]));
coeff[1] = 2 (src[4] - src[0] + 2 * w * (src[0] - src[2]));
coeff[2] = 2 * w * (src[2] - src[0]);
static bool rat_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) {
SkScalar coeff[3];
rat_deriv_coeff(src, w, coeff);
SkScalar tValues[2];
int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues);
SkASSERT(0 == roots || 1 == roots);
if (1 == roots) {
*t = tValues[0];
return true;
}
return false;
}
#endif
struct SkP3D {
SkScalar fX, fY, fZ;
@ -1470,8 +1487,8 @@ void SkRationalQuad::evalAt(SkScalar t, SkPoint* pt) const {
SkASSERT(t >= 0 && t <= SK_Scalar1);
if (pt) {
pt->set(eval_ratquad(&fPts[0].fX, fW, t),
eval_ratquad(&fPts[0].fY, fW, t));
pt->set(rat_eval_pos(&fPts[0].fX, fW, t),
rat_eval_pos(&fPts[0].fY, fW, t));
}
}
@ -1579,3 +1596,42 @@ int SkRationalQuad::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const {
SkASSERT(endPts - pts == (2 * (1 << pow2) + 1));
return 1 << pow2;
}
bool SkRationalQuad::findXExtrema(SkScalar* t) const {
return rat_find_extrema(&fPts[0].fX, fW, t);
}
bool SkRationalQuad::findYExtrema(SkScalar* t) const {
return rat_find_extrema(&fPts[0].fY, fW, t);
}
bool SkRationalQuad::chopAtXExtrema(SkRationalQuad dst[2]) const {
SkScalar t;
if (this->findXExtrema(&t)) {
this->chopAt(t, dst);
// now clean-up the middle, since we know t was meant to be at
// an X-extrema
SkScalar value = dst[0].fPts[2].fX;
dst[0].fPts[1].fX = value;
dst[1].fPts[0].fX = value;
dst[1].fPts[1].fX = value;
return true;
}
return false;
}
bool SkRationalQuad::chopAtYExtrema(SkRationalQuad dst[2]) const {
SkScalar t;
if (this->findYExtrema(&t)) {
this->chopAt(t, dst);
// now clean-up the middle, since we know t was meant to be at
// an Y-extrema
SkScalar value = dst[0].fPts[2].fY;
dst[0].fPts[1].fY = value;
dst[1].fPts[0].fY = value;
dst[1].fPts[1].fY = value;
return true;
}
return false;
}