remove prototype pathops code

experimental/Intersection/LineQuadraticIntersection.cpp

Index: experimental/Intersection/LineQuadraticIntersection.cpp
diff --git a/experimental/Intersection/LineQuadraticIntersection.cpp b/experimental/Intersection/LineQuadraticIntersection.cpp
deleted file mode 100644
index f855d97e4c4bca4a67a0905bc7fa373a2631ab67..0000000000000000000000000000000000000000
--- a/experimental/Intersection/LineQuadraticIntersection.cpp
+++ /dev/null
@@ -1,369 +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 "Intersections.h"
-#include "LineUtilities.h"
-#include "QuadraticUtilities.h"
-
-/*
-Find the interection of a line and quadratic by solving for valid t values.
-
-From http://stackoverflow.com/questions/1853637/how-to-find-the-mathematical-function-defining-a-bezier-curve
-
-"A Bezier curve is a parametric function. A quadratic Bezier curve (i.e. three
-control points) can be expressed as: F(t) = A(1 - t)^2 + B(1 - t)t + Ct^2 where
-A, B and C are points and t goes from zero to one.
-
-This will give you two equations:
-
-  x = a(1 - t)^2 + b(1 - t)t + ct^2
-  y = d(1 - t)^2 + e(1 - t)t + ft^2
-
-If you add for instance the line equation (y = kx + m) to that, you'll end up
-with three equations and three unknowns (x, y and t)."
-
-Similar to above, the quadratic is represented as
-  x = a(1-t)^2 + 2b(1-t)t + ct^2
-  y = d(1-t)^2 + 2e(1-t)t + ft^2
-and the line as
-  y = g*x + h
-
-Using Mathematica, solve for the values of t where the quadratic intersects the
-line:
-
-  (in)  t1 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - x,
-                       d*(1 - t)^2 + 2*e*(1 - t)*t  + f*t^2 - g*x - h, x]
-  (out) -d + h + 2 d t - 2 e t - d t^2 + 2 e t^2 - f t^2 +
-         g  (a - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2)
-  (in)  Solve[t1 == 0, t]
-  (out) {
-    {t -> (-2 d + 2 e +   2 a g - 2 b g    -
-      Sqrt[(2 d - 2 e -   2 a g + 2 b g)^2 -
-          4 (-d + 2 e - f + a g - 2 b g    + c g) (-d + a g + h)]) /
-         (2 (-d + 2 e - f + a g - 2 b g    + c g))
-         },
-    {t -> (-2 d + 2 e +   2 a g - 2 b g    +
-      Sqrt[(2 d - 2 e -   2 a g + 2 b g)^2 -
-          4 (-d + 2 e - f + a g - 2 b g    + c g) (-d + a g + h)]) /
-         (2 (-d + 2 e - f + a g - 2 b g    + c g))
-         }
-        }
-
-Using the results above (when the line tends towards horizontal)
-       A =   (-(d - 2*e + f) + g*(a - 2*b + c)     )
-       B = 2*( (d -   e    ) - g*(a -   b    )     )
-       C =   (-(d          ) + g*(a          ) + h )
-
-If g goes to infinity, we can rewrite the line in terms of x.
-  x = g'*y + h'
-
-And solve accordingly in Mathematica:
-
-  (in)  t2 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - g'*y - h',
-                       d*(1 - t)^2 + 2*e*(1 - t)*t  + f*t^2 - y, y]
-  (out)  a - h' - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2 -
-         g'  (d - 2 d t + 2 e t + d t^2 - 2 e t^2 + f t^2)
-  (in)  Solve[t2 == 0, t]
-  (out) {
-    {t -> (2 a - 2 b -   2 d g' + 2 e g'    -
-    Sqrt[(-2 a + 2 b +   2 d g' - 2 e g')^2 -
-          4 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')]) /
-         (2 (a - 2 b + c - d g' + 2 e g' - f g'))
-         },
-    {t -> (2 a - 2 b -   2 d g' + 2 e g'    +
-    Sqrt[(-2 a + 2 b +   2 d g' - 2 e g')^2 -
-          4 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')])/
-         (2 (a - 2 b + c - d g' + 2 e g' - f g'))
-         }
-        }
-
-Thus, if the slope of the line tends towards vertical, we use:
-       A =   ( (a - 2*b + c) - g'*(d  - 2*e + f)      )
-       B = 2*(-(a -   b    ) + g'*(d  -   e    )      )
-       C =   ( (a          ) - g'*(d           ) - h' )
- */
-
-
-class LineQuadraticIntersections {
-public:
-
-LineQuadraticIntersections(const Quadratic& q, const _Line& l, Intersections& i)
-    : quad(q)
-    , line(l)
-    , intersections(i) {
-}
-
-int intersectRay(double roots[2]) {
-/*
-    solve by rotating line+quad so line is horizontal, then finding the roots
-    set up matrix to rotate quad to x-axis
-    |cos(a) -sin(a)|
-    |sin(a)  cos(a)|
-    note that cos(a) = A(djacent) / Hypoteneuse
-              sin(a) = O(pposite) / Hypoteneuse
-    since we are computing Ts, we can ignore hypoteneuse, the scale factor:
-    |  A     -O    |
-    |  O      A    |
-    A = line[1].x - line[0].x (adjacent side of the right triangle)
-    O = line[1].y - line[0].y (opposite side of the right triangle)
-    for each of the three points (e.g. n = 0 to 2)
-    quad[n].y' = (quad[n].y - line[0].y) * A - (quad[n].x - line[0].x) * O
-*/
-    double adj = line[1].x - line[0].x;
-    double opp = line[1].y - line[0].y;
-    double r[3];
-    for (int n = 0; n < 3; ++n) {
-        r[n] = (quad[n].y - line[0].y) * adj - (quad[n].x - line[0].x) * opp;
-    }
-    double A = r[2];
-    double B = r[1];
-    double C = r[0];
-    A += C - 2 * B; // A = a - 2*b + c
-    B -= C; // B = -(b - c)
-    return quadraticRootsValidT(A, 2 * B, C, roots);
-}
-
-int intersect() {
-    addEndPoints();
-    double rootVals[2];
-    int roots = intersectRay(rootVals);
-    for (int index = 0; index < roots; ++index) {
-        double quadT = rootVals[index];
-        double lineT = findLineT(quadT);
-        if (pinTs(quadT, lineT)) {
-            _Point pt;
-            xy_at_t(line, lineT, pt.x, pt.y);
-            intersections.insert(quadT, lineT, pt);
-        }
-    }
-    return intersections.fUsed;
-}
-
-int horizontalIntersect(double axisIntercept, double roots[2]) {
-    double D = quad[2].y; // f
-    double E = quad[1].y; // e
-    double F = quad[0].y; // d
-    D += F - 2 * E; // D = d - 2*e + f
-    E -= F; // E = -(d - e)
-    F -= axisIntercept;
-    return quadraticRootsValidT(D, 2 * E, F, roots);
-}
-
-int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) {
-    addHorizontalEndPoints(left, right, axisIntercept);
-    double rootVals[2];
-    int roots = horizontalIntersect(axisIntercept, rootVals);
-    for (int index = 0; index < roots; ++index) {
-        _Point pt;
-        double quadT = rootVals[index];
-        xy_at_t(quad, quadT, pt.x, pt.y);
-        double lineT = (pt.x - left) / (right - left);
-        if (pinTs(quadT, lineT)) {
-            intersections.insert(quadT, lineT, pt);
-        }
-    }
-    if (flipped) {
-        flip();
-    }
-    return intersections.fUsed;
-}
-
-int verticalIntersect(double axisIntercept, double roots[2]) {
-    double D = quad[2].x; // f
-    double E = quad[1].x; // e
-    double F = quad[0].x; // d
-    D += F - 2 * E; // D = d - 2*e + f
-    E -= F; // E = -(d - e)
-    F -= axisIntercept;
-    return quadraticRootsValidT(D, 2 * E, F, roots);
-}
-
-int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) {
-    addVerticalEndPoints(top, bottom, axisIntercept);
-    double rootVals[2];
-    int roots = verticalIntersect(axisIntercept, rootVals);
-    for (int index = 0; index < roots; ++index) {
-        _Point pt;
-        double quadT = rootVals[index];
-        xy_at_t(quad, quadT, pt.x, pt.y);
-        double lineT = (pt.y - top) / (bottom - top);
-        if (pinTs(quadT, lineT)) {
-            intersections.insert(quadT, lineT, pt);
-        }
-    }
-    if (flipped) {
-        flip();
-    }
-    return intersections.fUsed;
-}
-
-protected:
-
-// add endpoints first to get zero and one t values exactly
-void addEndPoints()
-{
-    for (int qIndex = 0; qIndex < 3; qIndex += 2) {
-        for (int lIndex = 0; lIndex < 2; lIndex++) {
-            if (quad[qIndex] == line[lIndex]) {
-                intersections.insert(qIndex >> 1, lIndex, line[lIndex]);
-            }
-        }
-    }
-}
-
-void addHorizontalEndPoints(double left, double right, double y)
-{
-    for (int qIndex = 0; qIndex < 3; qIndex += 2) {
-        if (quad[qIndex].y != y) {
-            continue;
-        }
-        if (quad[qIndex].x == left) {
-            intersections.insert(qIndex >> 1, 0, quad[qIndex]);
-        }
-        if (quad[qIndex].x == right) {
-            intersections.insert(qIndex >> 1, 1, quad[qIndex]);
-        }
-    }
-}
-
-void addVerticalEndPoints(double top, double bottom, double x)
-{
-    for (int qIndex = 0; qIndex < 3; qIndex += 2) {
-        if (quad[qIndex].x != x) {
-            continue;
-        }
-        if (quad[qIndex].y == top) {
-            intersections.insert(qIndex >> 1, 0, quad[qIndex]);
-        }
-        if (quad[qIndex].y == bottom) {
-            intersections.insert(qIndex >> 1, 1, quad[qIndex]);
-        }
-    }
-}
-
-double findLineT(double t) {
-    double x, y;
-    xy_at_t(quad, t, x, y);
-    double dx = line[1].x - line[0].x;
-    double dy = line[1].y - line[0].y;
-    if (fabs(dx) > fabs(dy)) {
-        return (x - line[0].x) / dx;
-    }
-    return (y - line[0].y) / dy;
-}
-
-void flip() {
-    // OPTIMIZATION: instead of swapping, pass original line, use [1].y - [0].y
-    int roots = intersections.fUsed;
-    for (int index = 0; index < roots; ++index) {
-        intersections.fT[1][index] = 1 - intersections.fT[1][index];
-    }
-}
-
-static bool pinTs(double& quadT, double& lineT) {
-    if (!approximately_one_or_less(lineT)) {
-        return false;
-    }
-    if (!approximately_zero_or_more(lineT)) {
-        return false;
-    }
-    if (precisely_less_than_zero(quadT)) {
-        quadT = 0;
-    } else if (precisely_greater_than_one(quadT)) {
-        quadT = 1;
-    }
-    if (precisely_less_than_zero(lineT)) {
-        lineT = 0;
-    } else if (precisely_greater_than_one(lineT)) {
-        lineT = 1;
-    }
-    return true;
-}
-
-private:
-
-const Quadratic& quad;
-const _Line& line;
-Intersections& intersections;
-};
-
-// utility for pairs of coincident quads
-static double horizontalIntersect(const Quadratic& quad, const _Point& pt) {
-    LineQuadraticIntersections q(quad, *((_Line*) 0), *((Intersections*) 0));
-    double rootVals[2];
-    int roots = q.horizontalIntersect(pt.y, rootVals);
-    for (int index = 0; index < roots; ++index) {
-        double x;
-        double t = rootVals[index];
-        xy_at_t(quad, t, x, *(double*) 0);
-        if (AlmostEqualUlps(x, pt.x)) {
-            return t;
-        }
-    }
-    return -1;
-}
-
-static double verticalIntersect(const Quadratic& quad, const _Point& pt) {
-    LineQuadraticIntersections q(quad, *((_Line*) 0), *((Intersections*) 0));
-    double rootVals[2];
-    int roots = q.verticalIntersect(pt.x, rootVals);
-    for (int index = 0; index < roots; ++index) {
-        double y;
-        double t = rootVals[index];
-        xy_at_t(quad, t, *(double*) 0, y);
-        if (AlmostEqualUlps(y, pt.y)) {
-            return t;
-        }
-    }
-    return -1;
-}
-
-double axialIntersect(const Quadratic& q1, const _Point& p, bool vertical) {
-    if (vertical) {
-        return verticalIntersect(q1, p);
-    }
-    return horizontalIntersect(q1, p);
-}
-
-int horizontalIntersect(const Quadratic& quad, double left, double right,
-        double y, double tRange[2]) {
-    LineQuadraticIntersections q(quad, *((_Line*) 0), *((Intersections*) 0));
-    double rootVals[2];
-    int result = q.horizontalIntersect(y, rootVals);
-    int tCount = 0;
-    for (int index = 0; index < result; ++index) {
-        double x, y;
-        xy_at_t(quad, rootVals[index], x, y);
-        if (x < left || x > right) {
-            continue;
-        }
-        tRange[tCount++] = rootVals[index];
-    }
-    return tCount;
-}
-
-int horizontalIntersect(const Quadratic& quad, double left, double right, double y,
-        bool flipped, Intersections& intersections) {
-    LineQuadraticIntersections q(quad, *((_Line*) 0), intersections);
-    return q.horizontalIntersect(y, left, right, flipped);
-}
-
-int verticalIntersect(const Quadratic& quad, double top, double bottom, double x,
-        bool flipped, Intersections& intersections) {
-    LineQuadraticIntersections q(quad, *((_Line*) 0), intersections);
-    return q.verticalIntersect(x, top, bottom, flipped);
-}
-
-int intersect(const Quadratic& quad, const _Line& line, Intersections& i) {
-    LineQuadraticIntersections q(quad, line, i);
-    return q.intersect();
-}
-
-int intersectRay(const Quadratic& quad, const _Line& line, Intersections& i) {
-    LineQuadraticIntersections q(quad, line, i);
-    return q.intersectRay(i.fT[0]);
-}