Polygons and Zones – Example4

This is the right example if you want to triangulate polygons or perform polygon clipping. In Fade, a Zone2 object defines a specific area of a triangulation. It allows you to combine shapes using the Boolean set operations union, difference, symmetric difference and intersection. The result is again a zone whose area and boundary can be computed and whose triangles can be extracted.

You can define a zone as the area…

• inside or outside a polygon
• grown from a seed point up to defined fences
• of the whole triangulation (global zone)
• of arbitrary triangles

The below example code (examples_2D/ex4_zones.cpp in the download) demonstrates it.

Preparing two initial polygons

This code snippet creates two polygons in a rectangle as shown in the above image.

// * 1 *   Insert 4 bounding box points
Fade_2D dt;
dt.insert(Point2(0,0));
dt.insert(Point2(+100,0));
dt.insert(Point2(100,50));
dt.insert(Point2(0,50));

// * 2 *   Create points on two circles
std::vector<Point2> vCircle0;
std::vector<Point2> vCircle1;
int numPoints(8);
double radius(22);
//generateCircle( num,centerX,centerY,radiusX,radiusY,vOut);
generateCircle(numPoints,25.0,25.0,radius,radius,vCircle0);
generateCircle(numPoints,75.0,25.0,radius,radius,vCircle1);

// * 3 *   Create segments
std::vector<Segment2> vSegments0;
std::vector<Segment2> vSegments1;
for(int i=0;i<numPoints;++i)
{
	Segment2 seg0(vCircle0[i],vCircle0[(i+1)%numPoints]);
	Segment2 seg1(vCircle1[i],vCircle1[(i+1)%numPoints]);
	vSegments0.push_back(seg0);
	vSegments1.push_back(seg1);
}

// * 4 *   Insert the segments as constraint graphs
ConstraintGraph2* pCG0=dt.createConstraint(vSegments0,CIS_CONSTRAINED_DELAUNAY);
ConstraintGraph2* pCG1=dt.createConstraint(vSegments1,CIS_CONSTRAINED_DELAUNAY);

// * 5 *  Visualize
dt.show("example4_constraints.ps",true);

1. Step 1 inserts 4 points into a new Fade_2D object.
2. Step 2 creates points on two circles (vCircle0,vCircle1)
3. The third step creates segments (vSegment0,vSegment1)
4. After that two polygons (ConstraintGraph2 pCG0, pCG1) are made.
5. Finally, Step 5 draws the triangulation.

Creating zones inside and outside of polygons

The ConstraintGraph2 pCG1 is the left polygon circle in the above image. Let’s create a Zone2 inside and another one outside this polygon now.

// + Zone inside pCG0:
Zone2* pZoneInside(dt.createZone(pCG0,ZL_INSIDE));
pZoneInside->show("example4_zoneInside.ps",true,true); 

// + Zone outside pCG0:
Zone2* pZoneOutside(dt.createZone(pCG0,ZL_OUTSIDE));
pZoneOutside->show("example4_zoneOutside.ps",true,true);

Growing a zone from a seed point

In addition to zones inside and outside a polygon, zones can also grow from a specific seed point.

vector<ConstraintGraph2*> vCG;
vCG.push_back(pCG0);
vCG.push_back(pCG1);
Point2 seedPoint(5.0,5.0); // Point near the lower left corner
Zone2* pZoneGrow(dt.createZone(vCG,ZL_GROW,seedPoint));
pZoneGrow->show("example4_zoneGrow.ps",true,true);

This is code uses a vector<ConstraintGraph2> and it creates a seedPoint near the lower left corner of the below image. Then it grows a zone from this seed point. The edges of the ConstraintGraph2 objects in vCG (in our case the two polygon circles) act as fence which stops the growing process.

The global zone

A global zone consists of all existing triangles.

Zone2* pZoneGlobal(dt.createZone(NULL,ZL_GLOBAL));
pZoneGlobal->show("example4_zoneGlobal.ps",true,true);

Zone creation from arbitrary triangles

This technique creates a zone from an arbitrary set of triangles, connected or not.

// + Zone defined by specific triangles
vector<Triangle2*> vT;
dt.getTrianglePointers(vT);
vT.resize(vT.size()/2);
Zone2* pZoneRandomTriangles(dt.createZone(vT));
pZoneRandomTriangles->show("example4_zoneFromTriangles.ps",true,true);

This code firstly fetches all triangles from the triangulation. Then it chooses only half of them to create a zone.

This article covered creation of zones while the next post Zone Operations computes the union, the intersection, the difference and symmetric difference of such zones.