remove prototype pathops code

experimental/Intersection/CubicUtilities.cpp

Index: experimental/Intersection/CubicUtilities.cpp
diff --git a/experimental/Intersection/CubicUtilities.cpp b/experimental/Intersection/CubicUtilities.cpp
deleted file mode 100644
index 474dc5e526ce6d5f8ca04e1fe16a5bfc7d24b2ec..0000000000000000000000000000000000000000
--- a/experimental/Intersection/CubicUtilities.cpp
+++ /dev/null
@@ -1,424 +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 "CubicUtilities.h"
-#include "Extrema.h"
-#include "LineUtilities.h"
-#include "QuadraticUtilities.h"
-
-const int gPrecisionUnit = 256; // FIXME: arbitrary -- should try different values in test framework
-
-// FIXME: cache keep the bounds and/or precision with the caller?
-double calcPrecision(const Cubic& cubic) {
-    _Rect dRect;
-    dRect.setBounds(cubic); // OPTIMIZATION: just use setRawBounds ?
-    double width = dRect.right - dRect.left;
-    double height = dRect.bottom - dRect.top;
-    return (width > height ? width : height) / gPrecisionUnit;
-}
-
-#ifdef SK_DEBUG
-double calcPrecision(const Cubic& cubic, double t, double scale) {
-    Cubic part;
-    sub_divide(cubic, SkTMax(0., t - scale), SkTMin(1., t + scale), part);
-    return calcPrecision(part);
-}
-#endif
-
-bool clockwise(const Cubic& c) {
-    double sum = (c[0].x - c[3].x) * (c[0].y + c[3].y);
-    for (int idx = 0; idx < 3; ++idx){
-        sum += (c[idx + 1].x - c[idx].x) * (c[idx + 1].y + c[idx].y);
-    }
-    return sum <= 0;
-}
-
-void coefficients(const double* cubic, double& A, double& B, double& C, double& D) {
-    A = cubic[6]; // d
-    B = cubic[4] * 3; // 3*c
-    C = cubic[2] * 3; // 3*b
-    D = cubic[0]; // a
-    A -= D - C + B;     // A =   -a + 3*b - 3*c + d
-    B += 3 * D - 2 * C; // B =  3*a - 6*b + 3*c
-    C -= 3 * D;         // C = -3*a + 3*b
-}
-
-bool controls_contained_by_ends(const Cubic& c) {
-    _Vector startTan = c[1] - c[0];
-    if (startTan.x == 0 && startTan.y == 0) {
-        startTan = c[2] - c[0];
-    }
-    _Vector endTan = c[2] - c[3];
-    if (endTan.x == 0 && endTan.y == 0) {
-        endTan = c[1] - c[3];
-    }
-    if (startTan.dot(endTan) >= 0) {
-        return false;
-    }
-    _Line startEdge = {c[0], c[0]};
-    startEdge[1].x -= startTan.y;
-    startEdge[1].y += startTan.x;
-    _Line endEdge = {c[3], c[3]};
-    endEdge[1].x -= endTan.y;
-    endEdge[1].y += endTan.x;
-    double leftStart1 = is_left(startEdge, c[1]);
-    if (leftStart1 * is_left(startEdge, c[2]) < 0) {
-        return false;
-    }
-    double leftEnd1 = is_left(endEdge, c[1]);
-    if (leftEnd1 * is_left(endEdge, c[2]) < 0) {
-        return false;
-    }
-    return leftStart1 * leftEnd1 >= 0;
-}
-
-bool ends_are_extrema_in_x_or_y(const Cubic& c) {
-    return (between(c[0].x, c[1].x, c[3].x) && between(c[0].x, c[2].x, c[3].x))
-            || (between(c[0].y, c[1].y, c[3].y) && between(c[0].y, c[2].y, c[3].y));
-}
-
-bool monotonic_in_y(const Cubic& c) {
-    return between(c[0].y, c[1].y, c[3].y) && between(c[0].y, c[2].y, c[3].y);
-}
-
-bool serpentine(const Cubic& c) {
-    if (!controls_contained_by_ends(c)) {
-        return false;
-    }
-    double wiggle = (c[0].x - c[2].x) * (c[0].y + c[2].y);
-    for (int idx = 0; idx < 2; ++idx){
-        wiggle += (c[idx + 1].x - c[idx].x) * (c[idx + 1].y + c[idx].y);
-    }
-    double waggle = (c[1].x - c[3].x) * (c[1].y + c[3].y);
-    for (int idx = 1; idx < 3; ++idx){
-        waggle += (c[idx + 1].x - c[idx].x) * (c[idx + 1].y + c[idx].y);
-    }
-    return wiggle * waggle < 0;
-}
-
-// cubic roots
-
-const double PI = 4 * atan(1);
-
-// from SkGeometry.cpp (and Numeric Solutions, 5.6)
-int cubicRootsValidT(double A, double B, double C, double D, double t[3]) {
-#if 0
-    if (approximately_zero(A)) {  // we're just a quadratic
-        return quadraticRootsValidT(B, C, D, t);
-    }
-    double a, b, c;
-    {
-        double invA = 1 / A;
-        a = B * invA;
-        b = C * invA;
-        c = D * invA;
-    }
-    double a2 = a * a;
-    double Q = (a2 - b * 3) / 9;
-    double R = (2 * a2 * a - 9 * a * b + 27 * c) / 54;
-    double Q3 = Q * Q * Q;
-    double R2MinusQ3 = R * R - Q3;
-    double adiv3 = a / 3;
-    double* roots = t;
-    double r;
-
-    if (R2MinusQ3 < 0)   // we have 3 real roots
-    {
-        double theta = acos(R / sqrt(Q3));
-        double neg2RootQ = -2 * sqrt(Q);
-
-        r = neg2RootQ * cos(theta / 3) - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-
-        r = neg2RootQ * cos((theta + 2 * PI) / 3) - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-
-        r = neg2RootQ * cos((theta - 2 * PI) / 3) - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-    }
-    else                // we have 1 real root
-    {
-        double A = fabs(R) + sqrt(R2MinusQ3);
-        A = cube_root(A);
-        if (R > 0) {
-            A = -A;
-        }
-        if (A != 0) {
-            A += Q / A;
-        }
-        r = A - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-    }
-    return (int)(roots - t);
-#else
-    double s[3];
-    int realRoots = cubicRootsReal(A, B, C, D, s);
-    int foundRoots = add_valid_ts(s, realRoots, t);
-    return foundRoots;
-#endif
-}
-
-int cubicRootsReal(double A, double B, double C, double D, double s[3]) {
-#ifdef SK_DEBUG
-    // create a string mathematica understands
-    // GDB set print repe 15 # if repeated digits is a bother
-    //     set print elements 400 # if line doesn't fit
-    char str[1024];
-    bzero(str, sizeof(str));
-    sprintf(str, "Solve[%1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]", A, B, C, D);
-    mathematica_ize(str, sizeof(str));
-#if ONE_OFF_DEBUG && ONE_OFF_DEBUG_MATHEMATICA
-    SkDebugf("%s\n", str);
-#endif
-#endif
-    if (approximately_zero(A)
-            && approximately_zero_when_compared_to(A, B)
-            && approximately_zero_when_compared_to(A, C)
-            && approximately_zero_when_compared_to(A, D)) {  // we're just a quadratic
-        return quadraticRootsReal(B, C, D, s);
-    }
-    if (approximately_zero_when_compared_to(D, A)
-            && approximately_zero_when_compared_to(D, B)
-            && approximately_zero_when_compared_to(D, C)) { // 0 is one root
-        int num = quadraticRootsReal(A, B, C, s);
-        for (int i = 0; i < num; ++i) {
-            if (approximately_zero(s[i])) {
-                return num;
-            }
-        }
-        s[num++] = 0;
-        return num;
-    }
-    if (approximately_zero(A + B + C + D)) { // 1 is one root
-        int num = quadraticRootsReal(A, A + B, -D, s);
-        for (int i = 0; i < num; ++i) {
-            if (AlmostEqualUlps(s[i], 1)) {
-                return num;
-            }
-        }
-        s[num++] = 1;
-        return num;
-    }
-    double a, b, c;
-    {
-        double invA = 1 / A;
-        a = B * invA;
-        b = C * invA;
-        c = D * invA;
-    }
-    double a2 = a * a;
-    double Q = (a2 - b * 3) / 9;
-    double R = (2 * a2 * a - 9 * a * b + 27 * c) / 54;
-    double R2 = R * R;
-    double Q3 = Q * Q * Q;
-    double R2MinusQ3 = R2 - Q3;
-    double adiv3 = a / 3;
-    double r;
-    double* roots = s;
-#if 0
-    if (approximately_zero_squared(R2MinusQ3) && AlmostEqualUlps(R2, Q3)) {
-        if (approximately_zero_squared(R)) {/* one triple solution */
-            *roots++ = -adiv3;
-        } else { /* one single and one double solution */
-
-            double u = cube_root(-R);
-            *roots++ = 2 * u - adiv3;
-            *roots++ = -u - adiv3;
-        }
-    }
-    else
-#endif
-    if (R2MinusQ3 < 0)   // we have 3 real roots
-    {
-        double theta = acos(R / sqrt(Q3));
-        double neg2RootQ = -2 * sqrt(Q);
-
-        r = neg2RootQ * cos(theta / 3) - adiv3;
-        *roots++ = r;
-
-        r = neg2RootQ * cos((theta + 2 * PI) / 3) - adiv3;
-        if (!AlmostEqualUlps(s[0], r)) {
-            *roots++ = r;
-        }
-        r = neg2RootQ * cos((theta - 2 * PI) / 3) - adiv3;
-        if (!AlmostEqualUlps(s[0], r) && (roots - s == 1 || !AlmostEqualUlps(s[1], r))) {
-            *roots++ = r;
-        }
-    }
-    else                // we have 1 real root
-    {
-        double sqrtR2MinusQ3 = sqrt(R2MinusQ3);
-        double A = fabs(R) + sqrtR2MinusQ3;
-        A = cube_root(A);
-        if (R > 0) {
-            A = -A;
-        }
-        if (A != 0) {
-            A += Q / A;
-        }
-        r = A - adiv3;
-        *roots++ = r;
-        if (AlmostEqualUlps(R2, Q3)) {
-            r = -A / 2 - adiv3;
-            if (!AlmostEqualUlps(s[0], r)) {
-                *roots++ = r;
-            }
-        }
-    }
-    return (int)(roots - s);
-}
-
-// from http://www.cs.sunysb.edu/~qin/courses/geometry/4.pdf
-// c(t)  = a(1-t)^3 + 3bt(1-t)^2 + 3c(1-t)t^2 + dt^3
-// c'(t) = -3a(1-t)^2 + 3b((1-t)^2 - 2t(1-t)) + 3c(2t(1-t) - t^2) + 3dt^2
-//       = 3(b-a)(1-t)^2 + 6(c-b)t(1-t) + 3(d-c)t^2
-static double derivativeAtT(const double* cubic, double t) {
-    double one_t = 1 - t;
-    double a = cubic[0];
-    double b = cubic[2];
-    double c = cubic[4];
-    double d = cubic[6];
-    return 3 * ((b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t);
-}
-
-double dx_at_t(const Cubic& cubic, double t) {
-    return derivativeAtT(&cubic[0].x, t);
-}
-
-double dy_at_t(const Cubic& cubic, double t) {
-    return derivativeAtT(&cubic[0].y, t);
-}
-
-// OPTIMIZE? compute t^2, t(1-t), and (1-t)^2 and pass them to another version of derivative at t?
-_Vector dxdy_at_t(const Cubic& cubic, double t) {
-    _Vector result = { derivativeAtT(&cubic[0].x, t), derivativeAtT(&cubic[0].y, t) };
-    return result;
-}
-
-// OPTIMIZE? share code with formulate_F1DotF2
-int find_cubic_inflections(const Cubic& src, double tValues[])
-{
-    double Ax = src[1].x - src[0].x;
-    double Ay = src[1].y - src[0].y;
-    double Bx = src[2].x - 2 * src[1].x + src[0].x;
-    double By = src[2].y - 2 * src[1].y + src[0].y;
-    double Cx = src[3].x + 3 * (src[1].x - src[2].x) - src[0].x;
-    double Cy = src[3].y + 3 * (src[1].y - src[2].y) - src[0].y;
-    return quadraticRootsValidT(Bx * Cy - By * Cx, Ax * Cy - Ay * Cx, Ax * By - Ay * Bx, tValues);
-}
-
-static void formulate_F1DotF2(const double src[], double coeff[4])
-{
-    double a = src[2] - src[0];
-    double b = src[4] - 2 * src[2] + src[0];
-    double c = src[6] + 3 * (src[2] - src[4]) - src[0];
-    coeff[0] = c * c;
-    coeff[1] = 3 * b * c;
-    coeff[2] = 2 * b * b + c * a;
-    coeff[3] = a * b;
-}
-
-/*  from SkGeometry.cpp
-    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 find_cubic_max_curvature(const Cubic& src, double tValues[])
-{
-    double coeffX[4], coeffY[4];
-    int i;
-    formulate_F1DotF2(&src[0].x, coeffX);
-    formulate_F1DotF2(&src[0].y, coeffY);
-    for (i = 0; i < 4; i++) {
-        coeffX[i] = coeffX[i] + coeffY[i];
-    }
-    return cubicRootsValidT(coeffX[0], coeffX[1], coeffX[2], coeffX[3], tValues);
-}
-
-
-bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath) {
-    double dy = cubic[index].y - cubic[zero].y;
-    double dx = cubic[index].x - cubic[zero].x;
-    if (approximately_zero(dy)) {
-        if (approximately_zero(dx)) {
-            return false;
-        }
-        memcpy(rotPath, cubic, sizeof(Cubic));
-        return true;
-    }
-    for (int index = 0; index < 4; ++index) {
-        rotPath[index].x = cubic[index].x * dx + cubic[index].y * dy;
-        rotPath[index].y = cubic[index].y * dx - cubic[index].x * dy;
-    }
-    return true;
-}
-
-#if 0 // unused for now
-double secondDerivativeAtT(const double* cubic, double t) {
-    double a = cubic[0];
-    double b = cubic[2];
-    double c = cubic[4];
-    double d = cubic[6];
-    return (c - 2 * b + a) * (1 - t) + (d - 2 * c + b) * t;
-}
-#endif
-
-_Point top(const Cubic& cubic, double startT, double endT) {
-    Cubic sub;
-    sub_divide(cubic, startT, endT, sub);
-    _Point topPt = sub[0];
-    if (topPt.y > sub[3].y || (topPt.y == sub[3].y && topPt.x > sub[3].x)) {
-        topPt = sub[3];
-    }
-    double extremeTs[2];
-    if (!monotonic_in_y(sub)) {
-        int roots = findExtrema(sub[0].y, sub[1].y, sub[2].y, sub[3].y, extremeTs);
-        for (int index = 0; index < roots; ++index) {
-            _Point mid;
-            double t = startT + (endT - startT) * extremeTs[index];
-            xy_at_t(cubic, t, mid.x, mid.y);
-            if (topPt.y > mid.y || (topPt.y == mid.y && topPt.x > mid.x)) {
-                topPt = mid;
-            }
-        }
-    }
-    return topPt;
-}
-
-// OPTIMIZE: avoid computing the unused half
-void xy_at_t(const Cubic& cubic, double t, double& x, double& y) {
-    _Point xy = xy_at_t(cubic, t);
-    if (&x) {
-        x = xy.x;
-    }
-    if (&y) {
-        y = xy.y;
-    }
-}
-
-_Point xy_at_t(const Cubic& cubic, double t) {
-    double one_t = 1 - t;
-    double one_t2 = one_t * one_t;
-    double a = one_t2 * one_t;
-    double b = 3 * one_t2 * t;
-    double t2 = t * t;
-    double c = 3 * one_t * t2;
-    double d = t2 * t;
-    _Point result = {a * cubic[0].x + b * cubic[1].x + c * cubic[2].x + d * cubic[3].x,
-            a * cubic[0].y + b * cubic[1].y + c * cubic[2].y + d * cubic[3].y};
-    return result;
-}