How to draw a trapezoid from scratch!

TrapezoidSprite.cs

using UnityEngine;
using System;

public class TrapezoidSprite : FSprite
{    
	public float trapezoidWidth;
	public float trapezoidHeight;
	public float insetFromSide;

   	public TrapezoidSprite (string imageName, float width, float height, float inset) : base() {
		trapezoidWidth = width;
		trapezoidHeight = height;
		insetFromSide = inset;
		
		// This initializes the sprite with a specified texture and indicates
        	// that we want to use triangles to draw the trapezoid. The third parameter is 3 because
        	// we are going to construct the trapezoid out of three triangles.
		Init(FFacetType.Triangle, Futile.atlasManager.GetElementWithName(imageName),3);
		
		// Just necessary setup code
		_isAlphaDirty = true;
		UpdateLocalVertices();
	}
	
	// Call this method if you make a change and want to redraw
	public void Refresh() {
		_isMeshDirty = true;	
	}
		
	override public void PopulateRenderLayer()
	{
		if(_isOnStage && _firstFacetIndex != -1) // if this is false, the sprite hasn't been initiated correctly yet
		{		
			// _isMeshDirty is set to true when things need to be rerendered,
			// so we need to set it to false here because that's what we're doing.
			_isMeshDirty = false;
			
			// Since each facet (triangle) has 3 vertices, the first vertex index
			// is the index of the first facet multiplied by 3.
			int vertexIndex0 = _firstFacetIndex * 3;
			
			// This array contains the vertices that are used to draw the triangles.
			// The size of this array is 9 because there are 3 facets (triangles)
			// with 3 vertices each (thus, 3 * 3 vertices total)
			Vector3[] triangleVertices = _renderLayer.vertices;
			
			// This array contains the vertices that are used to apply the texture to the triangles.
			// The size of this array is 9 because there are 3 facets (triangles)
			// with 3 vertices each (thus, 3 * 3 vertices total).
			Vector2[] triangleUVVertices = _renderLayer.uvs;
			
			// This array contains the actual local vertices of the trapezoid.
			Vector2[] trapezoidVertices = new Vector2[5];
			
			// This array contains the vertices on the texture that will be
			// stretched to fit right on top of the trapezoidVertices.
			Vector2[] textureUVVertices = new Vector2[5];
			
			// This holds the colors of each vertex for each triangle.
			Color[] colors = _renderLayer.colors;
			
			// Here we create all the vertices of the trapezoid.
			trapezoidVertices[0] = new Vector2(0, 0);
			trapezoidVertices[1] = new Vector2(insetFromSide, trapezoidHeight);
			trapezoidVertices[2] = new Vector2(trapezoidWidth / 2f, 0);
			trapezoidVertices[3] = new Vector2(trapezoidWidth - insetFromSide, trapezoidHeight);
			trapezoidVertices[4] = new Vector2(trapezoidWidth, 0);
			
			// Offset the vertices so that (0, 0) is the middle of the trapezoid
			// instead of the bottom left vertex.
			for (int i = 0; i < 5; i++) {
				trapezoidVertices[i].x -= trapezoidWidth / 2f;
				trapezoidVertices[i].y -= trapezoidHeight / 2f;
			}
			
			// This is the width of the specific image in relative uv values
			// (not the width of the image in pixels)
			float uvWidth = (_element.uvTopRight.x - _element.uvTopLeft.x);
			
			textureUVVertices[0] = new Vector2(_element.uvBottomLeft.x, _element.uvBottomLeft.y);
			textureUVVertices[1] = new Vector2(_element.uvTopLeft.x, _element.uvTopLeft.y);
			textureUVVertices[2] = new Vector2(_element.uvBottomLeft.x + uvWidth / 2f, _element.uvBottomLeft.y);
			textureUVVertices[3] = new Vector2(_element.uvTopRight.x,	_element.uvTopRight.y);
			textureUVVertices[4] = new Vector2(_element.uvBottomRight.x,	_element.uvBottomRight.y);
			
			// This just colors all the vertices on all the triangles
			// to whatever color is set for the sprite.
			for (int i = 0; i < 9; i++) {
				colors[vertexIndex0 + i] = _alphaColor;
			}
			
			// Here is where we construct the three triangles. We just tell it
			// which vertices on the trapezoid to use for each triangle and it
			// applies those values to the rendering matrix.
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 0], trapezoidVertices[0],0);
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 1], trapezoidVertices[1],0);
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 2], trapezoidVertices[2],0);
			
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 3], trapezoidVertices[1],0);
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 4], trapezoidVertices[2],0);
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 5], trapezoidVertices[3],0);
			
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 6], trapezoidVertices[2],0);
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 7], trapezoidVertices[3],0);
			_concatenatedMatrix.ApplyVector3FromLocalVector2(ref triangleVertices[vertexIndex0 + 8], trapezoidVertices[4],0);
			
			// Here is where we actually assign the points on the texture to
			// the points on the triangles. In other words, we are stretching the
			// texture so that the points on the texture line up with the vertices
			// of the trapezoid. Since we're drawing it with triangles, we have
			// to do this for each triangle so the renderer knows how to "paint" them.
			triangleUVVertices[vertexIndex0 +  0] = textureUVVertices[0];
			triangleUVVertices[vertexIndex0 +  1] = textureUVVertices[1];
			triangleUVVertices[vertexIndex0 +  2] = textureUVVertices[2];
			
			triangleUVVertices[vertexIndex0 +  3] = textureUVVertices[1];
			triangleUVVertices[vertexIndex0 +  4] = textureUVVertices[2];
			triangleUVVertices[vertexIndex0 +  5] = textureUVVertices[3];
			
			triangleUVVertices[vertexIndex0 +  6] = textureUVVertices[2];
			triangleUVVertices[vertexIndex0 +  7] = textureUVVertices[3];
			triangleUVVertices[vertexIndex0 +  8] = textureUVVertices[4];
			
			// This just tells the renderer that we made changes.
			_renderLayer.HandleVertsChange();
		}
	}
}

WTMain.cs

using UnityEngine;
using System.Collections;

public class WTMain : MonoBehaviour {
    public float offset = 0;
	TrapezoidSprite sprite;
	
	float widthChange = 9;
	float heightChange = 10;
	float insetChange = 11;
	
	void Start() {
		FutileParams fp = new FutileParams(true, true, false, false);
		fp.AddResolutionLevel(1024, 1.0f, 1.0f, "");
		fp.origin = Vector2.zero;
		fp.backgroundColor = new Color(0.12f, 0.12f, 0.12f, 1.0f);
		
		Futile.instance.Init(fp);
		
		Futile.instance.SignalUpdate += HandleUpdate;
		
		sprite = new TrapezoidSprite("Futile_White", 300, 100, 75);
		sprite.x = Futile.screen.halfWidth;
		sprite.y = Futile.screen.halfHeight;
		Futile.stage.AddChild(sprite);
	}
		
	public void HandleUpdate() {
		// Uncomment this stuff to see the trapezoid morph before your very eyes!
		
		/*sprite.trapezoidWidth += widthChange;
		sprite.trapezoidHeight += heightChange;
		sprite.insetFromSide += insetChange;
		
		if (sprite.trapezoidWidth > 500) {
			sprite.trapezoidWidth = 500;
			widthChange *= -1;
		}
		
		if (sprite.trapezoidHeight > 500) {
			sprite.trapezoidHeight = 500;
			heightChange *= -1;
		}
		
		if (sprite.insetFromSide > sprite.trapezoidWidth / 2f) {
			sprite.insetFromSide = sprite.trapezoidWidth / 2f;
			insetChange *= -1;
		}
		
		if (sprite.trapezoidWidth < 50) {
			sprite.trapezoidWidth = 50;
			widthChange *= -1;
		}
		
		if (sprite.trapezoidHeight < 50) {
			sprite.trapezoidHeight = 50;
			heightChange *= -1;
		}
		
		if (sprite.insetFromSide < -100) {
			sprite.insetFromSide = -100;
			insetChange *= -1;
		}
		
		sprite.Refresh();*/
	}
}