A polygon is a collection of three or more edges, connected in such a way to form a closed path. The points where the edges of a polygon meet are known as vertices.

To simplify 3D algorithms, and optimize for speed, we only use triangular polygons. If we want to create a rectangular shape, we use two triangular polygons as shown below.


Our polygon data structure is a class that has a vector array to store all the vertices of the polygon and a property to store the color of the polygon.

1. Open Xojo.
2. In the Project Chooser select Desktop.
3. Enter "Tutorial005" as the Application Name, and click OK.
4. Save your project.
5. Configure the following controls:

Control	Name	DoubleBuffer	Left	Top	Maximize Button
Window	SurfaceWindow	-	-	-	ON
OpenGLSurface	Surface	ON	0	0	-

6. Position and size Surface to fill the whole window, and set its locking to left, top, bottom and right.


7. Add the following code to the SurfaceWindow.Open event handler:

Self.MouseCursor = System.Cursors.StandardPointer

8. Add the following code to the SurfaceWindow.Paint event handler:

Surface.Render

9. Import the X3Core module, created in the previous tutorial.
10. Add the following code to the Surface.Resized event handler:

X3_SetPerspective Surface

11. Add a new class named "X3Color" to module X3Core.
12. Add the following properties to X3Color:

Name	Type
Red	Double
Green	Double
Blue	Double

13. Add the following method to class X3Color:

Sub Constructor(initRed As Double, initGreen As Double, initBlue As Double)   Red = initRed   Green = initGreen   Blue = initBlue End Sub

14. Add a new class named "X3Polygon" to module X3Core.
15. Add the following properties to X3Polygon:

Name	Type
FillColor	X3Color
Vertex()	X3Vector

16. Add the following code to the Surface.Render event handler:

Dim i, j As Integer Dim polygon() As X3Core.X3Polygon Dim poly As X3Core.X3Polygon polygon.Append new X3Core.X3Polygon() polygon(0).FillColor = new X3Core.X3Color(0.2, 0.2, 0.7) polygon(0).Vertex.Append new X3Core.X3Vector(-1, 1, 0) polygon(0).Vertex.Append new X3Core.X3Vector(1, -1, 0) polygon(0).Vertex.Append new X3Core.X3Vector(1, 1, 0) polygon.Append new X3Core.X3Polygon() polygon(1).FillColor = new X3Core.X3Color(0.4, 0.4, 0.8) polygon(1).Vertex.Append new X3Core.X3Vector(-1, 1, 0) polygon(1).Vertex.Append new X3Core.X3Vector(-1, -1, 0) polygon(1).Vertex.Append new X3Core.X3Vector(1, -1, 0) OpenGL.glPushMatrix OpenGL.glClearColor(0, 0, 0, 1) OpenGL.glClear(OpenGL.GL_COLOR_BUFFER_BIT) OpenGL.glTranslatef 0.0, 0.0, -3.0 OpenGL.glBegin OpenGL.GL_TRIANGLES for i = 0 to polygon.Ubound   poly = polygon(i)   if poly.FillColor <> nil then     OpenGL.glColor3d(poly.FillColor.Red, poly.FillColor.Green, poly.FillColor.Blue)   else     OpenGL.glColor3d(1, 1, 1)   end if   for j = 0 to polygon(i).Vertex.Ubound     OpenGL.glVertex3d poly.Vertex(j).X, poly.Vertex(j).Y, poly.Vertex(j).Z   next j next i OpenGL.glEnd OpenGL.glPopMatrix

17. Save and run your project.

X3Color.Constructor:

Sub Constructor(initRed As Double, initGreen As Double, initBlue As Double)   Red = initRed   Green = initGreen   Blue = initBlue End Sub

The constructor method of X3Color makes it easy to instantiate a new color with predefined values. In the constructor we simply set the Red, Green and Blue properties of the color equal to the given values.

Surface.Render:

Dim i, j As Integer Dim polygon() As X3Core.X3Polygon Dim poly As X3Core.X3Polygon poly = new X3Core.X3Polygon() poly.FillColor = new X3Core.X3Color(0.2, 0.2, 0.7) poly.Vertex.Append new X3Core.X3Vector(-1, 1, 0) ' top center vertex poly.Vertex.Append new X3Core.X3Vector(1, -1, 0) ' bottom left vertex poly.Vertex.Append new X3Core.X3Vector(1, 1, 0) ' bottom right vertex polygon.Append poly poly = new X3Core.X3Polygon() poly.FillColor = new X3Core.X3Color(0.4, 0.4, 0.8) poly.Vertex.Append new X3Core.X3Vector(-1, 1, 0) poly.Vertex.Append new X3Core.X3Vector(-1, -1, 0) poly.Vertex.Append new X3Core.X3Vector(1, -1, 0) polygon.Append poly OpenGL.glPushMatrix OpenGL.glClearColor(0, 0, 0, 1) OpenGL.glClear(OpenGL.GL_COLOR_BUFFER_BIT) OpenGL.glTranslatef 0.0, 0.0, -3.0 OpenGL.glBegin OpenGL.GL_TRIANGLES for i = 0 to polygon.Ubound   poly = polygon(i)   if poly.FillColor <> nil then     OpenGL.glColor3d(poly.FillColor.Red, poly.FillColor.Green, poly.FillColor.Blue)   else     OpenGL.glColor3d(1, 1, 1)   end if   for j = 0 to polygon(i).Vertex.Ubound     OpenGL.glVertex3d poly.Vertex(j).X, poly.Vertex(j).Y, poly.Vertex(j).Z   next j next i OpenGL.glEnd OpenGL.glPopMatrix

The polygon() array stores our polygons. The poly object is a temporary object used during the initialization and rendering of the polygons. Two polygons are created. With each polygon we first instantiate a new X3Polygon object. The FillColor property of each polygon is then set using the constructor method of the X3Color class. A "for" loop is used to iterate through the polygons stored in our polygon array. During each iteration we use an "if" statement to check if the FillColor of the polygon is set. If the FillColor is not null, we change the current drawing color of OpenGL to the polygon's color, else we set the drawing color to white. A second nested "for" loop is used to iterate through the vertices of the polygon. We can add as many polygons to the polygon array as we need, without having to change our rendering code.