Esempio n. 1
0
bool isLinear(const Cubic& cubic, int startIndex, int endIndex) {
    LineParameters lineParameters;
    lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
    double normalSquared = lineParameters.normalSquared();
    double distance[2]; // distance is not normalized
    int mask = other_two(startIndex, endIndex);
    int inner1 = startIndex ^ mask;
    int inner2 = endIndex ^ mask;
    lineParameters.controlPtDistance(cubic, inner1, inner2, distance);
    double limit = normalSquared;
    int index;
    for (index = 0; index < 2; ++index) {
        double distSq = distance[index];
        distSq *= distSq;
        if (approximately_greater(distSq, limit)) {
            return false;
        }
    }
    return true;
}
Esempio n. 2
0
// return false if unable to clip (e.g., unable to create implicit line)
// caller should subdivide, or create degenerate if the values are too small
bool bezier_clip(const Cubic& cubic1, const Cubic& cubic2, double& minT, double& maxT) {
    minT = 1;
    maxT = 0;
    // determine normalized implicit line equation for pt[0] to pt[3]
    //   of the form ax + by + c = 0, where a*a + b*b == 1
    
    // find the implicit line equation parameters
    LineParameters endLine;
    endLine.cubicEndPoints(cubic1);
    if (!endLine.normalize()) {
        printf("line cannot be normalized: need more code here\n");
        return false;
    }

    double distance[2];
    endLine.controlPtDistance(cubic1, distance);
    
    // find fat line
    double top = distance[0];
    double bottom = distance[1];
    if (top > bottom) {
        std::swap(top, bottom);
    }
    if (top * bottom >= 0) {
        const double scale = 3/4.0; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf (13)
        if (top < 0) {
            top *= scale;
            bottom = 0;
        } else {
            top = 0;
            bottom *= scale;
        }
    } else {
        const double scale = 4/9.0; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf (15)
        top *= scale;
        bottom *= scale;
    }
    
    // compute intersecting candidate distance
    Cubic distance2y; // points with X of (0, 1/3, 2/3, 1)
    endLine.cubicDistanceY(cubic2, distance2y);
    
    int flags = 0;
    if (approximately_lesser(distance2y[0].y, top)) {
        flags |= kFindTopMin;
    } else if (approximately_greater(distance2y[0].y, bottom)) {
        flags |= kFindBottomMin;
    } else {
        minT = 0;
    }

    if (approximately_lesser(distance2y[3].y, top)) {
        flags |= kFindTopMax;
    } else if (approximately_greater(distance2y[3].y, bottom)) {
        flags |= kFindBottomMax;
    } else {
        maxT = 1;
    }
    // Find the intersection of distance convex hull and fat line.
    char to_0[2];
    char to_3[2];
    bool do_1_2_edge = convex_x_hull(distance2y, to_0, to_3);
    x_at(distance2y[0], distance2y[to_0[0]], top, bottom, flags, minT, maxT);
    if (to_0[0] != to_0[1]) {
        x_at(distance2y[0], distance2y[to_0[1]], top, bottom, flags, minT, maxT);
    }
    x_at(distance2y[to_3[0]], distance2y[3], top, bottom, flags, minT, maxT);
    if (to_3[0] != to_3[1]) {
        x_at(distance2y[to_3[1]], distance2y[3], top, bottom, flags, minT, maxT);
    }
    if (do_1_2_edge) {
        x_at(distance2y[1], distance2y[2], top, bottom, flags, minT, maxT);
    }
    
    return minT < maxT; // returns false if distance shows no intersection
}
Esempio n. 3
0
// return false if unable to clip (e.g., unable to create implicit line)
// caller should subdivide, or create degenerate if the values are too small
bool bezier_clip(const Quadratic& q1, const Quadratic& q2, double& minT, double& maxT) {
    minT = 1;
    maxT = 0;
    // determine normalized implicit line equation for pt[0] to pt[3]
    //   of the form ax + by + c = 0, where a*a + b*b == 1

    // find the implicit line equation parameters
    LineParameters endLine;
    endLine.quadEndPoints(q1);
    if (!endLine.normalize()) {
        printf("line cannot be normalized: need more code here\n");
        assert(0);
        return false;
    }

    double distance = endLine.controlPtDistance(q1);

    // find fat line
    double top = 0;
    double bottom = distance / 2; // http://students.cs.byu.edu/~tom/557/text/cic.pdf (7.6)
    if (top > bottom) {
        std::swap(top, bottom);
    }

    // compute intersecting candidate distance
    Quadratic distance2y; // points with X of (0, 1/2, 1)
    endLine.quadDistanceY(q2, distance2y);

    int flags = 0;
    if (approximately_lesser(distance2y[0].y, top)) {
        flags |= kFindTopMin;
    } else if (approximately_greater(distance2y[0].y, bottom)) {
        flags |= kFindBottomMin;
    } else {
        minT = 0;
    }

    if (approximately_lesser(distance2y[2].y, top)) {
        flags |= kFindTopMax;
    } else if (approximately_greater(distance2y[2].y, bottom)) {
        flags |= kFindBottomMax;
    } else {
        maxT = 1;
    }
    // Find the intersection of distance convex hull and fat line.
    int idx = 0;
    do {
        int next = idx + 1;
        if (next == 3) {
            next = 0;
        }
        x_at(distance2y[idx], distance2y[next], top, bottom, flags, minT, maxT);
        idx = next;
    } while (idx);
#if DEBUG_BEZIER_CLIP
    _Rect r1, r2;
    r1.setBounds(q1);
    r2.setBounds(q2);
    _Point testPt = {0.487, 0.337};
    if (r1.contains(testPt) && r2.contains(testPt)) {
        printf("%s q1=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
                " q2=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) minT=%1.9g maxT=%1.9g\n",
                __FUNCTION__, q1[0].x, q1[0].y, q1[1].x, q1[1].y, q1[2].x, q1[2].y,
                q2[0].x, q2[0].y, q2[1].x, q2[1].y, q2[2].x, q2[2].y, minT, maxT);
    }
#endif
    return minT < maxT; // returns false if distance shows no intersection
}