The Tor Browser: gfx/skia/trunk/src/pathops/SkDCubicToQuads.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/pathops/SkDCubicToQuads.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/pathops/SkDCubicToQuads.cpp

Sat, 03 Jan 2015 20:18:00 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Sat, 03 Jan 2015 20:18:00 +0100
branch: TOR_BUG_3246
changeset 7: 129ffea94266
permissions: -rw-r--r--

Conditionally enable double key logic according to:
private browsing mode or privacy.thirdparty.isolate preference and
implement in GetCookieStringCommon and FindCookie where it counts...
With some reservations of how to convince FindCookie users to test
condition and pass a nullptr when disabling double key logic.

 /*
 http://stackoverflow.com/questions/2009160/how-do-i-convert-the-2-control-points-of-a-cubic-curve-to-the-single-control-poi
 */
 /*
 Let's call the control points of the cubic Q0..Q3 and the control points of the quadratic P0..P2.
 Then for degree elevation, the equations are:
 Q0 = P0
 Q1 = 1/3 P0 + 2/3 P1
 Q2 = 2/3 P1 + 1/3 P2
 Q3 = P2
 In your case you have Q0..Q3 and you're solving for P0..P2. There are two ways to compute P1 from
  the equations above:
 P1 = 3/2 Q1 - 1/2 Q0
 P1 = 3/2 Q2 - 1/2 Q3
 If this is a degree-elevated cubic, then both equations will give the same answer for P1. Since
  it's likely not, your best bet is to average them. So,
 P1 = -1/4 Q0 + 3/4 Q1 + 3/4 Q2 - 1/4 Q3
 SkDCubic defined by: P1/2 - anchor points, C1/C2 control points
 |x| is the euclidean norm of x
 mid-point approx of cubic: a quad that shares the same anchors with the cubic and has the
  control point at C = (3·C2 - P2 + 3·C1 - P1)/4
 Algorithm
 pick an absolute precision (prec)
 Compute the Tdiv as the root of (cubic) equation
 sqrt(3)/18 · |P2 - 3·C2 + 3·C1 - P1|/2 · Tdiv ^ 3 = prec
 if Tdiv < 0.5 divide the cubic at Tdiv. First segment [0..Tdiv] can be approximated with by a
  quadratic, with a defect less than prec, by the mid-point approximation.
  Repeat from step 2 with the second resulted segment (corresponding to 1-Tdiv)
 .5<=Tdiv<1 - simply divide the cubic in two. The two halves can be approximated by the mid-point
  approximation
 Tdiv>=1 - the entire cubic can be approximated by the mid-point approximation
 confirmed by (maybe stolen from)
 http://www.caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
 // maybe in turn derived from  http://www.cccg.ca/proceedings/2004/36.pdf
 // also stored at http://www.cis.usouthal.edu/~hain/general/Publications/Bezier/bezier%20cccg04%20paper.pdf
 */
 #include "SkPathOpsCubic.h"
 #include "SkPathOpsLine.h"
 #include "SkPathOpsQuad.h"
 #include "SkReduceOrder.h"
 #include "SkTArray.h"
 #include "SkTSort.h"
 #define USE_CUBIC_END_POINTS 1
 static double calc_t_div(const SkDCubic& cubic, double precision, double start) {
     const double adjust = sqrt(3.) / 36;
     SkDCubic sub;
     const SkDCubic* cPtr;
     if (start == 0) {
         cPtr = &cubic;
     } else {
         // OPTIMIZE: special-case half-split ?
         sub = cubic.subDivide(start, 1);
         cPtr = &sub;
     }
     const SkDCubic& c = *cPtr;
     double dx = c[3].fX - 3 * (c[2].fX - c[1].fX) - c[0].fX;
     double dy = c[3].fY - 3 * (c[2].fY - c[1].fY) - c[0].fY;
     double dist = sqrt(dx * dx + dy * dy);
     double tDiv3 = precision / (adjust * dist);
     double t = SkDCubeRoot(tDiv3);
     if (start > 0) {
         t = start + (1 - start) * t;
     }
     return t;
 }
 SkDQuad SkDCubic::toQuad() const {
     SkDQuad quad;
     quad[0] = fPts[0];
     const SkDPoint fromC1 = {(3 * fPts[1].fX - fPts[0].fX) / 2, (3 * fPts[1].fY - fPts[0].fY) / 2};
     const SkDPoint fromC2 = {(3 * fPts[2].fX - fPts[3].fX) / 2, (3 * fPts[2].fY - fPts[3].fY) / 2};
     quad[1].fX = (fromC1.fX + fromC2.fX) / 2;
     quad[1].fY = (fromC1.fY + fromC2.fY) / 2;
     quad[2] = fPts[3];
     return quad;
 }
 static bool add_simple_ts(const SkDCubic& cubic, double precision, SkTArray<double, true>* ts) {
     double tDiv = calc_t_div(cubic, precision, 0);
     if (tDiv >= 1) {
         return true;
     }
     if (tDiv >= 0.5) {
         ts->push_back(0.5);
         return true;
     }
     return false;
 }
 static void addTs(const SkDCubic& cubic, double precision, double start, double end,
         SkTArray<double, true>* ts) {
     double tDiv = calc_t_div(cubic, precision, 0);
     double parts = ceil(1.0 / tDiv);
     for (double index = 0; index < parts; ++index) {
         double newT = start + (index / parts) * (end - start);
         if (newT > 0 && newT < 1) {
             ts->push_back(newT);
         }
     }
 }
 // flavor that returns T values only, deferring computing the quads until they are needed
 // FIXME: when called from recursive intersect 2, this could take the original cubic
 // and do a more precise job when calling chop at and sub divide by computing the fractional ts.
 // it would still take the prechopped cubic for reduce order and find cubic inflections
 void SkDCubic::toQuadraticTs(double precision, SkTArray<double, true>* ts) const {
     SkReduceOrder reducer;
     int order = reducer.reduce(*this, SkReduceOrder::kAllow_Quadratics);
     if (order < 3) {
         return;
     }
     double inflectT[5];
     int inflections = findInflections(inflectT);
     SkASSERT(inflections <= 2);
     if (!endsAreExtremaInXOrY()) {
         inflections += findMaxCurvature(&inflectT[inflections]);
         SkASSERT(inflections <= 5);
     }
     SkTQSort<double>(inflectT, &inflectT[inflections - 1]);
     // OPTIMIZATION: is this filtering common enough that it needs to be pulled out into its
     // own subroutine?
     while (inflections && approximately_less_than_zero(inflectT[0])) {
         memmove(inflectT, &inflectT[1], sizeof(inflectT[0]) * --inflections);
     }
     int start = 0;
     int next = 1;
     while (next < inflections) {
         if (!approximately_equal(inflectT[start], inflectT[next])) {
             ++start;
         ++next;
             continue;
         }
         memmove(&inflectT[start], &inflectT[next], sizeof(inflectT[0]) * (--inflections - start));
     }
     while (inflections && approximately_greater_than_one(inflectT[inflections - 1])) {
         --inflections;
     }
     SkDCubicPair pair;
     if (inflections == 1) {
         pair = chopAt(inflectT[0]);
         int orderP1 = reducer.reduce(pair.first(), SkReduceOrder::kNo_Quadratics);
         if (orderP1 < 2) {
             --inflections;
         } else {
             int orderP2 = reducer.reduce(pair.second(), SkReduceOrder::kNo_Quadratics);
             if (orderP2 < 2) {
                 --inflections;
             }
         }
     }
     if (inflections == 0 && add_simple_ts(*this, precision, ts)) {
         return;
     }
     if (inflections == 1) {
         pair = chopAt(inflectT[0]);
         addTs(pair.first(), precision, 0, inflectT[0], ts);
         addTs(pair.second(), precision, inflectT[0], 1, ts);
         return;
     }
     if (inflections > 1) {
         SkDCubic part = subDivide(0, inflectT[0]);
         addTs(part, precision, 0, inflectT[0], ts);
         int last = inflections - 1;
         for (int idx = 0; idx < last; ++idx) {
             part = subDivide(inflectT[idx], inflectT[idx + 1]);
             addTs(part, precision, inflectT[idx], inflectT[idx + 1], ts);
         }
         part = subDivide(inflectT[last], 1);
         addTs(part, precision, inflectT[last], 1, ts);
         return;
     }
     addTs(*this, precision, 0, 1, ts);
 }

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gfx/skia/trunk/src/pathops/SkDCubicToQuads.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/pathops/SkDCubicToQuads.cpp