| /* |
| * Copyright (C) 2012 Adobe Systems Incorporated. All rights reserved. |
| * |
| * 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. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND 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 THE |
| * COPYRIGHT HOLDER OR 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/FloatPolygon.h" |
| |
| #include "wtf/MathExtras.h" |
| #include <memory> |
| |
| namespace blink { |
| |
| static inline float determinant(const FloatSize& a, const FloatSize& b) { |
| return a.width() * b.height() - a.height() * b.width(); |
| } |
| |
| static inline bool areCollinearPoints(const FloatPoint& p0, |
| const FloatPoint& p1, |
| const FloatPoint& p2) { |
| return !determinant(p1 - p0, p2 - p0); |
| } |
| |
| static inline bool areCoincidentPoints(const FloatPoint& p0, |
| const FloatPoint& p1) { |
| return p0.x() == p1.x() && p0.y() == p1.y(); |
| } |
| |
| static inline bool isPointOnLineSegment(const FloatPoint& vertex1, |
| const FloatPoint& vertex2, |
| const FloatPoint& point) { |
| return point.x() >= std::min(vertex1.x(), vertex2.x()) && |
| point.x() <= std::max(vertex1.x(), vertex2.x()) && |
| areCollinearPoints(vertex1, vertex2, point); |
| } |
| |
| static inline unsigned nextVertexIndex(unsigned vertexIndex, |
| unsigned nVertices, |
| bool clockwise) { |
| return ((clockwise) ? vertexIndex + 1 : vertexIndex - 1 + nVertices) % |
| nVertices; |
| } |
| |
| static unsigned findNextEdgeVertexIndex(const FloatPolygon& polygon, |
| unsigned vertexIndex1, |
| bool clockwise) { |
| unsigned nVertices = polygon.numberOfVertices(); |
| unsigned vertexIndex2 = nextVertexIndex(vertexIndex1, nVertices, clockwise); |
| |
| while (vertexIndex2 && areCoincidentPoints(polygon.vertexAt(vertexIndex1), |
| polygon.vertexAt(vertexIndex2))) |
| vertexIndex2 = nextVertexIndex(vertexIndex2, nVertices, clockwise); |
| |
| while (vertexIndex2) { |
| unsigned vertexIndex3 = nextVertexIndex(vertexIndex2, nVertices, clockwise); |
| if (!areCollinearPoints(polygon.vertexAt(vertexIndex1), |
| polygon.vertexAt(vertexIndex2), |
| polygon.vertexAt(vertexIndex3))) |
| break; |
| vertexIndex2 = vertexIndex3; |
| } |
| |
| return vertexIndex2; |
| } |
| |
| FloatPolygon::FloatPolygon(std::unique_ptr<Vector<FloatPoint>> vertices, |
| WindRule fillRule) |
| : m_vertices(std::move(vertices)), m_fillRule(fillRule) { |
| unsigned nVertices = numberOfVertices(); |
| m_edges.resize(nVertices); |
| m_empty = nVertices < 3; |
| |
| if (nVertices) |
| m_boundingBox.setLocation(vertexAt(0)); |
| |
| if (m_empty) |
| return; |
| |
| unsigned minVertexIndex = 0; |
| for (unsigned i = 1; i < nVertices; ++i) { |
| const FloatPoint& vertex = vertexAt(i); |
| if (vertex.y() < vertexAt(minVertexIndex).y() || |
| (vertex.y() == vertexAt(minVertexIndex).y() && |
| vertex.x() < vertexAt(minVertexIndex).x())) |
| minVertexIndex = i; |
| } |
| FloatPoint nextVertex = vertexAt((minVertexIndex + 1) % nVertices); |
| FloatPoint prevVertex = |
| vertexAt((minVertexIndex + nVertices - 1) % nVertices); |
| bool clockwise = determinant(vertexAt(minVertexIndex) - prevVertex, |
| nextVertex - prevVertex) > 0; |
| |
| unsigned edgeIndex = 0; |
| unsigned vertexIndex1 = 0; |
| do { |
| m_boundingBox.extend(vertexAt(vertexIndex1)); |
| unsigned vertexIndex2 = |
| findNextEdgeVertexIndex(*this, vertexIndex1, clockwise); |
| m_edges[edgeIndex].m_polygon = this; |
| m_edges[edgeIndex].m_vertexIndex1 = vertexIndex1; |
| m_edges[edgeIndex].m_vertexIndex2 = vertexIndex2; |
| m_edges[edgeIndex].m_edgeIndex = edgeIndex; |
| ++edgeIndex; |
| vertexIndex1 = vertexIndex2; |
| } while (vertexIndex1); |
| |
| if (edgeIndex > 3) { |
| const FloatPolygonEdge& firstEdge = m_edges[0]; |
| const FloatPolygonEdge& lastEdge = m_edges[edgeIndex - 1]; |
| if (areCollinearPoints(lastEdge.vertex1(), lastEdge.vertex2(), |
| firstEdge.vertex2())) { |
| m_edges[0].m_vertexIndex1 = lastEdge.m_vertexIndex1; |
| edgeIndex--; |
| } |
| } |
| |
| m_edges.resize(edgeIndex); |
| m_empty = m_edges.size() < 3; |
| |
| if (m_empty) |
| return; |
| |
| for (unsigned i = 0; i < m_edges.size(); ++i) { |
| FloatPolygonEdge* edge = &m_edges[i]; |
| m_edgeTree.add(EdgeInterval(edge->minY(), edge->maxY(), edge)); |
| } |
| } |
| |
| bool FloatPolygon::overlappingEdges( |
| float minY, |
| float maxY, |
| Vector<const FloatPolygonEdge*>& result) const { |
| Vector<FloatPolygon::EdgeInterval> overlappingEdgeIntervals; |
| m_edgeTree.allOverlaps(FloatPolygon::EdgeInterval(minY, maxY, 0), |
| overlappingEdgeIntervals); |
| unsigned overlappingEdgeIntervalsSize = overlappingEdgeIntervals.size(); |
| result.resize(overlappingEdgeIntervalsSize); |
| for (unsigned i = 0; i < overlappingEdgeIntervalsSize; ++i) { |
| const FloatPolygonEdge* edge = static_cast<const FloatPolygonEdge*>( |
| overlappingEdgeIntervals[i].data()); |
| ASSERT(edge); |
| result[i] = edge; |
| } |
| return overlappingEdgeIntervalsSize > 0; |
| } |
| |
| static inline float leftSide(const FloatPoint& vertex1, |
| const FloatPoint& vertex2, |
| const FloatPoint& point) { |
| return ((point.x() - vertex1.x()) * (vertex2.y() - vertex1.y())) - |
| ((vertex2.x() - vertex1.x()) * (point.y() - vertex1.y())); |
| } |
| |
| bool FloatPolygon::containsEvenOdd(const FloatPoint& point) const { |
| unsigned crossingCount = 0; |
| for (unsigned i = 0; i < numberOfEdges(); ++i) { |
| const FloatPoint& vertex1 = edgeAt(i).vertex1(); |
| const FloatPoint& vertex2 = edgeAt(i).vertex2(); |
| if (isPointOnLineSegment(vertex1, vertex2, point)) |
| return true; |
| if ((vertex1.y() <= point.y() && vertex2.y() > point.y()) || |
| (vertex1.y() > point.y() && vertex2.y() <= point.y())) { |
| float vt = (point.y() - vertex1.y()) / (vertex2.y() - vertex1.y()); |
| if (point.x() < vertex1.x() + vt * (vertex2.x() - vertex1.x())) |
| ++crossingCount; |
| } |
| } |
| return crossingCount & 1; |
| } |
| |
| bool FloatPolygon::containsNonZero(const FloatPoint& point) const { |
| int windingNumber = 0; |
| for (unsigned i = 0; i < numberOfEdges(); ++i) { |
| const FloatPoint& vertex1 = edgeAt(i).vertex1(); |
| const FloatPoint& vertex2 = edgeAt(i).vertex2(); |
| if (isPointOnLineSegment(vertex1, vertex2, point)) |
| return true; |
| if (vertex2.y() <= point.y()) { |
| if ((vertex1.y() > point.y()) && (leftSide(vertex1, vertex2, point) > 0)) |
| ++windingNumber; |
| } else if (vertex2.y() >= point.y()) { |
| if ((vertex1.y() <= point.y()) && (leftSide(vertex1, vertex2, point) < 0)) |
| --windingNumber; |
| } |
| } |
| return windingNumber; |
| } |
| |
| bool FloatPolygon::contains(const FloatPoint& point) const { |
| if (!m_boundingBox.contains(point)) |
| return false; |
| return (fillRule() == RULE_NONZERO) ? containsNonZero(point) |
| : containsEvenOdd(point); |
| } |
| |
| bool VertexPair::intersection(const VertexPair& other, |
| FloatPoint& point) const { |
| // See: http://paulbourke.net/geometry/pointlineplane/, |
| // "Intersection point of two lines in 2 dimensions" |
| |
| const FloatSize& thisDelta = vertex2() - vertex1(); |
| const FloatSize& otherDelta = other.vertex2() - other.vertex1(); |
| float denominator = determinant(thisDelta, otherDelta); |
| if (!denominator) |
| return false; |
| |
| // The two line segments: "this" vertex1,vertex2 and "other" vertex1,vertex2, |
| // have been defined in parametric form. Each point on the line segment is: |
| // vertex1 + u * (vertex2 - vertex1), when 0 <= u <= 1. We're computing the |
| // values of u for each line at their intersection point. |
| |
| const FloatSize& vertex1Delta = vertex1() - other.vertex1(); |
| float uThisLine = determinant(otherDelta, vertex1Delta) / denominator; |
| float uOtherLine = determinant(thisDelta, vertex1Delta) / denominator; |
| |
| if (uThisLine < 0 || uOtherLine < 0 || uThisLine > 1 || uOtherLine > 1) |
| return false; |
| |
| point = vertex1() + uThisLine * thisDelta; |
| return true; |
| } |
| |
| } // namespace blink |