From Marco Jez, added DelaunayTriangulator class.
This commit is contained in:
Robert Osfield
341
src/osgUtil/DelaunayTriangulator.cpp
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341
src/osgUtil/DelaunayTriangulator.cpp
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#include <osgUtil/DelaunayTriangulator>
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#include <osg/GL>
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#include <osg/Vec3>
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#include <osg/Array>
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#include <osg/Notify>
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#include <algorithm>
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#include <list>
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#include <set>
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namespace osgUtil
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{
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//////////////////////////////////////////////////////////////////////////////////////
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// MISC MATH FUNCTIONS
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// Compute the circumcircle of a triangle (only x and y coordinates are used),
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// return (Cx, Cy, r^2)
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inline osg::Vec3 compute_circumcircle(
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const osg::Vec3 &a,
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const osg::Vec3 &b,
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const osg::Vec3 &c)
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{
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float D =
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(a.x() - c.x()) * (b.y() - c.y()) -
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(b.x() - c.x()) * (a.y() - c.y());
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float cx =
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(((a.x() - c.x()) * (a.x() + c.x()) +
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(a.y() - c.y()) * (a.y() + c.y())) / 2 * (b.y() - c.y()) -
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((b.x() - c.x()) * (b.x() + c.x()) +
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(b.y() - c.y()) * (b.y() + c.y())) / 2 * (a.y() - c.y())) / D;
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float cy =
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(((b.x() - c.x()) * (b.x() + c.x()) +
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(b.y() - c.y()) * (b.y() + c.y())) / 2 * (a.x() - c.x()) -
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((a.x() - c.x()) * (a.x() + c.x()) +
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(a.y() - c.y()) * (a.y() + c.y())) / 2 * (b.x() - c.x())) / D;
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float r2 = (c.x() - cx) * (c.x() - cx) + (c.y() - cy) * (c.y() - cy);
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return osg::Vec3(cx, cy, r2);
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}
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// Test whether a point (only the x and y coordinates are used) lies inside
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// a circle; the circle is passed as a vector: (Cx, Cy, r^2).
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inline bool point_in_circle(const osg::Vec3 &point, const osg::Vec3 &circle)
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{
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float r2 =
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(point.x() - circle.x()) * (point.x() - circle.x()) +
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(point.y() - circle.y()) * (point.y() - circle.y());
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return r2 <= circle.z();
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}
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//
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//////////////////////////////////////////////////////////////////////////////////////
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// data type for vertex indices
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typedef GLuint Vertex_index;
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// CLASS: Edge
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// This class describes an edge of a triangle (it stores vertex indices to the two
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// endpoints).
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class Edge {
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public:
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// Comparison object (for sorting)
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struct Less {
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inline bool operator()(const Edge &e1, const Edge &e2) const
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{
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if (e1.ibs() < e2.ibs()) return true;
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if (e1.ibs() > e2.ibs()) return false;
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if (e1.ies() < e2.ies()) return true;
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return false;
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}
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};
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Edge() {}
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Edge(Vertex_index ib, Vertex_index ie) : ib_(ib), ie_(ie), ibs_(std::min(ib, ie)), ies_(std::max(ib, ie)), duplicate_(false) {}
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// first endpoint
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inline Vertex_index ib() const { return ib_; }
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// second endpoint
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inline Vertex_index ie() const { return ie_; }
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// first sorted endpoint
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inline Vertex_index ibs() const { return ibs_; }
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// second sorted endpoint
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inline Vertex_index ies() const { return ies_; }
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// get the "duplicate" flag
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inline bool get_duplicate() const { return duplicate_; }
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// set the "duplicate" flag
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inline void set_duplicate(bool v) { duplicate_ = v; }
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private:
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Vertex_index ib_, ie_;
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Vertex_index ibs_, ies_;
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bool duplicate_;
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};
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// CLASS: Triangle
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class Triangle {
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public:
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Triangle(Vertex_index a, Vertex_index b, Vertex_index c, osg::Vec3Array *points)
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: a_(a),
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b_(b),
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c_(c),
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cc_(compute_circumcircle((*points)[a_], (*points)[b_], (*points)[c_]))
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{
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edge_[0] = Edge(a_, b_);
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edge_[1] = Edge(b_, c_);
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edge_[2] = Edge(c_, a_);
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}
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inline Vertex_index a() const { return a_; }
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inline Vertex_index b() const { return b_; }
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inline Vertex_index c() const { return c_; }
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inline const Edge &get_edge(int idx) const { return edge_[idx]; }
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inline const osg::Vec3 &get_circumcircle() const { return cc_; }
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inline osg::Vec3 compute_normal(osg::Vec3Array *points) const
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{
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osg::Vec3 N = ((*points)[b_] - (*points)[a_]) ^ ((*points)[c_] - (*points)[a_]);
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return N / N.length();
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}
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private:
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Vertex_index a_;
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Vertex_index b_;
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Vertex_index c_;
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osg::Vec3 cc_;
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Edge edge_[3];
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};
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// comparison function for sorting sample points by the X coordinate
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bool Sample_point_compare(const osg::Vec3 &p1, const osg::Vec3 &p2)
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{
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return p1.x() < p2.x();
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}
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// container types
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typedef std::set<Edge, Edge::Less> Edge_set;
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typedef std::list<Triangle> Triangle_list;
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DelaunayTriangulator::DelaunayTriangulator():
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osg::Referenced()
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{
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}
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DelaunayTriangulator::DelaunayTriangulator(osg::Vec3Array *points, osg::Vec3Array *normals):
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osg::Referenced(),
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points_(points),
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normals_(normals)
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{
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}
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DelaunayTriangulator::DelaunayTriangulator(const DelaunayTriangulator ©, const osg::CopyOp ©op):
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osg::Referenced(copy),
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points_(static_cast<osg::Vec3Array *>(copyop(copy.points_.get()))),
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normals_(static_cast<osg::Vec3Array *>(copyop(copy.normals_.get()))),
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prim_tris_(static_cast<osg::DrawElementsUInt *>(copyop(copy.prim_tris_.get())))
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{
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}
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DelaunayTriangulator::~DelaunayTriangulator()
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{
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}
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bool DelaunayTriangulator::triangulate()
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{
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// check validity of input array
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if (!points_.valid()) {
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osg::notify(osg::WARN) << "Warning: DelaunayTriangulator::triangulate(): invalid sample point array" << std::endl;
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return false;
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}
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osg::Vec3Array *points = points_.get();
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if (points->size() < 1) {
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osg::notify(osg::WARN) << "Warning: DelaunayTriangulator::triangulate(): too few sample points" << std::endl;
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return false;
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}
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// initialize storage structures
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Triangle_list triangles;
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Triangle_list discarded_tris;
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// pre-sort sample points
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osg::notify(osg::INFO) << "DelaunayTriangulator: pre-sorting sample points\n";
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std::sort(points->begin(), points->end(), Sample_point_compare);
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// set the last valid index for the point list
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GLuint last_valid_index = points->size() - 1;
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// find the minimum and maximum x values in the point list
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float minx = (*points)[0].x();
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float maxx = minx;
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// find the minimum and maximum x values in the point list
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float miny = (*points)[0].y();
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float maxy = miny;
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osg::notify(osg::INFO) << "DelaunayTriangulator: finding minimum and maximum Y values\n";
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osg::Vec3Array::const_iterator mmi;
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for (mmi=points->begin(); mmi!=points->end(); ++mmi) {
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if (mmi->y() < miny) miny = mmi->y();
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if (mmi->y() > maxy) maxy = mmi->y();
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}
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// add supertriangle vertices to the point list
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points->push_back(osg::Vec3(minx - (maxx - minx), miny, 0));
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points->push_back(osg::Vec3(maxx, miny, 0));
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points->push_back(osg::Vec3(maxx, maxy + (maxy - miny), 0));
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// add supertriangle to triangle list
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triangles.push_back(Triangle(last_valid_index+1, last_valid_index+2, last_valid_index+3, points));
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// begin triangulation
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GLuint pidx = 0;
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osg::Vec3Array::const_iterator i;
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osg::notify(osg::INFO) << "DelaunayTriangulator: triangulating vertex grid (" << (points->size()-3) <<" points)\n";
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for (i=points->begin(); i!=points->end(); ++i, ++pidx) {
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// don't process supertriangle vertices
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if (pidx > last_valid_index) break;
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Edge_set edges;
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// iterate through triangles
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Triangle_list::iterator j, next_j;
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for (j=triangles.begin(); j!=triangles.end(); j = next_j) {
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next_j = j;
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++next_j;
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// compute the circumcircle
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osg::Vec3 cc = j->get_circumcircle();
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// OPTIMIZATION: since points are pre-sorted by the X component,
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// check whether we can discard this triangle for future operations
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float xdist = i->x() - cc.x();
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if ((xdist * xdist) > cc.z() && i->x() > cc.x()) {
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discarded_tris.push_back(*j);
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triangles.erase(j);
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} else {
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// if the point lies in the triangle's circumcircle then add
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// its edges to the edge list and remove the triangle
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if (point_in_circle(*i, cc))
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{
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for (int ei=0; ei<3; ++ei)
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{
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std::pair<Edge_set::iterator, bool> result = edges.insert(j->get_edge(ei));
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if (!result.second)
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{
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// cast away constness of a set element, which is
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// safe in this case since the set_duplicate is
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// not used as part of the Less operator.
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Edge& edge = const_cast<Edge&>(*(result.first));
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edge.set_duplicate(true);
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}
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}
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triangles.erase(j);
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}
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}
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}
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// remove duplicate edges and add new triangles
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Edge_set::iterator ci;
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for (ci=edges.begin(); ci!=edges.end(); ++ci) {
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if (!ci->get_duplicate()) {
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triangles.push_back(Triangle(pidx, ci->ib(), ci->ie(), points));
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}
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}
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}
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osg::notify(osg::INFO) << "DelaunayTriangulator: finalizing and cleaning up structures\n";
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// remove supertriangle vertices
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points->pop_back();
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points->pop_back();
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points->pop_back();
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// rejoin the two triangle lists
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triangles.insert(triangles.begin(), discarded_tris.begin(), discarded_tris.end());
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// initialize index storage vector
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std::vector<GLuint> pt_indices;
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pt_indices.reserve(triangles.size() * 3);
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// build osg primitive
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osg::notify(osg::INFO) << "DelaunayTriangulator: building primitive(s)\n";
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Triangle_list::const_iterator ti;
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for (ti=triangles.begin(); ti!=triangles.end(); ++ti) {
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// don't add this triangle to the primitive if it shares any vertex with
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// the supertriangle
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if (ti->a() <= last_valid_index && ti->b() <= last_valid_index && ti->c() <= last_valid_index) {
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if (normals_.valid()) {
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(normals_.get())->push_back(ti->compute_normal(points));
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}
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pt_indices.push_back(ti->a());
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pt_indices.push_back(ti->b());
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pt_indices.push_back(ti->c());
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}
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}
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prim_tris_ = new osg::DrawElementsUInt(GL_TRIANGLES, pt_indices.size(), &(pt_indices.front()));
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osg::notify(osg::INFO) << "DelaunayTriangulator: process done, " << (pt_indices.size() / 3) << " triangles created\n";
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return true;
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}
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}
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@@ -7,6 +7,7 @@ CXXFILES = \
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CullVisitor.cpp\
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DisplayListVisitor.cpp\
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DisplayRequirementsVisitor.cpp\
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DelaunayTriangulator.cpp\
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InsertImpostorsVisitor.cpp\
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IntersectVisitor.cpp\
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Optimizer.cpp\
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