src/pathops/SkDLineIntersection.cpp

/*
 * 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 "SkIntersections.h"
#include "SkPathOpsLine.h"

/* Determine the intersection point of two lines. This assumes the lines are not parallel,
   and that that the lines are infinite.
   From http://en.wikipedia.org/wiki/Line-line_intersection
 */
SkDPoint SkIntersections::Line(const SkDLine& a, const SkDLine& b) {
    double axLen = a[1].fX - a[0].fX;
    double ayLen = a[1].fY - a[0].fY;
    double bxLen = b[1].fX - b[0].fX;
    double byLen = b[1].fY - b[0].fY;
    double denom = byLen * axLen - ayLen * bxLen;
    SkASSERT(denom);
    double term1 = a[1].fX * a[0].fY - a[1].fY * a[0].fX;
    double term2 = b[1].fX * b[0].fY - b[1].fY * b[0].fX;
    SkDPoint p;
    p.fX = (term1 * bxLen - axLen * term2) / denom;
    p.fY = (term1 * byLen - ayLen * term2) / denom;
    return p;
}

int SkIntersections::computePoints(const SkDLine& line, int used) {
    fPt[0] = line.ptAtT(fT[0][0]);
    if ((fUsed = used) == 2) {
        fPt[1] = line.ptAtT(fT[0][1]);
    }
    return fUsed;
}

int SkIntersections::intersectRay(const SkDLine& a, const SkDLine& b) {
    SkDVector aLen = a[1] - a[0];
    SkDVector bLen = b[1] - b[0];
    /* Slopes match when denom goes to zero:
                      axLen / ayLen ==                   bxLen / byLen
    (ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
             byLen  * axLen         ==  ayLen          * bxLen
             byLen  * axLen         -   ayLen          * bxLen == 0 ( == denom )
     */
    double denom = bLen.fY * aLen.fX - aLen.fY * bLen.fX;
    SkDVector ab0 = a[0] - b[0];
    double numerA = ab0.fY * bLen.fX - bLen.fY * ab0.fX;
    double numerB = ab0.fY * aLen.fX - aLen.fY * ab0.fX;
    numerA /= denom;
    numerB /= denom;
    int used;
    if (!approximately_zero(denom)) {
        fT[0][0] = numerA;
        fT[1][0] = numerB;
        used = 1;
    } else {
       /* See if the axis intercepts match:
                  ay - ax * ayLen / axLen  ==          by - bx * ayLen / axLen
         axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
         axLen *  ay - ax * ayLen          == axLen *  by - bx * ayLen
        */
        if (!AlmostEqualUlps(aLen.fX * a[0].fY - aLen.fY * a[0].fX,
                aLen.fX * b[0].fY - aLen.fY * b[0].fX)) {
            return fUsed = 0;
        }
        // there's no great answer for intersection points for coincident rays, but return something
        fT[0][0] = fT[1][0] = 0;
        fT[1][0] = fT[1][1] = 1;
        used = 2;
    }
    return computePoints(a, used);
}

// note that this only works if both lines are neither horizontal nor vertical
int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) {
    // see if end points intersect the opposite line
    double t;
    for (int iA = 0; iA < 2; ++iA) {
        if ((t = b.exactPoint(a[iA])) >= 0) {
            insert(iA, t, a[iA]);
        }
    }
    for (int iB = 0; iB < 2; ++iB) {
        if ((t = a.exactPoint(b[iB])) >= 0) {
            insert(t, iB, b[iB]);
        }
    }
    /* Determine the intersection point of two line segments
       Return FALSE if the lines don't intersect
       from: http://paulbourke.net/geometry/lineline2d/ */
    double axLen = a[1].fX - a[0].fX;
    double ayLen = a[1].fY - a[0].fY;
    double bxLen = b[1].fX - b[0].fX;
    double byLen = b[1].fY - b[0].fY;
    /* Slopes match when denom goes to zero:
                      axLen / ayLen ==                   bxLen / byLen
    (ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
             byLen  * axLen         ==  ayLen          * bxLen
             byLen  * axLen         -   ayLen          * bxLen == 0 ( == denom )
     */
    double axByLen = axLen * byLen;
    double ayBxLen = ayLen * bxLen;
    // detect parallel lines the same way here and in SkOpAngle operator <
    // so that non-parallel means they are also sortable
    bool unparallel = NotAlmostEqualUlps(axByLen, ayBxLen);
    if (unparallel) {
        double ab0y = a[0].fY - b[0].fY;
        double ab0x = a[0].fX - b[0].fX;
        double numerA = ab0y * bxLen - byLen * ab0x;
        double numerB = ab0y * axLen - ayLen * ab0x;
        double denom = axByLen - ayBxLen;
        if (between(0, numerA, denom) && between(0, numerB, denom)) {
            fT[0][0] = numerA / denom;
            fT[1][0] = numerB / denom;
            computePoints(a, 1);
        }
    }
    if (fAllowNear || !unparallel) {
        for (int iA = 0; iA < 2; ++iA) {
            if ((t = b.nearPoint(a[iA])) >= 0) {
                insert(iA, t, a[iA]);
            }
        }
        for (int iB = 0; iB < 2; ++iB) {
            if ((t = a.nearPoint(b[iB])) >= 0) {
                insert(t, iB, b[iB]);
            }
        }
    }
    while (fUsed > 2) {
        removeOne(1);
    }
    if (fUsed == 2 && unparallel) {
        bool startMatch = fT[0][0] == 0 || fT[1][0] == 0 || fT[1][0] == 1;
        bool endMatch = fT[0][1] == 1 || fT[1][1] == 0 || fT[1][1] == 1;
        if (!startMatch && !endMatch) {
            SkASSERT(startMatch || endMatch);
            removeOne(endMatch);
        }
    }
    return fUsed;
}

static int horizontal_coincident(const SkDLine& line, double y) {
    double min = line[0].fY;
    double max = line[1].fY;
    if (min > max) {
        SkTSwap(min, max);
    }
    if (min > y || max < y) {
        return 0;
    }
    if (AlmostEqualUlps(min, max) && max - min < fabs(line[0].fX - line[1].fX)) {
        return 2;
    }
    return 1;
}

static double horizontal_intercept(const SkDLine& line, double y) {
     return (y - line[0].fY) / (line[1].fY - line[0].fY);
}

int SkIntersections::horizontal(const SkDLine& line, double y) {
    int horizontalType = horizontal_coincident(line, y);
    if (horizontalType == 1) {
        fT[0][0] = horizontal_intercept(line, y);
    } else if (horizontalType == 2) {
        fT[0][0] = 0;
        fT[0][1] = 1;
    }
    return fUsed = horizontalType;
}

int SkIntersections::horizontal(const SkDLine& line, double left, double right,
                                double y, bool flipped) {
    // see if end points intersect the opposite line
    double t;
    const SkDPoint leftPt = { left, y };
    if ((t = line.exactPoint(leftPt)) >= 0) {
        insert(t, (double) flipped, leftPt);
    }
    if (left != right) {
        const SkDPoint rightPt = { right, y };
        if ((t = line.exactPoint(rightPt)) >= 0) {
            insert(t, (double) !flipped, rightPt);
        }
        for (int index = 0; index < 2; ++index) {
            if ((t = SkDLine::ExactPointH(line[index], left, right, y)) >= 0) {
                insert((double) index, flipped ? 1 - t : t, line[index]);
            }
        }
    }
    int result = horizontal_coincident(line, y);
    if (result == 1 && fUsed == 0) {
        fT[0][0] = horizontal_intercept(line, y);
        double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
        if (between(left, xIntercept, right)) {
            fT[1][0] = (xIntercept - left) / (right - left);
            if (flipped) {
                // OPTIMIZATION: ? instead of swapping, pass original line, use [1].fX - [0].fX
                for (int index = 0; index < result; ++index) {
                    fT[1][index] = 1 - fT[1][index];
                }
            }
            return computePoints(line, result);
        }
    }
    if (!fAllowNear && result != 2) {
        return fUsed;
    }
    if ((t = line.nearPoint(leftPt)) >= 0) {
        insert(t, (double) flipped, leftPt);
    }
    if (left != right) {
        const SkDPoint rightPt = { right, y };
        if ((t = line.nearPoint(rightPt)) >= 0) {
            insert(t, (double) !flipped, rightPt);
        }
        for (int index = 0; index < 2; ++index) {
            if ((t = SkDLine::NearPointH(line[index], left, right, y)) >= 0) {
                insert((double) index, flipped ? 1 - t : t, line[index]);
            }
        }
    }
    return fUsed;
}

static int vertical_coincident(const SkDLine& line, double x) {
    double min = line[0].fX;
    double max = line[1].fX;
    if (min > max) {
        SkTSwap(min, max);
    }
    if (!precisely_between(min, x, max)) {
        return 0;
    }
    if (AlmostEqualUlps(min, max)) {
        return 2;
    }
    return 1;
}

static double vertical_intercept(const SkDLine& line, double x) {
    return (x - line[0].fX) / (line[1].fX - line[0].fX);
}

int SkIntersections::vertical(const SkDLine& line, double x) {
    int verticalType = vertical_coincident(line, x);
    if (verticalType == 1) {
        fT[0][0] = vertical_intercept(line, x);
    } else if (verticalType == 2) {
        fT[0][0] = 0;
        fT[0][1] = 1;
    }
    return fUsed = verticalType;
}

int SkIntersections::vertical(const SkDLine& line, double top, double bottom,
                              double x, bool flipped) {
    // see if end points intersect the opposite line
    double t;
    SkDPoint topPt = { x, top };
    if ((t = line.exactPoint(topPt)) >= 0) {
        insert(t, (double) flipped, topPt);
    }
    if (top != bottom) {
        SkDPoint bottomPt = { x, bottom };
        if ((t = line.exactPoint(bottomPt)) >= 0) {
            insert(t, (double) !flipped, bottomPt);
        }
        for (int index = 0; index < 2; ++index) {
            if ((t = SkDLine::ExactPointV(line[index], top, bottom, x)) >= 0) {
                insert((double) index, flipped ? 1 - t : t, line[index]);
            }
        }
    }
    int result = vertical_coincident(line, x);
    if (result == 1 && fUsed == 0) {
        fT[0][0] = vertical_intercept(line, x);
        double yIntercept = line[0].fY + fT[0][0] * (line[1].fY - line[0].fY);
        if (between(top, yIntercept, bottom)) {
            fT[1][0] = (yIntercept - top) / (bottom - top);
            if (flipped) {
                // OPTIMIZATION: instead of swapping, pass original line, use [1].fY - [0].fY
                for (int index = 0; index < result; ++index) {
                    fT[1][index] = 1 - fT[1][index];
                }
            }
            return computePoints(line, result);
        }
    }
    if (!fAllowNear && result != 2) {
        return fUsed;
    }
    if ((t = line.nearPoint(topPt)) >= 0) {
        insert(t, (double) flipped, topPt);
    }
    if (top != bottom) {
        SkDPoint bottomPt = { x, bottom };
        if ((t = line.nearPoint(bottomPt)) >= 0) {
            insert(t, (double) !flipped, bottomPt);
        }
        for (int index = 0; index < 2; ++index) {
            if ((t = SkDLine::NearPointV(line[index], top, bottom, x)) >= 0) {
                insert((double) index, flipped ? 1 - t : t, line[index]);
            }
        }
    }
    return fUsed;
}

// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
// 4 subs, 2 muls, 1 cmp
static bool ccw(const SkDPoint& A, const SkDPoint& B, const SkDPoint& C) {
    return (C.fY - A.fY) * (B.fX - A.fX) > (B.fY - A.fY) * (C.fX - A.fX);
}

// 16 subs, 8 muls, 6 cmps
bool SkIntersections::Test(const SkDLine& a, const SkDLine& b) {
    return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1])
            && ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]);
}