Using Cardinal method to construct the piecewise cubic spline of plug-in: Practice

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The following is a simple example: Click eight points in the window and draw the coordinates of these eight points ~~~, I used three paint brushes in total: a green pen draws these points using the GDI + method, and a blue pen draws these dots in a straight line, the third red pen is drawn using my cardinal method. From the result, we can see that when T = 0, the curve drawn by Cardinal completely overlaps with the curve of GDI +.

Development Environment: vs.net 2003

Usage: Create a Windows form project, copy the following code to form1.cs and overwrite it, run it, and click 8 at will.

Using system;
Using system. drawing;
Using system. Drawing. drawing2d;
Using system. collections;
Using system. componentmodel;
Using system. Windows. forms;
Using system. Data;

Namespace gdiplusapplication1
{
# Region the defination of myarraylist
Class myarraylist
{
Private arraylist DATA = new arraylist ();

Public myarraylist ()
{
}

Public object this [int idx]
{
Get
{
If (idx>-1 & idx <data. Count)
{
Return (data [idx]);
}
Else
{
Throw new invalidoperationexception ("[myarr. set_item] Index out of range ");
}
}
Set
{
If (idx>-1 & idx <data. Count)
{
Data [idx] = value;
}
Else if (idx = data. Count)
{
Data. Add (value );
}
Else if (idx> data. Count)
{
For (INT I = data. Count; I <idx; I ++)
{
Data. Add (null );
}
Data. Add (value );
}
Else
{
Throw new invalidoperationexception ("[myarr. set_item] Index out of range ");
}
}
}

Public int count
{
Get
{
Return data. count;
}
}

Public void add (Object OBJ)
{
Data. Add (OBJ );
}

Public array toarray (type)
{
If (type = NULL)
{
Throw new argumentnullexception ("type ");
}
Array array1 = array. createinstance (type, Data. Count );
Array1 = data. toarray (type );
Return array1;
}
}
# Endregion

/// <Summary>
/// Summary description for form1.
/// </Summary>
Public class form1: system. Windows. Forms. Form
{
Public struct point3d
{
Public float X;
Public float y;
Public float Z;
}

Private myarraylist mousepoints = new myarraylist ();
Pen redpen = new pen (color. Red, 2 );
Pen bluepen = new pen (color. Blue, 2 );
Pen greenpen = new pen (color. Green, 2 );
Pen brownpen = new pen (color. Brown, 2 );
Pointf lastpoint = new pointf (0, 0 );
Pointf currentpoint = new pointf (0, 0 );
System. Drawing. Graphics g;

/// <Summary>
/// Required designer variable.
/// </Summary>
Private system. componentmodel. Container components = NULL;

Public form1 ()
{
//
// Required for Windows Form Designer support
//
Initializecomponent ();
G = This. creategraphics ();

//
// Todo: add Any constructor code after initializecomponent call
//
}

/// <Summary>
/// Clean up any resources being used.
/// </Summary>
Protected override void dispose (bool disposing)
{
If (disposing)
{
If (components! = NULL)
{
Components. Dispose ();
}
}
Base. Dispose (disposing );
}

# Region windows Form Designer generated code
/// <Summary>
/// Required method for designer support-do not modify
/// The contents of this method with the code editor.
/// </Summary>
Private void initializecomponent ()
{
//
// Form1
//
This. autoscalebasesize = new system. Drawing. Size (5, 13 );
This. clientsize = new system. Drawing. Size (640,526 );
This. Name = "form1 ";
This. Text = "form1 ";
This. windowstate = system. Windows. Forms. formwindowstate. maximized;
This. Click + = new system. eventhandler (this. form1_click );

}
# Endregion

/// <Summary>
/// The main entry pointf for the application.
/// </Summary>
[Stathread]
Static void main ()
{
Application. Run (New form1 ());
}

# Region Cardinal Algorithm
Private pointf Cardinal (float U, float T, pointf A, pointf B, pointf C, pointf D)
{
Float S = (1-T)/2;
Pointf resultpoint = new pointf ();
Resultpoint. x = getresult (a.x, B. X, c.x, D. X, S, U );
Resultpoint. Y = getresult (A. Y, B .y, C. Y, d.y, S, U );
Return resultpoint;
}

Private float getresult (float a, float B, float C, float D, float S, float U)
{
Float result = 0.0f;
Result = A * (2 * S * u-s * u) + B * (2-S) * u + (S-3) * u + 1) +
C * (S-2) * u + (3-2 * s) * u + S * U) + D * (S * u-s * u * U );
Return result;
}
# Endregion

Private void form1_click (Object sender, system. eventargs E)
{
Point currentposition = control. mouseposition;
Pointf currentmouseposition = (pointf) This. pointtoclient (currentposition );
Mousepoints. Add (currentmouseposition );
Currentpoint = currentmouseposition;

If (mousepoints. Count = 8)
{
// The system curve, it's good
Graphicspath Path = new graphicspath ();
Path. addcurve (pointf []) mousepoints. toarray (typeof (pointf )));
Pointf [] newpoints = path. pathpoints;
System. Drawing. drawing2d. Matrix matrix = new matrix ();
G. drawlines (bluepen, (pointf []) mousepoints. toarray (typeof (pointf )));
G. drawpath (greenpen, PATH );

Arraylist newmousepoints = new arraylist ();
Pointf startpoint = (pointf) mousepoints [0];
Pointf starterpoint = new pointf (startpoint. X, startpoint. y );
Pointf endpoint = (pointf) mousepoints [mousepoints. Count-1];
Pointf enderpoint = new pointf (endpoint. X, endpoint. y );
Newmousepoints. Add (starterpoint );

For (INT I = 0; I <mousepoints. Count; I ++)
{
Newmousepoints. Add (mousepoints [I]);
}

Newmousepoints. Add (enderpoint );

Datetime nowtime = system. datetime. now;
Timespan startspan = new timespan (nowtime. Day, nowtime. Hour, nowtime. Minute, nowtime. Second, nowtime. millisecond );

For (INT I = 0; I <7; I ++)
{
Float uvaule = 0.000f;
Float step = 0.002f;
Arraylist ctlpoints = new arraylist ();
Ctlpoints. Add (newmousepoints [I + 1]);
While (uvaule <1.20.f)
{
Pointf newpoint = Cardinal (uvaule, 0.0f, (pointf) newmousepoints [I], (pointf) newmousepoints [I + 1],
(Pointf) newmousepoints [I + 2], (pointf) newmousepoints [I + 3]);
Ctlpoints. Add (newpoint );
Uvaule + = step;
}
Ctlpoints. Add (newmousepoints [I + 2]);
G. drawlines (redpen, (pointf []) ctlpoints. toarray (typeof (pointf )));
}

Datetime endtime = system. datetime. now;
Timespan endspan = new timespan (endtime. Day, endtime. Hour, endtime. Minute, endtime. Second, endtime. millisecond );
Timespan elipspan = endspan. Subtract (startspan );
Console. writeline (elipspan. tostring ());
}
}

}
}