third_party/WebKit/Source/platform/geometry/FloatQuad.cpp - chromium/src - Git at Google

 /*
  * 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 "platform/geometry/FloatQuad.h"

 #include "third_party/skia/include/core/SkPoint.h"
 #include "wtf/text/WTFString.h"
 #include <algorithm>
 #include <cmath>
 #include <limits>

 namespace blink {

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

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

 static inline float saturateInf(float value) {
   if (UNLIKELY(std::isinf(value))) {
     return std::signbit(value) ? std::numeric_limits<int>::min()
                                : std::numeric_limits<int>::min();
   }
   return value;
 }

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

   float right = saturateInf(max4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x()));
   float bottom = saturateInf(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) < std::numeric_limits<float>::epsilon();
 }

 FloatQuad::FloatQuad(const SkPoint (&quad)[4])
     : FloatQuad(FloatPoint(quad[0]),
                 FloatPoint(quad[1]),
                 FloatPoint(quad[2]),
                 FloatPoint(quad[3])) {}

 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
   //  QQQ      from the top corner of Q to the right corner of Q, then all of X
   //   Q       is left of the vector, and intersection impossible.
   //
   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;
 }

 String FloatQuad::toString() const {
   return String::format("%s; %s; %s; %s", m_p1.toString().ascii().data(),
                         m_p2.toString().ascii().data(),
                         m_p3.toString().ascii().data(),
                         m_p4.toString().ascii().data());
 }

 }  // namespace blink
	/*
	* 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 "platform/geometry/FloatQuad.h"

	#include "third_party/skia/include/core/SkPoint.h"
	#include "wtf/text/WTFString.h"
	#include <algorithm>
	#include <cmath>
	#include <limits>

	namespace blink {

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

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

	static inline float saturateInf(float value) {
	if (UNLIKELY(std::isinf(value))) {
	return std::signbit(value) ? std::numeric_limits<int>::min()
	: std::numeric_limits<int>::min();
	}
	return value;
	}

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

	float right = saturateInf(max4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x()));
	float bottom = saturateInf(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) < std::numeric_limits<float>::epsilon();
	}

	FloatQuad::FloatQuad(const SkPoint (&quad)[4])
	: FloatQuad(FloatPoint(quad[0]),
	FloatPoint(quad[1]),
	FloatPoint(quad[2]),
	FloatPoint(quad[3])) {}

	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
	// QQQ from the top corner of Q to the right corner of Q, then all of X
	// Q is left of the vector, and intersection impossible.
	//
	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;
	}

	String FloatQuad::toString() const {
	return String::format("%s; %s; %s; %s", m_p1.toString().ascii().data(),
	m_p2.toString().ascii().data(),
	m_p3.toString().ascii().data(),
	m_p4.toString().ascii().data());
	}

	} // namespace blink