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      1 /*
      2  * Copyright (C) 2010 Google Inc. All rights reserved.
      3  *
      4  * Redistribution and use in source and binary forms, with or without
      5  * modification, are permitted provided that the following conditions
      6  * are met:
      7  *
      8  * 1.  Redistributions of source code must retain the above copyright
      9  *     notice, this list of conditions and the following disclaimer.
     10  * 2.  Redistributions in binary form must reproduce the above copyright
     11  *     notice, this list of conditions and the following disclaimer in the
     12  *     documentation and/or other materials provided with the distribution.
     13  *
     14  * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
     15  * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
     16  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
     17  * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
     18  * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
     19  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
     20  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
     21  * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     22  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
     23  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     24  */
     25 
     26 #ifndef LoopBlinnMathUtils_h
     27 #define LoopBlinnMathUtils_h
     28 
     29 #include "FloatPoint.h"
     30 #include "FloatPoint3D.h"
     31 #include <math.h>
     32 
     33 namespace WebCore {
     34 
     35 // Use a namespace for these so we can easily import them.
     36 namespace LoopBlinnMathUtils {
     37 
     38 float roundToZero(float val);
     39 bool approxEqual(const FloatPoint& v0, const FloatPoint& v1);
     40 bool approxEqual(const FloatPoint3D& v0, const FloatPoint3D& v1);
     41 bool approxEqual(float f0, float f1);
     42 
     43 // Determines whether the line segment between (p1, q1) intersects
     44 // that between (p2, q2).
     45 bool linesIntersect(const FloatPoint& p1,
     46                     const FloatPoint& q1,
     47                     const FloatPoint& p2,
     48                     const FloatPoint& q2);
     49 
     50 // Determines whether "point" is inside the 2D triangle defined by
     51 // vertices a, b, and c. This test defines that points exactly on an
     52 // edge are not considered to be inside the triangle.
     53 bool pointInTriangle(const FloatPoint& point,
     54                      const FloatPoint& a,
     55                      const FloatPoint& b,
     56                      const FloatPoint& c);
     57 
     58 // Determines whether the triangles defined by the points (a1, b1, c1)
     59 // and (a2, b2, c2) overlap. The definition of this function is that
     60 // if the two triangles only share an adjacent edge or vertex, they
     61 // are not considered to overlap.
     62 bool trianglesOverlap(const FloatPoint& a1,
     63                       const FloatPoint& b1,
     64                       const FloatPoint& c1,
     65                       const FloatPoint& a2,
     66                       const FloatPoint& b2,
     67                       const FloatPoint& c2);
     68 
     69 // Given a src cubic bezier, chops it at the specified t value,
     70 // where 0 < t < 1, and returns the two new cubics in dst[0..3]
     71 // and dst[3..6].
     72 void chopCubicAt(const FloatPoint src[4], FloatPoint dst[7], float t);
     73 
     74 // "X-Ray" queries. An XRay is a half-line originating at the given
     75 // point and extending to x=+infinity.
     76 typedef FloatPoint XRay;
     77 
     78 // Given an arbitrary cubic bezier, return the number of times an XRay
     79 // crosses the cubic. Valid return values are [0..3].
     80 //
     81 // By definition the cubic is open at the starting point; in other
     82 // words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
     83 // left of the curve, the line is not considered to cross the curve,
     84 // but if it is equal to cubic[3].fY then it is considered to
     85 // cross.
     86 //
     87 // Outgoing "ambiguous" argument indicates whether the answer is ambiguous
     88 // because the query occurred exactly at one of the endpoints' y
     89 // coordinates or at a tangent point, indicating that another query y
     90 // coordinate is preferred for robustness.
     91 int numXRayCrossingsForCubic(const XRay& xRay,
     92                              const FloatPoint cubic[4],
     93                              bool& ambiguous);
     94 
     95 // Given a line segment from lineEndpoints[0] to lineEndpoints[1], and an
     96 // XRay, returns true if they intersect. Outgoing "ambiguous" argument
     97 // indicates whether the answer is ambiguous because the query occurred
     98 // exactly at one of the endpoints' y coordinates, indicating that another
     99 // query y coordinate is preferred for robustness.
    100 bool xRayCrossesLine(const XRay& xRay,
    101                      const FloatPoint lineEndpoints[2],
    102                      bool& ambiguous);
    103 
    104 
    105 bool isConvex(const FloatPoint* vertices, int nVertices);
    106 
    107 } // namespace LoopBlinnMathUtils
    108 
    109 } // namespace WebCore
    110 
    111 #endif // LoopBlinnMathUtils_h
    112