skia/sgl/SkGeometry.cpp - Issue 113827: Remove the remainder of the skia source code from the Chromium repo....

Unified Diff: skia/sgl/SkGeometry.cpp

Issue 113827: Remove the remainder of the skia source code from the Chromium repo.... (Closed) Base URL: svn://chrome-svn/chrome/trunk/src/

Patch Set: Created 11 years, 7 months ago

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Index: skia/sgl/SkGeometry.cpp

===================================================================

--- skia/sgl/SkGeometry.cpp (revision 16859)

+++ skia/sgl/SkGeometry.cpp (working copy)

@@ -1,1072 +0,0 @@

-/* libs/graphics/sgl/SkGeometry.cpp

-**

-** Licensed under the Apache License, Version 2.0 (the "License");

-** you may not use this file except in compliance with the License.

-** You may obtain a copy of the License at

-**

-** http://www.apache.org/licenses/LICENSE-2.0

-**

-** Unless required by applicable law or agreed to in writing, software

-** distributed under the License is distributed on an "AS IS" BASIS,

-** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

-** See the License for the specific language governing permissions and

-** limitations under the License.

-*/

-#include "SkGeometry.h"

-#include "Sk64.h"

-#include "SkMatrix.h"

-/** If defined, this makes eval_quad and eval_cubic do more setup (sometimes

- involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul.

- May also introduce overflow of fixed when we compute our setup.

-*/

-#ifdef SK_SCALAR_IS_FIXED

- #define DIRECT_EVAL_OF_POLYNOMIALS

-#endif

-////////////////////////////////////////////////////////////////////////

-#ifdef SK_SCALAR_IS_FIXED

- static int is_not_monotonic(int a, int b, int c, int d)

- {

- return (((a - b) | (b - c) | (c - d)) & ((b - a) | (c - b) | (d - c))) >> 31;

- }

- static int is_not_monotonic(int a, int b, int c)

- {

- return (((a - b) | (b - c)) & ((b - a) | (c - b))) >> 31;

- }

-#else

- static int is_not_monotonic(float a, float b, float c)

- {

- float ab = a - b;

- float bc = b - c;

- if (ab < 0)

- bc = -bc;

- return ab == 0 || bc < 0;

- }

-#endif

-////////////////////////////////////////////////////////////////////////

-static bool is_unit_interval(SkScalar x)

- return x > 0 && x < SK_Scalar1;

-static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio)

- SkASSERT(ratio);

- if (numer < 0)

- {

- numer = -numer;

- denom = -denom;

- }

- if (denom == 0 || numer == 0 || numer >= denom)

- return 0;

- SkScalar r = SkScalarDiv(numer, denom);

- SkASSERT(r >= 0 && r < SK_Scalar1);

- if (r == 0) // catch underflow if numer <<<< denom

- return 0;

- *ratio = r;

- return 1;

-/** From Numerical Recipes in C.

- Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C])

- x1 = Q / A

- x2 = C / Q

-*/

-int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2])

- SkASSERT(roots);

- if (A == 0)

- return valid_unit_divide(-C, B, roots);

- SkScalar* r = roots;

-#ifdef SK_SCALAR_IS_FLOAT

- float R = B*B - 4*A*C;

- if (R < 0) // complex roots

- return 0;

- R = sk_float_sqrt(R);

-#else

- Sk64 RR, tmp;

- RR.setMul(B,B);

- tmp.setMul(A,C);

- tmp.shiftLeft(2);

- RR.sub(tmp);

- if (RR.isNeg())

- return 0;

- SkFixed R = RR.getSqrt();

-#endif

- SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2;

- r += valid_unit_divide(Q, A, r);

- r += valid_unit_divide(C, Q, r);

- if (r - roots == 2)

- {

- if (roots[0] > roots[1])

- SkTSwap<SkScalar>(roots[0], roots[1]);

- else if (roots[0] == roots[1]) // nearly-equal?

- r -= 1; // skip the double root

- }

- return (int)(r - roots);

-#ifdef SK_SCALAR_IS_FIXED

-/** Trim A/B/C down so that they are all <= 32bits

- and then call SkFindUnitQuadRoots()

-*/

-static int Sk64FindFixedQuadRoots(const Sk64& A, const Sk64& B, const Sk64& C, SkFixed roots[2])

- int na = A.shiftToMake32();

- int nb = B.shiftToMake32();

- int nc = C.shiftToMake32();

- int shift = SkMax32(na, SkMax32(nb, nc));

- SkASSERT(shift >= 0);

- return SkFindUnitQuadRoots(A.getShiftRight(shift), B.getShiftRight(shift), C.getShiftRight(shift), roots);

-#endif

-/////////////////////////////////////////////////////////////////////////////////////

-static SkScalar eval_quad(const SkScalar src[], SkScalar t)

- SkASSERT(src);

- SkASSERT(t >= 0 && t <= SK_Scalar1);

-#ifdef DIRECT_EVAL_OF_POLYNOMIALS

- SkScalar C = src[0];

- SkScalar A = src[4] - 2 * src[2] + C;

- SkScalar B = 2 * (src[2] - C);

- return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);

-#else

- SkScalar ab = SkScalarInterp(src[0], src[2], t);

- SkScalar bc = SkScalarInterp(src[2], src[4], t);

- return SkScalarInterp(ab, bc, t);

-#endif

-static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t)

- SkScalar A = src[4] - 2 * src[2] + src[0];

- SkScalar B = src[2] - src[0];

- return 2 * SkScalarMulAdd(A, t, B);

-static SkScalar eval_quad_derivative_at_half(const SkScalar src[])

- SkScalar A = src[4] - 2 * src[2] + src[0];

- SkScalar B = src[2] - src[0];

- return A + 2 * B;

-void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent)

- SkASSERT(src);

- SkASSERT(t >= 0 && t <= SK_Scalar1);

- if (pt)

- pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t));

- if (tangent)

- tangent->set(eval_quad_derivative(&src[0].fX, t),

- eval_quad_derivative(&src[0].fY, t));

-void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent)

- SkASSERT(src);

- if (pt)

- {

- SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);

- SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);

- SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);

- SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);

- pt->set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));

- }

- if (tangent)

- tangent->set(eval_quad_derivative_at_half(&src[0].fX),

- eval_quad_derivative_at_half(&src[0].fY));

-static void interp_quad_coords(const SkScalar* src, SkScalar* dst, SkScalar t)

- SkScalar ab = SkScalarInterp(src[0], src[2], t);

- SkScalar bc = SkScalarInterp(src[2], src[4], t);

- dst[0] = src[0];

- dst[2] = ab;

- dst[4] = SkScalarInterp(ab, bc, t);

- dst[6] = bc;

- dst[8] = src[4];

-void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t)

- SkASSERT(t > 0 && t < SK_Scalar1);

- interp_quad_coords(&src[0].fX, &dst[0].fX, t);

- interp_quad_coords(&src[0].fY, &dst[0].fY, t);

-void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5])

- SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);

- SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);

- SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);

- SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);

- dst[0] = src[0];

- dst[1].set(x01, y01);

- dst[2].set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));

- dst[3].set(x12, y12);

- dst[4] = src[2];

-/** Quad'(t) = At + B, where

- A = 2(a - 2b + c)

- B = 2(b - a)

- Solve for t, only if it fits between 0 < t < 1

-*/

-int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1])

- /* At + B == 0

- t = -B / A

- */

-#ifdef SK_SCALAR_IS_FIXED

- return is_not_monotonic(a, b, c) && valid_unit_divide(a - b, a - b - b + c, tValue);

-#else

- return valid_unit_divide(a - b, a - b - b + c, tValue);

-#endif

-static void flatten_double_quad_extrema(SkScalar coords[14])

- coords[2] = coords[6] = coords[4];

-static void force_quad_monotonic_in_y(SkPoint pts[3])

- // zap pts[1].fY to the nearest value

- SkScalar ab = SkScalarAbs(pts[0].fY - pts[1].fY);

- SkScalar bc = SkScalarAbs(pts[1].fY - pts[2].fY);

- pts[1].fY = ab < bc ? pts[0].fY : pts[2].fY;

-/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is

- stored in dst[]. Guarantees that the 1/2 quads will be monotonic.

-*/

-int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5])

- SkASSERT(src);

- SkASSERT(dst);

-#if 0

- static bool once = true;

- if (once)

- {

- once = false;

- SkPoint s[3] = { 0, 26398, 0, 26331, 0, 20621428 };

- SkPoint d[6];

- int n = SkChopQuadAtYExtrema(s, d);

- SkDebugf("chop=%d, Y=[%x %x %x %x %x %x]\n", n, d[0].fY, d[1].fY, d[2].fY, d[3].fY, d[4].fY, d[5].fY);

- }

-#endif

- SkScalar a = src[0].fY;

- SkScalar b = src[1].fY;

- SkScalar c = src[2].fY;

- if (is_not_monotonic(a, b, c))

- {

- SkScalar tValue;

- if (valid_unit_divide(a - b, a - b - b + c, &tValue))

- {

- SkChopQuadAt(src, dst, tValue);

- flatten_double_quad_extrema(&dst[0].fY);

- return 1;

- }

- // if we get here, we need to force dst to be monotonic, even though

- // we couldn't compute a unit_divide value (probably underflow).

- b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c;

- }

- dst[0].set(src[0].fX, a);

- dst[1].set(src[1].fX, b);

- dst[2].set(src[2].fX, c);

- return 0;

-// F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2

-// F'(t) = 2 (b - a) + 2 (a - 2b + c) t

-// F''(t) = 2 (a - 2b + c)

-//

-// A = 2 (b - a)

-// B = 2 (a - 2b + c)

-//

-// Maximum curvature for a quadratic means solving

-// Fx' Fx'' + Fy' Fy'' = 0

-//

-// t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2)

-//

-int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5])

- SkScalar Ax = src[1].fX - src[0].fX;

- SkScalar Ay = src[1].fY - src[0].fY;

- SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX;

- SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY;

- SkScalar t = 0; // 0 means don't chop

-#ifdef SK_SCALAR_IS_FLOAT

- (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t);

-#else

- // !!! should I use SkFloat here? seems like it

- Sk64 numer, denom, tmp;

- numer.setMul(Ax, -Bx);

- tmp.setMul(Ay, -By);

- numer.add(tmp);

- if (numer.isPos()) // do nothing if numer <= 0

- {

- denom.setMul(Bx, Bx);

- tmp.setMul(By, By);

- denom.add(tmp);

- SkASSERT(!denom.isNeg());

- if (numer < denom)

- {

- t = numer.getFixedDiv(denom);

- SkASSERT(t >= 0 && t <= SK_Fixed1); // assert that we're numerically stable (ha!)

- if ((unsigned)t >= SK_Fixed1) // runtime check for numerical stability

- t = 0; // ignore the chop

- }

-#endif

- if (t == 0)

- {

- memcpy(dst, src, 3 * sizeof(SkPoint));

- return 1;

- }

- else

- {

- SkChopQuadAt(src, dst, t);

- return 2;

- }

-////////////////////////////////////////////////////////////////////////////////////////

-///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS /////

-////////////////////////////////////////////////////////////////////////////////////////

-static void get_cubic_coeff(const SkScalar pt[], SkScalar coeff[4])

- coeff[0] = pt[6] + 3*(pt[2] - pt[4]) - pt[0];

- coeff[1] = 3*(pt[4] - pt[2] - pt[2] + pt[0]);

- coeff[2] = 3*(pt[2] - pt[0]);

- coeff[3] = pt[0];

-void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4])

- SkASSERT(pts);

- if (cx)

- get_cubic_coeff(&pts[0].fX, cx);

- if (cy)

- get_cubic_coeff(&pts[0].fY, cy);

-static SkScalar eval_cubic(const SkScalar src[], SkScalar t)

- SkASSERT(src);

- SkASSERT(t >= 0 && t <= SK_Scalar1);

- if (t == 0)

- return src[0];

-#ifdef DIRECT_EVAL_OF_POLYNOMIALS

- SkScalar D = src[0];

- SkScalar A = src[6] + 3*(src[2] - src[4]) - D;

- SkScalar B = 3*(src[4] - src[2] - src[2] + D);

- SkScalar C = 3*(src[2] - D);

- return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D);

-#else

- SkScalar ab = SkScalarInterp(src[0], src[2], t);

- SkScalar bc = SkScalarInterp(src[2], src[4], t);

- SkScalar cd = SkScalarInterp(src[4], src[6], t);

- SkScalar abc = SkScalarInterp(ab, bc, t);

- SkScalar bcd = SkScalarInterp(bc, cd, t);

- return SkScalarInterp(abc, bcd, t);

-#endif

-/** return At^2 + Bt + C

-*/

-static SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t)

- SkASSERT(t >= 0 && t <= SK_Scalar1);

- return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);

-static SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t)

- SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];

- SkScalar B = 2*(src[4] - 2 * src[2] + src[0]);

- SkScalar C = src[2] - src[0];

- return eval_quadratic(A, B, C, t);

-static SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t)

- SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];

- SkScalar B = src[4] - 2 * src[2] + src[0];

- return SkScalarMulAdd(A, t, B);

-void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, SkVector* tangent, SkVector* curvature)

- SkASSERT(src);

- SkASSERT(t >= 0 && t <= SK_Scalar1);

- if (loc)

- loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t));

- if (tangent)

- tangent->set(eval_cubic_derivative(&src[0].fX, t),

- eval_cubic_derivative(&src[0].fY, t));

- if (curvature)

- curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),

- eval_cubic_2ndDerivative(&src[0].fY, t));

-/** Cubic'(t) = At^2 + Bt + C, where

- A = 3(-a + 3(b - c) + d)

- B = 6(a - 2b + c)

- C = 3(b - a)

- Solve for t, keeping only those that fit betwee 0 < t < 1

-*/

-int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, SkScalar tValues[2])

-#ifdef SK_SCALAR_IS_FIXED

- if (!is_not_monotonic(a, b, c, d))

- return 0;

-#endif

- // we divide A,B,C by 3 to simplify

- SkScalar A = d - a + 3*(b - c);

- SkScalar B = 2*(a - b - b + c);

- SkScalar C = b - a;

- return SkFindUnitQuadRoots(A, B, C, tValues);

-static void interp_cubic_coords(const SkScalar* src, SkScalar* dst, SkScalar t)

- SkScalar ab = SkScalarInterp(src[0], src[2], t);

- SkScalar bc = SkScalarInterp(src[2], src[4], t);

- SkScalar cd = SkScalarInterp(src[4], src[6], t);

- SkScalar abc = SkScalarInterp(ab, bc, t);

- SkScalar bcd = SkScalarInterp(bc, cd, t);

- SkScalar abcd = SkScalarInterp(abc, bcd, t);

- dst[0] = src[0];

- dst[2] = ab;

- dst[4] = abc;

- dst[6] = abcd;

- dst[8] = bcd;

- dst[10] = cd;

- dst[12] = src[6];

-void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t)

- SkASSERT(t > 0 && t < SK_Scalar1);

- interp_cubic_coords(&src[0].fX, &dst[0].fX, t);

- interp_cubic_coords(&src[0].fY, &dst[0].fY, t);

-void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar tValues[], int roots)

-#ifdef SK_DEBUG

- {

- for (int i = 0; i < roots - 1; i++)

- {

- SkASSERT(is_unit_interval(tValues[i]));

- SkASSERT(is_unit_interval(tValues[i+1]));

- SkASSERT(tValues[i] < tValues[i+1]);

- }

-#endif

- if (dst)

- {

- if (roots == 0) // nothing to chop

- memcpy(dst, src, 4*sizeof(SkPoint));

- else

- {

- SkScalar t = tValues[0];

- SkPoint tmp[4];

- for (int i = 0; i < roots; i++)

- {

- SkChopCubicAt(src, dst, t);

- if (i == roots - 1)

- break;

- SkDEBUGCODE(int valid =) valid_unit_divide(tValues[i+1] - tValues[i], SK_Scalar1 - tValues[i], &t);

- SkASSERT(valid);

- dst += 3;

- memcpy(tmp, dst, 4 * sizeof(SkPoint));

- src = tmp;

- }

-void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7])

- SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);

- SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);

- SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);

- SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);

- SkScalar x23 = SkScalarAve(src[2].fX, src[3].fX);

- SkScalar y23 = SkScalarAve(src[2].fY, src[3].fY);

- SkScalar x012 = SkScalarAve(x01, x12);

- SkScalar y012 = SkScalarAve(y01, y12);

- SkScalar x123 = SkScalarAve(x12, x23);

- SkScalar y123 = SkScalarAve(y12, y23);

- dst[0] = src[0];

- dst[1].set(x01, y01);

- dst[2].set(x012, y012);

- dst[3].set(SkScalarAve(x012, x123), SkScalarAve(y012, y123));

- dst[4].set(x123, y123);

- dst[5].set(x23, y23);

- dst[6] = src[3];

-static void flatten_double_cubic_extrema(SkScalar coords[14])

- coords[4] = coords[8] = coords[6];

-/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that

- the resulting beziers are monotonic in Y. This is called by the scan converter.

- Depending on what is returned, dst[] is treated as follows

- 0 dst[0..3] is the original cubic

- 1 dst[0..3] and dst[3..6] are the two new cubics

- 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics

- If dst == null, it is ignored and only the count is returned.

-*/

-int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10])

- SkScalar tValues[2];

- int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, src[3].fY, tValues);

- SkChopCubicAt(src, dst, tValues, roots);

- if (dst && roots > 0)

- {

- // we do some cleanup to ensure our Y extrema are flat

- flatten_double_cubic_extrema(&dst[0].fY);

- if (roots == 2)

- flatten_double_cubic_extrema(&dst[3].fY);

- }

- return roots;

-/** http://www.faculty.idc.ac.il/arik/quality/appendixA.html

- Inflection means that curvature is zero.

- Curvature is [F' x F''] / [F'^3]

- So we solve F'x X F''y - F'y X F''y == 0

- After some canceling of the cubic term, we get

- A = b - a

- B = c - 2b + a

- C = d - 3c + 3b - a

- (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0

-*/

-int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[])

- SkScalar Ax = src[1].fX - src[0].fX;

- SkScalar Ay = src[1].fY - src[0].fY;

- SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX;

- SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY;

- SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX;

- SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY;

- int count;

-#ifdef SK_SCALAR_IS_FLOAT

- count = SkFindUnitQuadRoots(Bx*Cy - By*Cx, Ax*Cy - Ay*Cx, Ax*By - Ay*Bx, tValues);

-#else

- Sk64 A, B, C, tmp;

- A.setMul(Bx, Cy);

- tmp.setMul(By, Cx);

- A.sub(tmp);

- B.setMul(Ax, Cy);

- tmp.setMul(Ay, Cx);

- B.sub(tmp);

- C.setMul(Ax, By);

- tmp.setMul(Ay, Bx);

- C.sub(tmp);

- count = Sk64FindFixedQuadRoots(A, B, C, tValues);

-#endif

- return count;

-int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10])

- SkScalar tValues[2];

- int count = SkFindCubicInflections(src, tValues);

- if (dst)

- {

- if (count == 0)

- memcpy(dst, src, 4 * sizeof(SkPoint));

- else

- SkChopCubicAt(src, dst, tValues, count);

- }

- return count + 1;

-template <typename T> void bubble_sort(T array[], int count)

- for (int i = count - 1; i > 0; --i)

- for (int j = i; j > 0; --j)

- if (array[j] < array[j-1])

- {

- T tmp(array[j]);

- array[j] = array[j-1];

- array[j-1] = tmp;

- }

-#include "SkFP.h"

-// newton refinement

-#if 0

-static SkScalar refine_cubic_root(const SkFP coeff[4], SkScalar root)

- // x1 = x0 - f(t) / f'(t)

- SkFP T = SkScalarToFloat(root);

- SkFP N, D;

- // f' = 3*coeff[0]*T^2 + 2*coeff[1]*T + coeff[2]

- D = SkFPMul(SkFPMul(coeff[0], SkFPMul(T,T)), 3);

- D = SkFPAdd(D, SkFPMulInt(SkFPMul(coeff[1], T), 2));

- D = SkFPAdd(D, coeff[2]);

- if (D == 0)

- return root;

- // f = coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3]

- N = SkFPMul(SkFPMul(SkFPMul(T, T), T), coeff[0]);

- N = SkFPAdd(N, SkFPMul(SkFPMul(T, T), coeff[1]));

- N = SkFPAdd(N, SkFPMul(T, coeff[2]));

- N = SkFPAdd(N, coeff[3]);

- if (N)

- {

- SkScalar delta = SkFPToScalar(SkFPDiv(N, D));

- if (delta)

- root -= delta;

- }

- return root;

-#endif

-#if defined _WIN32 && _MSC_VER >= 1300 && defined SK_SCALAR_IS_FIXED // disable warning : unreachable code if building fixed point for windows desktop

-#pragma warning ( disable : 4702 )

-#endif

-/* Solve coeff(t) == 0, returning the number of roots that

- lie withing 0 < t < 1.

- coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3]

-*/

-static int solve_cubic_polynomial(const SkFP coeff[4], SkScalar tValues[3])

-#ifndef SK_SCALAR_IS_FLOAT

- return 0; // this is not yet implemented for software float

-#endif

- if (SkScalarNearlyZero(coeff[0])) // we're just a quadratic

- {

- return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues);

- }

- SkFP a, b, c, Q, R;

- {

- SkASSERT(coeff[0] != 0);

- SkFP inva = SkFPInvert(coeff[0]);

- a = SkFPMul(coeff[1], inva);

- b = SkFPMul(coeff[2], inva);

- c = SkFPMul(coeff[3], inva);

- }

- Q = SkFPDivInt(SkFPSub(SkFPMul(a,a), SkFPMulInt(b, 3)), 9);

-// R = (2*a*a*a - 9*a*b + 27*c) / 54;

- R = SkFPMulInt(SkFPMul(SkFPMul(a, a), a), 2);

- R = SkFPSub(R, SkFPMulInt(SkFPMul(a, b), 9));

- R = SkFPAdd(R, SkFPMulInt(c, 27));

- R = SkFPDivInt(R, 54);

- SkFP Q3 = SkFPMul(SkFPMul(Q, Q), Q);

- SkFP R2MinusQ3 = SkFPSub(SkFPMul(R,R), Q3);

- SkFP adiv3 = SkFPDivInt(a, 3);

- SkScalar* roots = tValues;

- SkScalar r;

- if (SkFPLT(R2MinusQ3, 0)) // we have 3 real roots

- {

-#ifdef SK_SCALAR_IS_FLOAT

- float theta = sk_float_acos(R / sk_float_sqrt(Q3));

- float neg2RootQ = -2 * sk_float_sqrt(Q);

- r = neg2RootQ * sk_float_cos(theta/3) - adiv3;

- if (is_unit_interval(r))

- *roots++ = r;

- r = neg2RootQ * sk_float_cos((theta + 2*SK_ScalarPI)/3) - adiv3;

- if (is_unit_interval(r))

- *roots++ = r;

- r = neg2RootQ * sk_float_cos((theta - 2*SK_ScalarPI)/3) - adiv3;

- if (is_unit_interval(r))

- *roots++ = r;

- // now sort the roots

- bubble_sort(tValues, (int)(roots - tValues));

-#endif

- }

- else // we have 1 real root

- {

- SkFP A = SkFPAdd(SkFPAbs(R), SkFPSqrt(R2MinusQ3));

- A = SkFPCubeRoot(A);

- if (SkFPGT(R, 0))

- A = SkFPNeg(A);

- if (A != 0)

- A = SkFPAdd(A, SkFPDiv(Q, A));

- r = SkFPToScalar(SkFPSub(A, adiv3));

- if (is_unit_interval(r))

- *roots++ = r;

- }

- return (int)(roots - tValues);

-/* Looking for F' dot F'' == 0

- A = b - a

- B = c - 2b + a

- C = d - 3c + 3b - a

- F' = 3Ct^2 + 6Bt + 3A

- F'' = 6Ct + 6B

- F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB

-*/

-static void formulate_F1DotF2(const SkScalar src[], SkFP coeff[4])

- SkScalar a = src[2] - src[0];

- SkScalar b = src[4] - 2 * src[2] + src[0];

- SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0];

- SkFP A = SkScalarToFP(a);

- SkFP B = SkScalarToFP(b);

- SkFP C = SkScalarToFP(c);

- coeff[0] = SkFPMul(C, C);

- coeff[1] = SkFPMulInt(SkFPMul(B, C), 3);

- coeff[2] = SkFPMulInt(SkFPMul(B, B), 2);

- coeff[2] = SkFPAdd(coeff[2], SkFPMul(C, A));

- coeff[3] = SkFPMul(A, B);

-// EXPERIMENTAL: can set this to zero to accept all t-values 0 < t < 1

-//#define kMinTValueForChopping (SK_Scalar1 / 256)

-#define kMinTValueForChopping 0

-/* Looking for F' dot F'' == 0

- A = b - a

- B = c - 2b + a

- C = d - 3c + 3b - a

- F' = 3Ct^2 + 6Bt + 3A

- F'' = 6Ct + 6B

- F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB

-*/

-int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3])

- SkFP coeffX[4], coeffY[4];

- int i;

- formulate_F1DotF2(&src[0].fX, coeffX);

- formulate_F1DotF2(&src[0].fY, coeffY);

- for (i = 0; i < 4; i++)

- coeffX[i] = SkFPAdd(coeffX[i],coeffY[i]);

- SkScalar t[3];

- int count = solve_cubic_polynomial(coeffX, t);

- int maxCount = 0;

- // now remove extrema where the curvature is zero (mins)

- // !!!! need a test for this !!!!

- for (i = 0; i < count; i++)

- {

- // if (not_min_curvature())

- if (t[i] > kMinTValueForChopping && t[i] < SK_Scalar1 - kMinTValueForChopping)

- tValues[maxCount++] = t[i];

- }

- return maxCount;

-int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], SkScalar tValues[3])

- SkScalar t_storage[3];

- if (tValues == NULL)

- tValues = t_storage;

- int count = SkFindCubicMaxCurvature(src, tValues);

- if (dst)

- {

- if (count == 0)

- memcpy(dst, src, 4 * sizeof(SkPoint));

- else

- SkChopCubicAt(src, dst, tValues, count);

- }

- return count + 1;

-////////////////////////////////////////////////////////////////////////////////

-/* Find t value for quadratic [a, b, c] = d.

- Return 0 if there is no solution within [0, 1)

-*/

-static SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d)

- // At^2 + Bt + C = d

- SkScalar A = a - 2 * b + c;

- SkScalar B = 2 * (b - a);

- SkScalar C = a - d;

- SkScalar roots[2];

- int count = SkFindUnitQuadRoots(A, B, C, roots);

- SkASSERT(count <= 1);

- return count == 1 ? roots[0] : 0;

-/* given a quad-curve and a point (x,y), chop the quad at that point and return

- the new quad's offCurve point. Should only return false if the computed pos

- is the start of the curve (i.e. root == 0)

-*/

-static bool quad_pt2OffCurve(const SkPoint quad[3], SkScalar x, SkScalar y, SkPoint* offCurve)

- const SkScalar* base;

- SkScalar value;

- if (SkScalarAbs(x) < SkScalarAbs(y)) {

- base = &quad[0].fX;

- value = x;

- } else {

- base = &quad[0].fY;

- value = y;

- }

- // note: this returns 0 if it thinks value is out of range, meaning the

- // root might return something outside of [0, 1)

- SkScalar t = quad_solve(base[0], base[2], base[4], value);

- if (t > 0)

- {

- SkPoint tmp[5];

- SkChopQuadAt(quad, tmp, t);

- *offCurve = tmp[1];

- return true;

- } else {

- /* t == 0 means either the value triggered a root outside of [0, 1)

- For our purposes, we can ignore the <= 0 roots, but we want to

- catch the >= 1 roots (which given our caller, will basically mean

- a root of 1, give-or-take numerical instability). If we are in the

- >= 1 case, return the existing offCurve point.

- The test below checks to see if we are close to the "end" of the

- curve (near base[4]). Rather than specifying a tolerance, I just

- check to see if value is on to the right/left of the middle point

- (depending on the direction/sign of the end points).

- */

- if ((base[0] < base[4] && value > base[2]) ||

- (base[0] > base[4] && value < base[2])) // should root have been 1

- {

- *offCurve = quad[1];

- return true;

- }

- return false;

-static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = {

- { SK_Scalar1, 0 },

- { SK_Scalar1, SK_ScalarTanPIOver8 },

- { SK_ScalarRoot2Over2, SK_ScalarRoot2Over2 },

- { SK_ScalarTanPIOver8, SK_Scalar1 },

- { 0, SK_Scalar1 },

- { -SK_ScalarTanPIOver8, SK_Scalar1 },

- { -SK_ScalarRoot2Over2, SK_ScalarRoot2Over2 },

- { -SK_Scalar1, SK_ScalarTanPIOver8 },

- { -SK_Scalar1, 0 },

- { -SK_Scalar1, -SK_ScalarTanPIOver8 },

- { -SK_ScalarRoot2Over2, -SK_ScalarRoot2Over2 },

- { -SK_ScalarTanPIOver8, -SK_Scalar1 },

- { 0, -SK_Scalar1 },

- { SK_ScalarTanPIOver8, -SK_Scalar1 },

- { SK_ScalarRoot2Over2, -SK_ScalarRoot2Over2 },

- { SK_Scalar1, -SK_ScalarTanPIOver8 },

- { SK_Scalar1, 0 }

-};

-int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,

- SkRotationDirection dir, const SkMatrix* userMatrix,

- SkPoint quadPoints[])

- // rotate by x,y so that uStart is (1.0)

- SkScalar x = SkPoint::DotProduct(uStart, uStop);

- SkScalar y = SkPoint::CrossProduct(uStart, uStop);

- SkScalar absX = SkScalarAbs(x);

- SkScalar absY = SkScalarAbs(y);

- int pointCount;

- // check for (effectively) coincident vectors

- // this can happen if our angle is nearly 0 or nearly 180 (y == 0)

- // ... we use the dot-prod to distinguish between 0 and 180 (x > 0)

- if (absY <= SK_ScalarNearlyZero && x > 0 &&

- ((y >= 0 && kCW_SkRotationDirection == dir) ||

- (y <= 0 && kCCW_SkRotationDirection == dir))) {

- // just return the start-point

- quadPoints[0].set(SK_Scalar1, 0);

- pointCount = 1;

- } else {

- if (dir == kCCW_SkRotationDirection)

- y = -y;

- // what octant (quadratic curve) is [xy] in?

- int oct = 0;

- bool sameSign = true;

- if (0 == y)

- {

- oct = 4; // 180

- SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero);

- }

- else if (0 == x)

- {

- SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero);

- if (y > 0)

- oct = 2; // 90

- else

- oct = 6; // 270

- }

- else

- {

- if (y < 0)

- oct += 4;

- if ((x < 0) != (y < 0))

- {

- oct += 2;

- sameSign = false;

- }

- if ((absX < absY) == sameSign)

- oct += 1;

- }

- int wholeCount = oct << 1;

- memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint));

- const SkPoint* arc = &gQuadCirclePts[wholeCount];

- if (quad_pt2OffCurve(arc, x, y, &quadPoints[wholeCount + 1]))

- {

- quadPoints[wholeCount + 2].set(x, y);

- wholeCount += 2;

- }

- pointCount = wholeCount + 1;

- }

- // now handle counter-clockwise and the initial unitStart rotation

- SkMatrix matrix;

- matrix.setSinCos(uStart.fY, uStart.fX);

- if (dir == kCCW_SkRotationDirection) {

- matrix.preScale(SK_Scalar1, -SK_Scalar1);

- }

- if (userMatrix) {

- matrix.postConcat(*userMatrix);

- }

- matrix.mapPoints(quadPoints, pointCount);

- return pointCount;

-/////////////////////////////////////////////////////////////////////////////////////////

-#ifdef SK_DEBUG

-void SkGeometry::UnitTest()

-#ifdef SK_SUPPORT_UNITTEST

- SkPoint pts[3], dst[5];

- pts[0].set(0, 0);

- pts[1].set(100, 50);

- pts[2].set(0, 100);

- int count = SkChopQuadAtMaxCurvature(pts, dst);

- SkASSERT(count == 1 || count == 2);

-#endif

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