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polygon_3darea.cpp
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polygon_3darea.cpp
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#include "triangleCube.h"
#include <vector>
using namespace std;
// Copyright 2000 softSurfer, 2012 Dan Sunday
// This code may be freely used and modified for any purpose
// providing that this copyright notice is included with it.
// iSurfer.org makes no warranty for this code, and cannot be held
// liable for any real or imagined damage resulting from its use.
// Users of this code must verify correctness for their application.
// a Triangle is given by three points: Point3 V0, V1, V2
// a Polygon is given by:
// int n = number of vertex points
// Point3* V[] = an array of n+1 vertex points with V[n]=V[0]
// Note: for efficiency low-level short functions are declared to be inline.
// isLeft(): test if a point is Left|On|Right of an infinite 2D line.
// Input: three points P0, P1, and P2
// Return: >0 for P2 left of the line through P0 to P1
// =0 for P2 on the line
// <0 for P2 right of the line
inline int
isLeft( Point3 P0, Point3 P1, Point3 P2 )
{
return ( (P1.x - P0.x) * (P2.y - P0.y)
- (P2.x - P0.x) * (P1.y - P0.y) );
}
//===================================================================
// orientation2D_Triangle(): test the orientation of a 2D triangle
// Input: three vertex points V0, V1, V2
// Return: >0 for counterclockwise
// =0 for none (degenerate)
// <0 for clockwise
inline int
orientation2D_Triangle( Point3 V0, Point3 V1, Point3 V2 )
{
return isLeft(V0, V1, V2);
}
//===================================================================
// area2D_Triangle(): compute the area of a 2D triangle
// Input: three vertex points V0, V1, V2
// Return: the (float) area of triangle T
inline float
area2D_Triangle( Point3 V0, Point3 V1, Point3 V2 )
{
return (float)isLeft(V0, V1, V2) / 2.0;
}
//===================================================================
// orientation2D_Polygon(): test the orientation of a simple 2D polygon
// Input: int n = the number of vertices in the polygon
// Point3* V = an array of n+1 vertex points with V[n]=V[0]
// Return: >0 for counterclockwise
// =0 for none (degenerate)
// <0 for clockwise
// Note: this algorithm is faster than computing the signed area.
int
orientation2D_Polygon( int n, vector<Point3>& V )
{
// first find rightmost lowest vertex of the polygon
int rmin = 0;
int xmin = V[0].x;
int ymin = V[0].y;
for (int i=1; i<n; i++) {
if (V[i].y > ymin)
continue;
if (V[i].y == ymin) { // just as low
if (V[i].x < xmin) // and to left
continue;
}
rmin = i; // a new rightmost lowest vertex
xmin = V[i].x;
ymin = V[i].y;
}
// test orientation at the rmin vertex
// ccw <=> the edge leaving V[rmin] is left of the entering edge
if (rmin == 0)
return isLeft( V[n-1], V[0], V[1] );
else
return isLeft( V[rmin-1], V[rmin], V[rmin+1] );
}
//===================================================================
// area2D_Polygon(): compute the area of a 2D polygon
// Input: int n = the number of vertices in the polygon
// Point3* V = an array of n+1 vertex points with V[n]=V[0]
// Return: the (float) area of the polygon
float
area2D_Polygon( int n, vector<Point3>& V )
{
float area = 0;
int i, j, k; // indices
if (n < 3) return 0; // a degenerate polygon
for (i=1, j=2, k=0; i<n; i++, j++, k++) {
area += V[i].x * (V[j].y - V[k].y);
}
area += V[n].x * (V[1].y - V[n-1].y); // wrap-around term
return area / 2.0;
}
//===================================================================
// area3D_Polygon(): compute the area of a 3D planar polygon
// Input: int n = the number of vertices in the polygon
// Point3* V = an array of n+1 points in a 2D plane with V[n]=V[0]
// Point3 N = a normal vector of the polygon's plane
// Return: the (float) area of the polygon
float
area3D_Polygon( int n, vector<Point3>& V, Point3 N )
{
float area = 0;
float an, ax, ay, az; // abs value of normal and its coords
int coord; // coord to ignore: 1=x, 2=y, 3=z
int i, j, k; // loop indices
if (n < 3) return 0; // a degenerate polygon
// select largest abs coordinate to ignore for projection
ax = (N.x>0 ? N.x : -N.x); // abs x-coord
ay = (N.y>0 ? N.y : -N.y); // abs y-coord
az = (N.z>0 ? N.z : -N.z); // abs z-coord
coord = 3; // ignore z-coord
if (ax > ay) {
if (ax > az) coord = 1; // ignore x-coord
}
else if (ay > az) coord = 2; // ignore y-coord
// compute area of the 2D projection
switch (coord) {
case 1:
for (i=1, j=2, k=0; i<n; i++, j++, k++)
area += (V[i].y * (V[j].z - V[k].z));
break;
case 2:
for (i=1, j=2, k=0; i<n; i++, j++, k++)
area += (V[i].z * (V[j].x - V[k].x));
break;
case 3:
for (i=1, j=2, k=0; i<n; i++, j++, k++)
area += (V[i].x * (V[j].y - V[k].y));
break;
}
switch (coord) { // wrap-around term
case 1:
area += (V[n].y * (V[1].z - V[n-1].z));
break;
case 2:
area += (V[n].z * (V[1].x - V[n-1].x));
break;
case 3:
area += (V[n].x * (V[1].y - V[n-1].y));
break;
}
// scale to get area before projection
an = sqrt( ax*ax + ay*ay + az*az); // length of normal vector
switch (coord) {
case 1:
area *= (an / (2 * N.x));
break;
case 2:
area *= (an / (2 * N.y));
break;
case 3:
area *= (an / (2 * N.z));
}
return area;
}
//===================================================================