cumulative pathops patch

Replace the implicit curve intersection with a geometric curve intersection. The implicit intersection proved mathematically unstable and took a long time to zero in on an answer.

Use pointers instead of indices to refer to parts of curves. Indices required awkward renumbering.

Unify t and point values so that small intervals can be eliminated in one pass.

Break cubics up front to eliminate loops and cusps.

Make the Simplify and Op code more regular and eliminate arbitrary differences.

Add a builder that takes an array of paths and operators.

Delete unused code.

BUG=skia:3588
R=reed@google.com

Review URL: https://codereview.chromium.org/1037573004

1 files changed, 8 insertions, 150 deletions

diff --git a/src/pathops/SkDCubicToQuads.cpp b/src/pathops/SkDCubicToQuads.cpp
index a28564d4c2..272b997d6c 100644
--- a/src/pathops/SkDCubicToQuads.cpp
+++ b/src/pathops/SkDCubicToQuads.cpp
@@ -1,4 +1,11 @@
 /*
+ * Copyright 2015 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+/*
 http://stackoverflow.com/questions/2009160/how-do-i-convert-the-2-control-points-of-a-cubic-curve-to-the-single-control-poi
 */
 
@@ -19,63 +26,12 @@ If this is a degree-elevated cubic, then both equations will give the same answe
  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)
-0.5<=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;
-}
 
+// used for testing only
 SkDQuad SkDCubic::toQuad() const {
     SkDQuad quad;
     quad[0] = fPts[0];
@@ -86,101 +42,3 @@ SkDQuad SkDCubic::toQuad() const {
     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);
-}