remove prototype pathops code

experimental/Intersection/CubicReduceOrder.cpp

Index: experimental/Intersection/CubicReduceOrder.cpp
diff --git a/experimental/Intersection/CubicReduceOrder.cpp b/experimental/Intersection/CubicReduceOrder.cpp
deleted file mode 100644
index f7c0c12d4cced69c65bf4cfe66908abe3126c52a..0000000000000000000000000000000000000000
--- a/experimental/Intersection/CubicReduceOrder.cpp
+++ /dev/null
@@ -1,254 +0,0 @@
-/*
- * Copyright 2012 Google Inc.
- *
- * Use of this source code is governed by a BSD-style license that can be
- * found in the LICENSE file.
- */
-#include "CurveIntersection.h"
-#include "Extrema.h"
-#include "IntersectionUtilities.h"
-#include "LineParameters.h"
-
-static double interp_cubic_coords(const double* src, double t)
-{
-    double ab = interp(src[0], src[2], t);
-    double bc = interp(src[2], src[4], t);
-    double cd = interp(src[4], src[6], t);
-    double abc = interp(ab, bc, t);
-    double bcd = interp(bc, cd, t);
-    return interp(abc, bcd, t);
-}
-
-static int coincident_line(const Cubic& cubic, Cubic& reduction) {
-    reduction[0] = reduction[1] = cubic[0];
-    return 1;
-}
-
-static int vertical_line(const Cubic& cubic, ReduceOrder_Styles reduceStyle, Cubic& reduction) {
-    double tValues[2];
-    reduction[0] = cubic[0];
-    reduction[1] = cubic[3];
-    if (reduceStyle == kReduceOrder_TreatAsFill) {
-        return 2;
-    }
-    int smaller = reduction[1].y > reduction[0].y;
-    int larger = smaller ^ 1;
-    int roots = findExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
-    for (int index = 0; index < roots; ++index) {
-        double yExtrema = interp_cubic_coords(&cubic[0].y, tValues[index]);
-        if (reduction[smaller].y > yExtrema) {
-            reduction[smaller].y = yExtrema;
-            continue;
-        }
-        if (reduction[larger].y < yExtrema) {
-            reduction[larger].y = yExtrema;
-        }
-    }
-    return 2;
-}
-
-static int horizontal_line(const Cubic& cubic, ReduceOrder_Styles reduceStyle, Cubic& reduction) {
-    double tValues[2];
-    reduction[0] = cubic[0];
-    reduction[1] = cubic[3];
-    if (reduceStyle == kReduceOrder_TreatAsFill) {
-        return 2;
-    }
-    int smaller = reduction[1].x > reduction[0].x;
-    int larger = smaller ^ 1;
-    int roots = findExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
-    for (int index = 0; index < roots; ++index) {
-        double xExtrema = interp_cubic_coords(&cubic[0].x, tValues[index]);
-        if (reduction[smaller].x > xExtrema) {
-            reduction[smaller].x = xExtrema;
-            continue;
-        }
-        if (reduction[larger].x < xExtrema) {
-            reduction[larger].x = xExtrema;
-        }
-    }
-    return 2;
-}
-
-// check to see if it is a quadratic or a line
-static int check_quadratic(const Cubic& cubic, Cubic& reduction) {
-    double dx10 = cubic[1].x - cubic[0].x;
-    double dx23 = cubic[2].x - cubic[3].x;
-    double midX = cubic[0].x + dx10 * 3 / 2;
-    if (!AlmostEqualUlps(midX - cubic[3].x, dx23 * 3 / 2)) {
-        return 0;
-    }
-    double dy10 = cubic[1].y - cubic[0].y;
-    double dy23 = cubic[2].y - cubic[3].y;
-    double midY = cubic[0].y + dy10 * 3 / 2;
-    if (!AlmostEqualUlps(midY - cubic[3].y, dy23 * 3 / 2)) {
-        return 0;
-    }
-    reduction[0] = cubic[0];
-    reduction[1].x = midX;
-    reduction[1].y = midY;
-    reduction[2] = cubic[3];
-    return 3;
-}
-
-static int check_linear(const Cubic& cubic, ReduceOrder_Styles reduceStyle,
-        int minX, int maxX, int minY, int maxY, Cubic& reduction) {
-    int startIndex = 0;
-    int endIndex = 3;
-    while (cubic[startIndex].approximatelyEqual(cubic[endIndex])) {
-        --endIndex;
-        if (endIndex == 0) {
-            printf("%s shouldn't get here if all four points are about equal\n", __FUNCTION__);
-            SkASSERT(0);
-        }
-    }
-    if (!isLinear(cubic, startIndex, endIndex)) {
-        return 0;
-    }
-    // four are colinear: return line formed by outside
-    reduction[0] = cubic[0];
-    reduction[1] = cubic[3];
-    if (reduceStyle == kReduceOrder_TreatAsFill) {
-        return 2;
-    }
-    int sameSide1;
-    int sameSide2;
-    bool useX = cubic[maxX].x - cubic[minX].x >= cubic[maxY].y - cubic[minY].y;
-    if (useX) {
-        sameSide1 = sign(cubic[0].x - cubic[1].x) + sign(cubic[3].x - cubic[1].x);
-        sameSide2 = sign(cubic[0].x - cubic[2].x) + sign(cubic[3].x - cubic[2].x);
-    } else {
-        sameSide1 = sign(cubic[0].y - cubic[1].y) + sign(cubic[3].y - cubic[1].y);
-        sameSide2 = sign(cubic[0].y - cubic[2].y) + sign(cubic[3].y - cubic[2].y);
-    }
-    if (sameSide1 == sameSide2 && (sameSide1 & 3) != 2) {
-        return 2;
-    }
-    double tValues[2];
-    int roots;
-    if (useX) {
-        roots = findExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
-    } else {
-        roots = findExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
-    }
-    for (int index = 0; index < roots; ++index) {
-        _Point extrema;
-        extrema.x = interp_cubic_coords(&cubic[0].x, tValues[index]);
-        extrema.y = interp_cubic_coords(&cubic[0].y, tValues[index]);
-        // sameSide > 0 means mid is smaller than either [0] or [3], so replace smaller
-        int replace;
-        if (useX) {
-            if (extrema.x < cubic[0].x ^ extrema.x < cubic[3].x) {
-                continue;
-            }
-            replace = (extrema.x < cubic[0].x | extrema.x < cubic[3].x)
-                    ^ (cubic[0].x < cubic[3].x);
-        } else {
-            if (extrema.y < cubic[0].y ^ extrema.y < cubic[3].y) {
-                continue;
-            }
-            replace = (extrema.y < cubic[0].y | extrema.y < cubic[3].y)
-                    ^ (cubic[0].y < cubic[3].y);
-        }
-        reduction[replace] = extrema;
-    }
-    return 2;
-}
-
-bool isLinear(const Cubic& cubic, int startIndex, int endIndex) {
-    LineParameters lineParameters;
-    lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
-    // FIXME: maybe it's possible to avoid this and compare non-normalized
-    lineParameters.normalize();
-    double distance = lineParameters.controlPtDistance(cubic, 1);
-    if (!approximately_zero(distance)) {
-        return false;
-    }
-    distance = lineParameters.controlPtDistance(cubic, 2);
-    return approximately_zero(distance);
-}
-
-/* food for thought:
-http://objectmix.com/graphics/132906-fast-precision-driven-cubic-quadratic-piecewise-degree-reduction-algos-2-a.html
-
-Given points c1, c2, c3 and c4 of a cubic Bezier, the points of the
-corresponding quadratic Bezier are (given in convex combinations of
-points):
-
-q1 = (11/13)c1 + (3/13)c2 -(3/13)c3 + (2/13)c4
-q2 = -c1 + (3/2)c2 + (3/2)c3 - c4
-q3 = (2/13)c1 - (3/13)c2 + (3/13)c3 + (11/13)c4
-
-Of course, this curve does not interpolate the end-points, but it would
-be interesting to see the behaviour of such a curve in an applet.
-
---
-Kalle Rutanen
-http://kaba.hilvi.org
-
-*/
-
-// reduce to a quadratic or smaller
-// look for identical points
-// look for all four points in a line
-    // note that three points in a line doesn't simplify a cubic
-// look for approximation with single quadratic
-    // save approximation with multiple quadratics for later
-int reduceOrder(const Cubic& cubic, Cubic& reduction, ReduceOrder_Quadratics allowQuadratics,
-        ReduceOrder_Styles reduceStyle) {
-    int index, minX, maxX, minY, maxY;
-    int minXSet, minYSet;
-    minX = maxX = minY = maxY = 0;
-    minXSet = minYSet = 0;
-    for (index = 1; index < 4; ++index) {
-        if (cubic[minX].x > cubic[index].x) {
-            minX = index;
-        }
-        if (cubic[minY].y > cubic[index].y) {
-            minY = index;
-        }
-        if (cubic[maxX].x < cubic[index].x) {
-            maxX = index;
-        }
-        if (cubic[maxY].y < cubic[index].y) {
-            maxY = index;
-        }
-    }
-    for (index = 0; index < 4; ++index) {
-        double cx = cubic[index].x;
-        double cy = cubic[index].y;
-        double denom = SkTMax(fabs(cx), SkTMax(fabs(cy),
-                SkTMax(fabs(cubic[minX].x), fabs(cubic[minY].y))));
-        if (denom == 0) {
-            minXSet |= 1 << index;
-            minYSet |= 1 << index;
-            continue;
-        }
-        double inv = 1 / denom;
-        if (approximately_equal_half(cx * inv, cubic[minX].x * inv)) {
-            minXSet |= 1 << index;
-        }
-        if (approximately_equal_half(cy * inv, cubic[minY].y * inv)) {
-            minYSet |= 1 << index;
-        }
-    }
-    if (minXSet == 0xF) { // test for vertical line
-        if (minYSet == 0xF) { // return 1 if all four are coincident
-            return coincident_line(cubic, reduction);
-        }
-        return vertical_line(cubic, reduceStyle, reduction);
-    }
-    if (minYSet == 0xF) { // test for horizontal line
-        return horizontal_line(cubic, reduceStyle, reduction);
-    }
-    int result = check_linear(cubic, reduceStyle, minX, maxX, minY, maxY, reduction);
-    if (result) {
-        return result;
-    }
-    if (allowQuadratics == kReduceOrder_QuadraticsAllowed
-            && (result = check_quadratic(cubic, reduction))) {
-        return result;
-    }
-    memcpy(reduction, cubic, sizeof(Cubic));
-    return 4;
-}