IntelliTriangulation.cpp

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#include "IntelliTriangulation.h"
#include <algorithm>
#include <queue>
#include <cmath>
#define pi 3.1415926535897932384626433832795
 
std::vector<Triangle> IntelliTriangulation::calculateTriangles(std::vector<QPoint> polyPoints){
        // helper for managing the triangle vertices and their state
        struct TriangleHelper {
                QPoint vertex;
                float interiorAngle;
                int idx;
                bool isTip;
        };
 
        // calculates the inner angle of 'point'
        auto calculateInner = [] (QPoint& point, QPoint& prev, QPoint& post) {
                                      QPoint AP(point.x() - prev.x(), point.y() - prev.y());
                                      QPoint BP(point.x() - post.x(), point.y() - post.y());
 
                                      float topSclar = AP.x() * BP.x() + AP.y() * BP.y();
                                      float absolute = static_cast<float>(sqrt(pow(AP.x(),2.) + pow(AP.y(),2.)) * sqrt(pow(BP.x(),2.) + pow(BP.y(),2.)));
                                      return acos(topSclar / absolute);
                              };
 
        // gets the first element of vec for which element.isTip == true holds
        auto getTip = [] (const std::vector<TriangleHelper>& vec) {
                              size_t min = 0;
                              for(size_t i = 0; i<vec.size(); i++) {
                                      if(vec[i].interiorAngle<vec[min].interiorAngle) {
                                              min = i;
                                      }
                              }
                              return vec[min];
                      };
 
        // get the vertex idx bevor idx in relation to the container length
        auto getPrev = [] (int idx, int length) {
                               return (idx - 1)>=0 ? (idx - 1) : (length - 1);
                       };
 
        // get the vertex idx after idx in relation to the container lenght
        auto getPost = [] (int idx, int length) {
                               return (idx + 1) % length;
                       };
 
        // return if the vertex is a tip
        auto isTip = [] (float angle) {
                             return static_cast<double>(angle)<(pi / 2.);
                     };
 
        std::vector<TriangleHelper>  Vertices;
        std::vector<Triangle> Triangles;
 
        // set up all vertices and calculate intirior angle
        for(int i = 0; i<static_cast<int>(polyPoints.size()); i++) {
                TriangleHelper helper;
                int prev = getPrev(i, static_cast<int>(polyPoints.size()));
                int post = getPost(i, static_cast<int>(polyPoints.size()));
 
                helper.vertex = polyPoints[static_cast<size_t>(i)];
                helper.idx = i;
 
                helper.interiorAngle = calculateInner(polyPoints[static_cast<size_t>(i)],
                                                      polyPoints[static_cast<size_t>(prev)],
                                                      polyPoints[static_cast<size_t>(post)]);
                helper.isTip = isTip(helper.interiorAngle);
                Vertices.push_back(helper);
        }
 
        // search triangles based on the intirior angles of each vertey
        while(Triangles.size() != polyPoints.size() - 2) {
                Triangle tri;
                TriangleHelper smallest = getTip(Vertices);
                int prev = getPrev(smallest.idx, static_cast<int>(Vertices.size()));
                int post = getPost(smallest.idx, static_cast<int>(Vertices.size()));
 
                // set triangle and push it
                tri.A = Vertices[static_cast<size_t>(prev)].vertex;
                tri.B = Vertices[static_cast<size_t>(smallest.idx)].vertex;
                tri.C = Vertices[static_cast<size_t>(post)].vertex;
                Triangles.push_back(tri);
 
                // update Vertice array
                Vertices.erase(Vertices.begin() + smallest.idx);
                for(size_t i = static_cast<size_t>(smallest.idx); i<Vertices.size(); i++) {
                        Vertices[i].idx -= 1;
                }
 
                // update post und prev idx
                post = getPrev(post, Vertices.size());
                prev = prev<smallest.idx ? prev : (prev - 1);
 
                // calcultae neighboors of prev and post to calculate new interior angles
                int prevOfPrev = getPrev(prev, static_cast<int>(Vertices.size()));
                int postOfPrev = getPost(prev, static_cast<int>(Vertices.size()));
 
                int prevOfPost = getPrev(post, static_cast<int>(Vertices.size()));
                int postOfPost = getPost(post, static_cast<int>(Vertices.size()));
 
                // update vertices with interior angles
                // updtae prev
                Vertices[static_cast<size_t>(prev)].interiorAngle = calculateInner(Vertices[static_cast<size_t>(prev)].vertex,
                                                                                   Vertices[static_cast<size_t>(prevOfPrev)].vertex,
                                                                                   Vertices[static_cast<size_t>(postOfPrev)].vertex);
                Vertices[static_cast<size_t>(prev)].isTip = isTip(Vertices[static_cast<size_t>(prev)].interiorAngle);
                // update post
                Vertices[static_cast<size_t>(post)].interiorAngle = calculateInner(Vertices[static_cast<size_t>(post)].vertex,
                                                                                   Vertices[static_cast<size_t>(prevOfPost)].vertex,
                                                                                   Vertices[static_cast<size_t>(postOfPost)].vertex);
                Vertices[static_cast<size_t>(post)].isTip = isTip(Vertices[static_cast<size_t>(post)].interiorAngle);
        }
        return Triangles;
}
 
bool IntelliTriangulation::isInPolygon(const std::vector<Triangle> &triangles, QPoint &point){
        for(auto triangle : triangles) {
                if(IntelliTriangulation::isInTriangle(triangle, point)) {
                        return true;
                }
        }
        return false;
}