Implementing Cyrus Beck algorithm for convex polygons - c++

Question

I tried implementing the Cyrus Beck algorithm for convex polygons. The problem that I was encountering was to find the direction of normal vectors as they must always point inside. For solving this I found the coordinates of the centroid, which always lie inside a convex polygon. This method seems to work in the cases I tested. Is this fool proof ? Are there any better alternatives ?
CyrusBeck.cpp
#include<iostream>
#include<cmath>
#include"graphics.hpp"
#define P pair<double, double>
vector<P> V, N;
P C;
double dot(P A, P B){
return (A.first*B.first + A.second*B.second);
}
P operator - (const P &A, const P &B){
return make_pair(A.first-B.first, A.second-B.second);
}
P operator + (const P &A, const P &B){
return make_pair(A.first+B.first, A.second+B.second);
}
P operator * (const P &A, const double t){
return make_pair(t*A.first, t*A.second);
}
void computeNormal(int n = V.size()){
double m;
P prev = V[0];
double x=-1, y;
for(int i=1; i<n; ++i){
m = -(V[i].first-prev.first)/(V[i].second-prev.second);
P d = V[i]-prev;
int lr=1, tb=1;
if(V[i-1].first>C.first)
lr = -1;
if(V[i-1].second>C.second)
tb=-1;
N[i-1].first = lr*abs(cos(atan(m)));
N[i-1].second = tb*abs(sin(atan(m)));
prev = V[i];
}
m = -(V[0].first-prev.first)/(V[0].second-prev.second);
int lr=1, tb=1;
if(V[n-1].first>C.first)
lr = -1;
if(V[n-1].second>C.second)
tb=-1;
N[n-1].first = lr*abs(cos(atan(m)));
N[n-1].second = tb*abs(sin(atan(m)));
}
int check(P A, P B, int n){
P p = B - V[0];
double d1 = dot(p, N[0]);
P q = A - V[0];
double d2 = dot(q, N[0]);
if(d1<0&&d2<0)
return 0;
if(d1>=0&&d2>=0)
return 1;
return -1;
}
void Clip(P A, P B, double &tE, double &tL, int n = V.size()){
tE = 0; tL = 1;
for(int i=0; i<n; ++i){
double d = dot((B-A), N[i]);
if(d==0)
continue;
double t = dot((A-V[i]), N[i])/dot((A-B), N[i]);
if(d>0&&t>tE)
tE = t;
else if(d<0&&t<tL)
tL = t;
}
}
void display(){
cout<<"Enter the number of vertices\n";
int n; cin>>n;
V.resize(n);
N.resize(n);
cout<<"Enter the coordinates of the vertices in order\n";
for(int i=0; i<n; ++i){
cin>>V[i].first>>V[i].second;
C = C + V[i];
}
C.first/=n; C.second/=n;
drawPolygon(V, n, white);
glutSwapBuffers();
cout<<"Enter the co-ordinates of the line(4)\n";
P A, B;
cin>>A.first>>A.second>>B.first>>B.second;
drawLine(A.first, A.second, B.first, B.second, red);
glutSwapBuffers();
char c = '\0';
while(c!='Y'&&c!='y'){
cout<<"Clip? (Y/N)\n";
cin>>c;
}
computeNormal();
int chk = check(A, B, n);
glClearColor(0, 0, 0, 1);
glClear(GL_COLOR_BUFFER_BIT);
drawPolygon(V, n, white);
if(chk==-1){
double tE, tL;
Clip(A, B, tE, tL);
if(tE>tL)
chk = 0;
else{
P E = A + (B-A)*tE;
P L = A + (B-A)*tL;
drawLine(E.first, E.second, L.first, L.second, blue);
}
}
if(chk==1)
drawLine(A.first, A.second, B.first, B.second, blue);
glutSwapBuffers();
}
int main(int argc, char *argv[]){
init(&argc, argv);
}
graphics.hpp
#ifndef GRAPHICS_H
#define GRAPHICS_H
#include<GL/glut.h>
#include<vector>
using namespace std;
extern float red[3];
extern float green[3];
extern float blue[3];
extern float white[3];
int roundoff(double x);
void init(int* argc, char** argv);
void putpixel(float x, float y, float z, float a[3]);
void drawLine(double x1, double y1, double x2, double y2, float a[3]);
void drawRectangle(double x1, double y1, double x2, double y2, float a[3]);
void drawPolygon(vector<pair<double, double>> v, int n, float a[3]);
void MatrixMultiply(vector<vector<double>> &mat1, vector<vector<double>> &mat2, vector<vector<double>> &res,
int n, int m, int r);
void display();
#endif
graphics.cpp
#include<iostream>
#include"graphics.hpp"
float red[3] = { 1.0f, 0.0f, 0.0f };
float green[3] = { 0.0f, 1.0f, 0.0f };
float blue[3] = { 0.0f, 0.0f, 1.0f };
float white[3] = { 1.0f, 1.0f, 1.0f };
int roundoff(double x){
if (x < 0.0)
return (int)(x - 0.5);
else
return (int)(x + 0.5);
}
void init(int *argc, char** argv){
glutInit(argc, argv); // Initialize GLUT
glutInitWindowSize(800, 800); // Set the window's initial width & height
glutInitWindowPosition(0, 0); // Position the window's initial top-left corner
glutCreateWindow("Graphics"); // Create a window with the given title
gluOrtho2D(0, 800, 0, 800); // specifies the projection matrix
glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Set background color to black and opaque
glClear(GL_COLOR_BUFFER_BIT); // Clear the color buffer (background)
glutDisplayFunc(display); // Register display callback handler for window re-paint
glutMainLoop(); // Enter the event-processing loop
}
void putpixel(float x, float y, float z, float a[3]){
glPointSize(2);
glBegin(GL_POINTS); // HERE THE POINTS SHOULD BE CREATED
glColor3f(a[0], a[1], a[2]);
glVertex3f(x, y, z); // Specify points in 3d plane
std::cout<<x<<' '<<y<<' '<<z<<'\n';
glEnd();
}
void drawLine(double x1, double y1, double x2, double y2, float a[3]){
glLineWidth(2.5);
glColor3f(a[0], a[1], a[2]);
glBegin(GL_LINES);
glVertex2d(x1, y1);
glVertex2d(x2, y2);
glEnd();
}
void drawRectangle(double x1, double y1, double x2, double y2, float a[3]){
glColor3f(a[0], a[1], a[2]);
glRectd(x1, y1, x2, y2);
}
void drawPolygon(vector<pair<double, double>> v, int n, float a[3]){
glColor3f(a[0], a[1], a[2]);
glBegin(GL_POLYGON);
for(int i=0; i<n; ++i)
glVertex2d(v[i].first, v[i].second);
glEnd();
}
void MatrixMultiply(vector<vector<double>> &mat1, vector<vector<double>> &mat2, vector<vector<double>> &res,
int n, int m, int r){
int x, i, j;
for(i = 0; i < n; i++){
for (j = 0; j < r; j++){
res[i][j] = 0;
for (x = 0; x < m; x++){
res[i][j] += mat1[i][x] * mat2[x][j];
}
}
}
}