root/Source/platform/geometry/FloatQuad.cpp

DEFINITIONS

1. min4
2. max4
3. dot
4. determinant
5. isPointInTriangle
6. boundingBox
7. withinEpsilon
8. isRectilinear
9. containsPoint
10. containsQuad
11. rightMostCornerToVector
12. intersectsRect
13. lineIntersectsCircle
14. intersectsCircle
15. intersectsEllipse
16. isCounterclockwise

/*
 * Copyright (C) 2008 Apple Inc. All rights reserved.
 * Copyright (C) 2012 Nokia Corporation and/or its subsidiary(-ies)
 * Copyright (C) 2013 Xidorn Quan (quanxunzhen@gmail.com)
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1.  Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 * 2.  Redistributions in binary form must reproduce the above copyright
 *     notice, this list of conditions and the following disclaimer in the
 *     documentation and/or other materials provided with the distribution.
 * 3.  Neither the name of Apple Computer, Inc. ("Apple") nor the names of
 *     its contributors may be used to endorse or promote products derived
 *     from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#include "config.h"
#include "platform/geometry/FloatQuad.h"

#include <algorithm>
#include <limits>

using namespace std;

namespace WebCore {

static inline float min4(float a, float b, float c, float d)
{
    return min(min(a, b), min(c, d));
}

static inline float max4(float a, float b, float c, float d)
{
    return max(max(a, b), max(c, d));
}

inline float dot(const FloatSize& a, const FloatSize& b)
{
    return a.width() * b.width() + a.height() * b.height();
}

inline float determinant(const FloatSize& a, const FloatSize& b)
{
    return a.width() * b.height() - a.height() * b.width();
}

inline bool isPointInTriangle(const FloatPoint& p, const FloatPoint& t1, const FloatPoint& t2, const FloatPoint& t3)
{
    // Compute vectors
    FloatSize v0 = t3 - t1;
    FloatSize v1 = t2 - t1;
    FloatSize v2 = p - t1;

    // Compute dot products
    float dot00 = dot(v0, v0);
    float dot01 = dot(v0, v1);
    float dot02 = dot(v0, v2);
    float dot11 = dot(v1, v1);
    float dot12 = dot(v1, v2);

    // Compute barycentric coordinates
    float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
    float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
    float v = (dot00 * dot12 - dot01 * dot02) * invDenom;

    // Check if point is in triangle
    return (u >= 0) && (v >= 0) && (u + v <= 1);
}

FloatRect FloatQuad::boundingBox() const
{
    float left   = min4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
    float top    = min4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());

    float right  = max4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
    float bottom = max4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());

    return FloatRect(left, top, right - left, bottom - top);
}

static inline bool withinEpsilon(float a, float b)
{
    return fabs(a - b) < numeric_limits<float>::epsilon();
}

bool FloatQuad::isRectilinear() const
{
    return (withinEpsilon(m_p1.x(), m_p2.x()) && withinEpsilon(m_p2.y(), m_p3.y()) && withinEpsilon(m_p3.x(), m_p4.x()) && withinEpsilon(m_p4.y(), m_p1.y()))
        || (withinEpsilon(m_p1.y(), m_p2.y()) && withinEpsilon(m_p2.x(), m_p3.x()) && withinEpsilon(m_p3.y(), m_p4.y()) && withinEpsilon(m_p4.x(), m_p1.x()));
}

bool FloatQuad::containsPoint(const FloatPoint& p) const
{
    return isPointInTriangle(p, m_p1, m_p2, m_p3) || isPointInTriangle(p, m_p1, m_p3, m_p4);
}

// Note that we only handle convex quads here.
bool FloatQuad::containsQuad(const FloatQuad& other) const
{
    return containsPoint(other.p1()) && containsPoint(other.p2()) && containsPoint(other.p3()) && containsPoint(other.p4());
}

static inline FloatPoint rightMostCornerToVector(const FloatRect& rect, const FloatSize& vector)
{
    // Return the corner of the rectangle that if it is to the left of the vector
    // would mean all of the rectangle is to the left of the vector.
    // The vector here represents the side between two points in a clockwise convex polygon.
    //
    //  Q  XXX
    // QQQ XXX   If the lower left corner of X is left of the vector that goes from the top corner of Q to
    //  QQQ      the right corner of Q, then all of X is left of the vector, and intersection impossible.
    //   Q
    //
    FloatPoint point;
    if (vector.width() >= 0)
        point.setY(rect.maxY());
    else
        point.setY(rect.y());
    if (vector.height() >= 0)
        point.setX(rect.x());
    else
        point.setX(rect.maxX());
    return point;
}

bool FloatQuad::intersectsRect(const FloatRect& rect) const
{
    // For each side of the quad clockwise we check if the rectangle is to the left of it
    // since only content on the right can onlap with the quad.
    // This only works if the quad is convex.
    FloatSize v1, v2, v3, v4;

    // Ensure we use clockwise vectors.
    if (!isCounterclockwise()) {
        v1 = m_p2 - m_p1;
        v2 = m_p3 - m_p2;
        v3 = m_p4 - m_p3;
        v4 = m_p1 - m_p4;
    } else {
        v1 = m_p4 - m_p1;
        v2 = m_p1 - m_p2;
        v3 = m_p2 - m_p3;
        v4 = m_p3 - m_p4;
    }

    FloatPoint p = rightMostCornerToVector(rect, v1);
    if (determinant(v1, p - m_p1) < 0)
        return false;

    p = rightMostCornerToVector(rect, v2);
    if (determinant(v2, p - m_p2) < 0)
        return false;

    p = rightMostCornerToVector(rect, v3);
    if (determinant(v3, p - m_p3) < 0)
        return false;

    p = rightMostCornerToVector(rect, v4);
    if (determinant(v4, p - m_p4) < 0)
        return false;

    // If not all of the rectangle is outside one of the quad's four sides, then that means at least
    // a part of the rectangle is overlapping the quad.
    return true;
}

// Tests whether the line is contained by or intersected with the circle.
static inline bool lineIntersectsCircle(const FloatPoint& center, float radius, const FloatPoint& p0, const FloatPoint& p1)
{
    float x0 = p0.x() - center.x(), y0 = p0.y() - center.y();
    float x1 = p1.x() - center.x(), y1 = p1.y() - center.y();
    float radius2 = radius * radius;
    if ((x0 * x0 + y0 * y0) <= radius2 || (x1 * x1 + y1 * y1) <= radius2)
        return true;
    if (p0 == p1)
        return false;

    float a = y0 - y1;
    float b = x1 - x0;
    float c = x0 * y1 - x1 * y0;
    float distance2 = c * c / (a * a + b * b);
    // If distance between the center point and the line > the radius,
    // the line doesn't cross (or is contained by) the ellipse.
    if (distance2 > radius2)
        return false;

    // The nearest point on the line is between p0 and p1?
    float x = - a * c / (a * a + b * b);
    float y = - b * c / (a * a + b * b);
    return (((x0 <= x && x <= x1) || (x0 >= x && x >= x1))
        && ((y0 <= y && y <= y1) || (y1 <= y && y <= y0)));
}

bool FloatQuad::intersectsCircle(const FloatPoint& center, float radius) const
{
    return containsPoint(center) // The circle may be totally contained by the quad.
        || lineIntersectsCircle(center, radius, m_p1, m_p2)
        || lineIntersectsCircle(center, radius, m_p2, m_p3)
        || lineIntersectsCircle(center, radius, m_p3, m_p4)
        || lineIntersectsCircle(center, radius, m_p4, m_p1);
}

bool FloatQuad::intersectsEllipse(const FloatPoint& center, const FloatSize& radii) const
{
    // Transform the ellipse to an origin-centered circle whose radius is the product of major radius and minor radius.
    // Here we apply the same transformation to the quad.
    FloatQuad transformedQuad(*this);
    transformedQuad.move(-center.x(), -center.y());
    transformedQuad.scale(radii.height(), radii.width());

    FloatPoint originPoint;
    return transformedQuad.intersectsCircle(originPoint, radii.height() * radii.width());

}

bool FloatQuad::isCounterclockwise() const
{
    // Return if the two first vectors are turning clockwise. If the quad is convex then all following vectors will turn the same way.
    return determinant(m_p2 - m_p1, m_p3 - m_p2) < 0;
}

} // namespace WebCore