Extreme Optimization > QuickStart Samples > Line Curve QuickStart Sample (C#)

Extreme Optimization QuickStart Samples

Line Curve QuickStart Sample (C#)

Illustrates the use of the Point structure and Line class (Extreme.Mathematics.Curves namespace) in C#.

VB.NET code Back to QuickStart Samples

using System;

namespace Extreme.Mathematics.QuickStart.CSharp
{
    // The Point structure and Line class reside in the 
    // Extreme.Mathematics.Curves namespace.
    using Extreme.Mathematics.Curves;

    /// <summary>
    /// Illustrates the use of the Point structure and the Line
    /// class in the Extreme.Mathematics.Curve namespace of the Extreme
    /// Optimization Mathematics Library for .NET.
    /// </summary>
    class LineCurves
    {
        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main(string[] args)
        {
            // All curves inherit from the Curve abstract base
            // class. The Line class overrides implements all
            // the methods and properties of the Curve class,
            // and adds a few more.
            //
            // In a few places, we will need the Point structure.
            // It simply containts an X and a Y component, much
            // like the PointF structure in the System.Drawing
            // namespace.
            //
            // Let's create some points:
            Point point1 = new Point(1, 3);
            Point point2 = new Point(4, 9);

            //
            // Line constructors
            //

            // The Line class has multiple constructors. Each
            // constructor derives from a different way to define
            // a straight line.

            // 1st option: a line through 2 points.
            Line line1 = new Line(point1, point2);
            // 2nd option: same as above, but we use the x and 
            // y coordinates of the points directly.
            Line line2 = new Line(point1.X, point1.Y, point2.X, point2.Y);
            // 3rd option: a line through a point with a specified
            // slope,
            Line line3 = new Line(point1, 2);
            // 4th option: same as above, but we use the x and 
            // y coordinates of the point directly.
            Line line4 = new Line(point1.X, point1.Y, 2);
            // 5th option: a line with specified slope and 
            // specified value at x = 0
            Line line5 = new Line(2, 1);

            //
            // Curve Parameters
            //

            // The shape of any curve is determined by a set of parameters.
            // These parameters can be retrieved and set through the
            // Parameters collection. The number of parameters for a curve
            // is given by this collection's Count property.
            //
            // Lines have two parameters: the y value at x = 0
            // and the slope.
            Console.WriteLine("line1.Parameters.Count = {0}", 
                line1.Parameters.Count);
            // Parameters can easily be retrieved:
            Console.WriteLine("line1 parameters; {0}, {1}", 
                line1.Parameters[0], line1.Parameters[1]);
            // We can see that line2, line3, line4 and line5
            // all define the same line as line1:
            Console.WriteLine("line2 parameters; {0}, {1}", 
                line2.Parameters[0], line2.Parameters[1]);
            Console.WriteLine("line3 parameters; {0}, {1}", 
                line3.Parameters[0], line3.Parameters[1]);
            Console.WriteLine("line4 parameters; {0}, {1}", 
                line4.Parameters[0], line4.Parameters[1]);
            Console.WriteLine("line5 parameters; {0}, {1}", 
                line5.Parameters[0], line5.Parameters[1]);
            // Parameters can also be set:
            line1.Parameters[0] = 1;

            //
            // Curve Methods
            //

            // The ValueAt method returns the y value of the
            // curve at the specified x value:
            Console.WriteLine("line1.ValueAt(2) = {0}", line1.ValueAt(2));

            // The SlopeAt method returns the slope of the curve
            // a the specified x value:
            Console.WriteLine("line1.SlopeAt(2) = {0}", line1.SlopeAt(2));

            // You can also create a new curve that is the 
            // derivative of the original:
            Curve derivative = line1.GetDerivative();
            Console.WriteLine("Slope at 2 (derivative) = {0}", derivative.ValueAt(2));

            // For Line curves, you can access the slope directly
            // through the Slope property:
            Console.WriteLine("Slope of the line = {0}", line1.Slope);

            // You can get a Line that is the tangent to a curve
            // at a specified x value using the TangentAt method:
            Line tangent = line1.TangentAt(2);
            Console.WriteLine("Slope of tangent line at 2 = {0}",
                tangent.Slope);

            // For many curves, you can evaluate a definite
            // integral exactly:
            Console.WriteLine("Integral of line1 between 0 and 1 = {0}",
                line1.Integral(0, 1));

            // You can find the zeroes or roots of the curve
            // by calling the FindRoots method:
            double[] roots = line1.FindRoots();
            Console.WriteLine("Number of roots of line1: {0}",
                roots.Length);
            Console.WriteLine("Value of root = {0}", roots[0]);

            Console.Write("Press Enter key to exit...");
            Console.ReadLine();
        }
    }
}

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