Path triangulation

using VectSharp;
using VectSharp.Raster.ImageSharp;

// Font to draw some text.
FontFamily family = FontFamily.ResolveFontFamily(FontFamily.StandardFontFamilies.Helvetica);
Font font = new Font(family, 15);

// Original GraphicsPath containing some text.
GraphicsPath path = new GraphicsPath().AddText(15, 8, "VectSharp", font);

// List to contain the vertices of the triangles.
List<List<Point>> trianglePoints = new List<List<Point>>();

// Triangulate the path and add the vertices of the triangles to the list.
foreach (GraphicsPath triangle in path.Triangulate(2, true))
{
    List<Point> currTriangle = new List<Point>();
    foreach (List<Point> pathFigure in triangle.GetPoints())
    {
        currTriangle.AddRange(pathFigure);
    }
    trianglePoints.Add(currTriangle);
}

// Origin point for the explosion.
Point explosionPoint = new Point(50, 25);

// Initial velocity for the triangles.
double initialVelocity = 10;

// Friction coefficient.
double friction = 0.25;

// Gravitational constant.
double gravity = 4;

// Will hold the initial velocities of the points.
List<List<Point>> initialVelocities = new List<List<Point>>();

// The initial velocity of the vertices of a triangle will be in the direction connecting
// the barycenter of the triangle to the explosion point, and will have modulus equal to initialVelocity.
for (int i = 0; i < trianglePoints.Count; i++)
{
    initialVelocities.Add(new List<Point>());

    // Compute the barycenter of the triangle.
    Point barycenter = new Point();
    for (int j = 0; j < trianglePoints[i].Count; j++)
    {
        barycenter = new Point(barycenter.X + trianglePoints[i][j].X, barycenter.Y + trianglePoints[i][j].Y);
    }
    barycenter = new Point(barycenter.X / trianglePoints[i].Count, barycenter.Y / trianglePoints[i].Count);

    Point direction = new Point(barycenter.X - explosionPoint.X, barycenter.Y - explosionPoint.Y);
    double r = direction.Modulus();

    double velocityModulus = initialVelocity;

    for (int j = 0; j < trianglePoints[i].Count; j++)
    {
        initialVelocities[i].Add(new Point(direction.X / r * velocityModulus, -direction.Y / r * velocityModulus));
    }
}

// Colours to colour each triangle differently.
Colour[] colours = new Colour[]
{
    Colour.FromRgb(230, 159, 0),
    Colour.FromRgb(86, 180, 233),
    Colour.FromRgb(0, 158, 115),
    Colour.FromRgb(240, 228, 66),
    Colour.FromRgb(0, 114, 178),
    Colour.FromRgb(213, 94, 0),
    Colour.FromRgb(204, 121, 167)
};

// Create the animation that will contain all the frames.
Animation animation = new Animation(132, 31, 1) { Background = Colours.White };

// Loop over time
for (double t = 0; t <= 6.5; t += 0.075)
{
    // Create a new graphics for the frame.
    Graphics graphics = new Graphics();
    graphics.Translate(16, 3);

    // Loop over the triangles.
    for (int i = 0; i < trianglePoints.Count; i++)
    {
        // Create the new path to hold the triangle.
        GraphicsPath triangle = new GraphicsPath();

        for (int j = 0; j < trianglePoints[i].Count; j++)
        {
            // Compute the current position of each point, based on initial velocity, gravity and friction.
            double currX = trianglePoints[i][j].X + initialVelocities[i][j].X / friction * (1 - Math.Exp(-friction * t));
            double currY = trianglePoints[i][j].Y + gravity * t / friction + (initialVelocities[i][j].Y / friction + gravity / (friction * friction)) * (Math.Exp(-friction * t) - 1);

            // When a point reaches y = 25, it has arrived to the "floor".
            currY = Math.Min(currY, 25);

            // Add the point to the path.
            if (j == 0)
            {
                triangle.MoveTo(currX, currY);
            }
            else
            {
                triangle.LineTo(currX, currY);
            }
        }

        // Close the triangle.
        triangle.Close();

        // Fill the triangle.
        graphics.FillPath(triangle, colours[i % colours.Length]);
    }

    // Create the frame and set the duration. We use a larger duration for the first frame.
    Frame frame;

    if (t == 0)
    {
        frame = new Frame(graphics, 250);
    }
    else
    {
        frame = new Frame(graphics, 16);
    }

    // Add the frame to the animation.
    animation.AddFrame(frame);
}


// Add the reverse animation.
for (double t = 6.5; t >= 0; t -= 0.075)
{
    // Create a new graphics for the frame.
    Graphics graphics = new Graphics();
    graphics.Translate(16, 3);

    // Loop over the triangles.
    for (int i = 0; i < trianglePoints.Count; i++)
    {
        // Create the new path to hold the triangle.
        GraphicsPath triangle = new GraphicsPath();

        for (int j = 0; j < trianglePoints[i].Count; j++)
        {
            // Compute the current position of each point, based on initial velocity, gravity and friction.
            double currX = trianglePoints[i][j].X + initialVelocities[i][j].X / friction * (1 - Math.Exp(-friction * t));
            double currY = trianglePoints[i][j].Y + gravity * t / friction + (initialVelocities[i][j].Y / friction + gravity / (friction * friction)) * (Math.Exp(-friction * t) - 1);

            // When a point reaches y = 25, it has arrived to the "floor".
            currY = Math.Min(currY, 25);

            // Add the point to the path.
            if (j == 0)
            {
                triangle.MoveTo(currX, currY);
            }
            else
            {
                triangle.LineTo(currX, currY);
            }
        }

        // Close the triangle.
        triangle.Close();

        // Fill the triangle.
        graphics.FillPath(triangle, colours[i % colours.Length]);
    }

    // Create the frame.
    Frame frame = new Frame(graphics, 16);

    // Add the frame to the animation.
    animation.AddFrame(frame);
}

// Save the animation as an animated GIF, with a scale factor of 10.
animation.SaveAsAnimatedGIF("TriangulationAnimation.gif", 10);