By means of Mates8, graph coding becomes a bit easier.
The web page has four textboxes so the figure gets bounded to the left, right, top and bottom; and a draw button.
Additionally, a panel control will contain the image generated by the code after the button is pressed.
Mates8 grapher
<%@ Page Language="vb" AutoEventWireup="false" CodeBehind="WebForm1.aspx.vb" Inherits="mates4.WebForm1" %>
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title>Graph</title>
<style type="text/css" media="screen">
.margin { margin-left: 9px; position:relative; top:-3px;}
.grPos { position:relative; left: 0px; top: 5px; width:<% =w %>px; height: <% =h %>px;}
</style>
</head>
<body>
<form id="form1" runat="server">
<div>
<asp:Table ID="Table1" runat="server" CssClass="margin" Width="708" BackColor="#EADA90" BorderColor="#C0C0C0" BorderWidth="1">
<asp:TableRow>
<asp:TableCell>
<asp:Table ID="Table2" runat="server" Width="100%">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label1" runat="server" Text="Left: "></asp:Label><br />
<asp:TextBox ID="tbLeft" runat="server" Width="100">-4</asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label2" runat="server" Text="Right: "></asp:Label><br />
<asp:TextBox ID="tbRight" runat="server" Width="100">4</asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label3" runat="server" Text="Bottom: "></asp:Label><br />
<asp:TextBox ID="tbBottom" runat="server" Width="100"></asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label4" runat="server" Text="Top: "></asp:Label><br />
<asp:TextBox ID="tbTop" runat="server" Width="100"></asp:TextBox>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell>
<asp:Label ID="Label5" runat="server" Text="Function 1:" ForeColor="black"></asp:Label><br />
<asp:Textbox id="f1" runat="server" Columns="18" TextMode="MultiLine" Rows="5">x^3-1</asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label6" runat="server" Text="Function 2:" ForeColor="blue"></asp:Label><br />
<asp:Textbox id="f2" runat="server" Columns="18" TextMode="MultiLine" Rows="5"></asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label7" runat="server" Text="Function 3:" ForeColor="green"></asp:Label><br />
<asp:Textbox id="f3" runat="server" Columns="18" TextMode="MultiLine" Rows="5"></asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label8" runat="server" Text="Function 4:" ForeColor="red"></asp:Label><br />
<asp:Textbox id="f4" runat="server" Columns="18" TextMode="MultiLine" Rows="5">0</asp:Textbox>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell ColumnSpan="4" HorizontalAlign="Center">
<asp:CheckBox ID="chkAutoTopBottom" Text="Auto top-bottom" runat="server" Checked="true" />
<asp:Button ID="btnDraw" runat="server" Text="Draw" />
<asp:Label runat="server" ID="lblMessage" Text="" ForeColor="Red" />
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell ColumnSpan="4">
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell>
<asp:Table ID="TableGraphic" runat="server" Height="690" Width="100%" BackColor="#FAFAFA">
<asp:TableRow>
<asp:TableCell>
<asp:Panel runat="server" ID="Panel1">
</asp:Panel>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</div>
</form>
</body>
</html>
=================================================
Imports System.Drawing
Imports System.Drawing.Drawing2D
Imports System.Drawing.Image
Imports System.IO
Partial Public Class graphic
Inherits System.Web.UI.Page
Dim nID As Int32
Const nFn As Int32 = 4
Const nDiv As Int32 = 10
Public Const w As Int32 = 650
Public Const h As Int32 = 650
Dim vMtxParser(nFn - 1) As matrixParser
Dim vPoly(nFn - 1) As Polynomial, iP As Int32
Dim oVars(nFn - 1) As VarsAndFns
Dim vIsEmptyStr(nFn - 1) As Boolean
Dim vIsPoly(nFn - 1) As Boolean
Dim vDbl(3) As Double
Dim sErrMsg As String = "Graphic n/a"
Dim min As Single = Single.MaxValue
Dim max As Single = -min
Dim cImg As HtmlImage
Dim origH, origW As Int32
Protected Sub Page_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
Dim sImagePath As String = MapPath("~/precis/images/grTable.png")
Try
cImg = New UI.HtmlControls.HtmlImage
cImg.Alt = "Graphic"
cImg.Attributes.Add("class", "grPos")
If Page.IsPostBack Then
GetGraphic(sImagePath)
Else
Try
C_session.contador( _
Page, _
Request, _
Response)
nID = C_session.getID(Page)
Catch ex2 As Exception
End Try
Using ms As New MemoryStream
Dim img As Image = Image.FromFile(sImagePath)
img.Save(ms, Imaging.ImageFormat.Png)
cImg.Attributes.Add("src", _
"data:image/png;base64," + Convert.ToBase64String(ms.ToArray))
cImg.Attributes.Add("style", "position:relative; left:20px; top: 10px;")
End Using
End If
Me.Panel1.Controls.Add(cImg)
Catch ex As Exception
lblMessage.Text = "n/a"
End Try
End Sub
Private Sub btnDraw_Click(sender As Object, e As EventArgs) Handles btnDraw.Click
'Dim sImagePath As String = MapPath("~/precis/images/grTable.png")
'GetGraphic(sImagePath)
End Sub
Sub GetGraphic(sGridImagePath As String)
Try
If Not validateInputs() Then
lblMessage.Text = sErrMsg
Exit Try
End If
Dim sFn() As String = {f1.Text, _
f2.Text, _
f3.Text, _
f4.Text}
Me.getvMtxP_and_vPoly(sFn)
' Load a square grid of ten rows
' and columns (i.e. 11 horizontal lines
' and 11 vertical lines):
Dim bmp As New Bitmap(sGridImagePath)
origH = bmp.Height
origW = bmp.Width
Dim gr As Graphics = Graphics.FromImage(bmp)
gr.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias
gr.InterpolationMode = InterpolationMode.NearestNeighbor
Dim vPen() As Pen = {New Pen(Brushes.Black, 0), _
New Pen(Brushes.Blue, 0), _
New Pen(Brushes.Green, 0), _
New Pen(Brushes.Red, 0)}
Dim grPath(nFn - 1) As GraphicsPath
For i As Int32 = 0 To vIsEmptyStr.Length - 1
If Not vIsEmptyStr(i) Then
' Get function's path points:
grPath(i) = _
Me.evalFnToGraphicsPath( _
i, vDbl(0), vDbl(1), w)
End If
Next
If chkAutoTopBottom.Checked Then
vDbl(2) = max
vDbl(3) = min
tbTop.Text = vDbl(2).ToString(MathGlobal8.us)
tbBottom.Text = vDbl(3).ToString(MathGlobal8.us)
Else
max = vDbl(2)
min = vDbl(3)
End If
For i As Int32 = 0 To vIsEmptyStr.Length - 1
If grPath(i) IsNot Nothing AndAlso _
grPath(i).PathData.Points.Count Then
' Translate Y origin:
gr.TranslateTransform(0, -min, MatrixOrder.Append)
' Scale X, Y axis:
If max = min Then
Throw New Exception("n/a")
End If
gr.ScaleTransform(bmp.Width / w, _
bmp.Height / (max - min), MatrixOrder.Append)
' Add into image's Graphics gr:
gr.DrawPath(vPen(i), grPath(i))
' restore origin and scale:
gr.ResetTransform()
End If
Next
' Flip image because gr's vertical axis increments
' downwards and graphic's Y axis will increment
' upwards:
bmp.RotateFlip(RotateFlipType.Rotate180FlipX)
' Get a bigger bitmap...
Dim bmp1 As New Bitmap(bmp.Width + 125, bmp.Height + 60)
Dim gr1 As Graphics = Graphics.FromImage(bmp1)
gr1.Clear(Color.White)
' ...and copy former image to (100,50) to allow
' space on the left and top for the strings:
gr1.DrawImage(bmp, New Point(100, 50))
gr1.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias
' Draw X's and Y's coordinates values as strings:
drawStrings(gr1)
' Release resources:
gr.Dispose()
bmp.Dispose()
Using ms As New MemoryStream
' Save bmp1 into memory...
bmp1.Save(ms, Imaging.ImageFormat.Png)
' ...and set, to the image control on the
' aspx page, the memory file in base64 string format:
cImg.Src = "data:image/png;base64," + Convert.ToBase64String(ms.ToArray)
End Using
' Release resources:
gr1.Dispose()
bmp1.Dispose()
Catch ex As Exception
Throw ex
'lblMessage.Text = sErrMsg
End Try
End Sub
Function validateInputs() As Boolean
Dim mP As New matrixParser
Try
' Axis' X values will be in the
' interval [vDbl(0), vDbl(1)]
' Verify tbLeft -- tbRight
' ------------------------
' eval eventual arithmetic (for ex. 2/3) ...
mP.parse(tbLeft.Text)
' ...but must reduce to a double value:
vDbl(0) = mP.retCjo(0).pRe.ToDouble
mP.parse(tbRight.Text)
vDbl(1) = mP.retCjo(0).pRe.ToDouble
If vDbl(1) < vDbl(0) Then
' If left < right, swap values:
Dim dbl As Double = vDbl(0)
vDbl(0) = vDbl(1)
vDbl(1) = dbl
ElseIf vDbl(0) = vDbl(1) Then
Return False
End If
If vDbl(1) - vDbl(0) <= 1000 * Double.MinValue Then
Return False
End If
If chkAutoTopBottom.Checked = False Then
' Axis' Y values will be in the
' interval [vDbl(2), vDbl(3)]:
' values outside these bounds
' will not be graphed.
' If not auto-Top-Bottom checked, consider
' inputs in textboxes tbTop, tbBottom.
' Verify tbTop -- tbBottom
' ------------------------
mP.parse(tbTop.Text)
vDbl(3) = mP.retCjo(0).pRe.ToDouble
mP.parse(tbBottom.Text)
vDbl(2) = mP.retCjo(0).pRe.ToDouble
If vDbl(2) < vDbl(3) Then
' If top < bottom, swap values:
Dim dbl As Double = vDbl(2)
vDbl(2) = vDbl(3)
vDbl(3) = dbl
ElseIf vDbl(2) = vDbl(3) Then
Return False
End If
If vDbl(2) - vDbl(3) <= 1000 * Double.MinValue Then
Return False
End If
Else
' If auto-Top-Bottom checked
' allow any double value:
vDbl(2) = Double.MaxValue
vDbl(3) = -Double.MaxValue
End If
Catch ex As Exception
Throw ex
'Return False
End Try
Return True
End Function
Private Sub getvMtxP_and_vPoly(sFn() As String)
Try
For i As Int32 = 0 To nFn - 1
If sFn(i) IsNot Nothing AndAlso _
sFn(i).Length Then
vMtxParser(i) = New matrixParser()
vMtxParser(i).parse(sFn(i), "", oVars(i))
' Find out if sFn is a Polynomial expression
' because, if so, evaluation will be less
' time consuming:
If vMtxParser(i).ret.exprMtx.IsPolynomial Then
vIsPoly(i) = True
vPoly(i) = vMtxParser(i).ret.curExpr.getPolynomial
End If
Else
vIsEmptyStr(i) = True
End If
Next
Catch ex As Exception
Throw ex
End Try
End Sub
Private Sub drawStrings(ByRef gr As Graphics) ' Get graph's strings
Try
Dim iv As Int32 = 0
Dim incrV As Double = (max - min) / nDiv
Dim incrH As Double = (vDbl(1) - vDbl(0)) / nDiv
Dim dist As Double = origH / nDiv
Dim fntStr As New Font("Arial Narrow", 12)
Dim ptImg As New Point(100, 30)
Dim Vert As Double = max
Dim Horiz As Double = vDbl(0)
Dim oldsX As String = " "
Dim oldsY As String = " "
Dim nDec As Int32 = 3
Dim maxDec As Int32 = 9
Dim curPos As Single = 0
For row = 0 To 10
' Left side strings:
If Math.Abs(Vert) > 1000 Then
maxDec = 0 : nDec = 0
Else
maxDec = 9 : nDec = 3
End If
Dim curDec As Int32 = nDec
Dim sX As String = ""
Do
sX = Math.Round(Vert, curDec).ToString(MathGlobal8.us)
curDec += 1
Loop While sX = oldsX AndAlso curDec < maxDec
oldsX = sX
Dim s As SizeF = gr.MeasureString(sX, fntStr)
gr.DrawString(sX, fntStr, _
Brushes.Black, _
New Point(ptImg.X - s.Width - 3, _
ptImg.Y + s.Height / 2 + dist * row))
Vert = max - incrV * (row + 1)
' Strings at the top:
If Math.Abs(Horiz) > 1000 Then
maxDec = 0 : nDec = 0
Else
maxDec = 9 : nDec = 3
End If
curDec = nDec
Dim sY As String = ""
Do
sY = Math.Round(Horiz, curDec).ToString(MathGlobal8.us)
curDec += 1
Loop While sY = oldsY AndAlso curDec < maxDec
oldsY = sY
s = gr.MeasureString(sY, fntStr)
gr.DrawString(sY, fntStr, _
Brushes.Black, _
New Point(ptImg.X - s.Width / 2 + 3 + dist * row, _
ptImg.Y - 18))
Horiz = vDbl(0) + incrH * (row + 1)
Next
gr.ScaleTransform(origW / w, _
origH / (max - min), MatrixOrder.Append)
gr.ResetTransform()
Catch ex As Exception
Throw ex
End Try
End Sub
Function evalFnToGraphicsPath(iFn As Int32, x1 As Double, x2 As Double, nPts As Int32) As GraphicsPath
Dim retGP As New GraphicsPath
Try
Dim xStep As Single = (x2 - x1) / nPts
Dim x As Single = x1
Dim y As Double
Dim i As Int32
If vIsPoly(iFn) Then
Dim Pa As Polynomial = vPoly(iFn)
y = Pa.evalPrecis(New Precis(x)).ToDouble
Dim curPt As New PointF(x, y)
Dim bClosed As Boolean = False
Dim nxtPt As New PointF
i = 1
Dim bExclude As Boolean = False
Do
x = xStep * CSng(i)
' Try-catch in case of for ex. singular points:
Try
' Evaluate Pa(x+x1):
y = Pa.evalPrecis(New Precis(x + x1)).ToDouble
Catch ex As Exception
bExclude = True
End Try
If Not bExclude AndAlso _
vDbl(3) <= y AndAlso y <= vDbl(2) Then
nxtPt.X = i
nxtPt.Y = y
retGP.AddLine(curPt, nxtPt)
min = Math.Min(min, y)
max = Math.Max(max, y)
bClosed = False
Else
' 'y' value out of bounds:
If Not bClosed Then
retGP.StartFigure()
bClosed = True
End If
End If
curPt.X = i
curPt.Y = y
i += 1
Loop While i <= nPts
Else
Dim cjo As Complex
Dim bExclude As Boolean = True ' Exclude the starting point
Dim curPt As New PointF
Dim bClosed As Boolean = True
Dim nxtPt As New PointF
Do
x = xStep * i
' Try-catch in case of for ex. singular points:
Try
' Evaluate Fn(x+x1):
cjo = vMtxParser(iFn).ret.exprMtx.getExpr(0, 0).eval_1var_DblToCjo(x + x1)
If cjo IsNot Nothing Then
If cjo.pIm.IsZero Then
y = cjo.pRe.ToDouble
Else
bExclude = True
End If
Else
bExclude = True
End If
Catch ex As Exception
bExclude = True
End Try
If Not bExclude AndAlso _
vDbl(3) <= y AndAlso y <= vDbl(2) Then
nxtPt.X = i
nxtPt.Y = y
retGP.AddLine(curPt, nxtPt)
min = Math.Min(min, y)
max = Math.Max(max, y)
bClosed = False
Else
' 'y' value out of bounds (or first)
If Not bClosed Then
retGP.StartFigure()
bClosed = True
End If
bExclude = False
End If
curPt.X = i
curPt.Y = y
i += 1
Loop While i <= nPts
End If
Catch ex As Exception
Throw ex
End Try
Return retGP
End Function
End Class
xrjf 213 Posting Whiz
The above code has been replaced by this new one.
Here, the points of discontinuity have been taken into account.
So, for example, function tan(x) does not joint adjacent points Yi>>0 and Yi+1<<0 with a line.
<%@ Page Language="vb" MasterPageFile="~/mates4.Master" AutoEventWireup="false" CodeBehind="graphic.aspx.vb" Inherits="mates4.graphic" %>
<asp:Content ID="Content5" ContentPlaceHolderID="head" runat="server">
<style type="text/css" media="screen">
.margin { margin-left: 10px; position:relative; top:0px;}
.grPos { position:relative; left: 20px; top: 0px;}
</style>
</asp:Content>
<asp:Content ID="Content1" ContentPlaceHolderID="content2L" runat="server" Visible="false">
<h3><asp:Label runat="server" > Function grapher</asp:Label></h3>
</asp:Content>
<asp:Content ID="Content6" ContentPlaceHolderID="scriptID" runat="server" Visible="false">
<script type="text/javascript">
if (document.getElementById)
getElemById = function (id) {
return document.getElementById(id);
}
else if (document.all)
getElemById = function (id) {
return document.all[id];
// note that we use square brackets here
}
function coord(e, mi) {
try {
var Xm,Xb,Xmargin,Ym,Yb,Ymargin,Xmin;
Xm = getElemById('<% = Xm.ClientID %>').value; Xm = parseFloat(Xm);
Xb = getElemById('<% = Xb.ClientID%>').value; Xb = parseFloat(Xb);
Xmargin = getElemById('<% = Xmargin.ClientID%>').value; Xmargin = parseFloat(Xmargin);
Xmin = getElemById('<% = Xmin.ClientID%>').value; Xmin = parseFloat(Xmin);
Ym = getElemById('<% = Ym.ClientID%>').value; Ym = parseFloat(Ym);
Yb = getElemById('<% = Yb.ClientID%>').value; Yb = parseFloat(Yb);
Ymargin = getElemById('<% = Ymargin.ClientID%>').value; Ymargin = parseFloat(Ymargin);
var rct = mi.getBoundingClientRect();
var x0 = e.clientX - rct.left - Xmargin;
var y0 = e.clientY - rct.top - Ymargin;
var oX = getElemById('<% =tbX.ClientID %>');
var oY = getElemById('<% =tbY.ClientID%>');
oX.value = Xm * x0 + Xb;
oY.value = -Ym * y0 + Yb;
var str = '' + oX.value;
var pos = str.indexOf('.');
if(pos>-1 && str.length - pos>2 && Math.abs(oX.value)>1)
{ oX.value = Math.round(oX.value * 1000 + 0.005) / 1000;}
str = '' + oY.value;
pos = str.indexOf('.');
if (pos > -1 && str.length - pos > 2 && Math.abs(oY.value) > 1)
{ oY.value = Math.round(oY.value * 1000 + 0.005) / 1000; }
}
catch (err) {
alert(err);
}
}
</script>
</asp:Content>
<asp:Content ID="Content3" ContentPlaceHolderID="content2R" runat="server" Visible="false">
</asp:Content>
<asp:Content ID="Content2" ContentPlaceHolderID="maincontent" runat="server">
<asp:Table ID="Table1" runat="server" CssClass="margin" Width="700" BackColor="#EADA90" BorderColor="#C0C0C0" BorderWidth="1">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Table ID="Table2" runat="server" Width="100%">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label1" runat="server" Text="Left: "></asp:Label><br />
<asp:TextBox ID="tbLeft" runat="server" Width="100">-4</asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label2" runat="server" Text="Right: "></asp:Label><br />
<asp:TextBox ID="tbRight" runat="server" Width="100">4</asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label3" runat="server" Text="Bottom: "></asp:Label><br />
<asp:TextBox ID="tbBottom" runat="server" Width="100"></asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label4" runat="server" Text="Top: "></asp:Label><br />
<asp:TextBox ID="tbTop" runat="server" Width="100"></asp:TextBox>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell>
<asp:Label ID="Label5" runat="server" Text="Function 1:" ForeColor="black"></asp:Label><br />
<asp:Textbox id="f1" runat="server" Columns="18" TextMode="MultiLine" Rows="5">x^3-1</asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label6" runat="server" Text="Function 2:" ForeColor="blue"></asp:Label><br />
<asp:Textbox id="f2" runat="server" Columns="18" TextMode="MultiLine" Rows="5"></asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label7" runat="server" Text="Function 3:" ForeColor="green"></asp:Label><br />
<asp:Textbox id="f3" runat="server" Columns="18" TextMode="MultiLine" Rows="5"></asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label8" runat="server" Text="Function 4:" ForeColor="red"></asp:Label><br />
<asp:Textbox id="f4" runat="server" Columns="18" TextMode="MultiLine" Rows="5">0</asp:Textbox>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Table runat="server">
<asp:TableRow>
<asp:TableCell>
<asp:Label runat="server" ForeColor="Red" Text="X: " />
<asp:TextBox runat="server" ID="tbX" Text="" Width="120" />
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Left">
<asp:Table runat="server">
<asp:TableRow>
<asp:TableCell>
<asp:Label runat="server" ForeColor="Red" Text="Y: " />
<asp:TextBox runat="server" ID="tbY" Text="" Width="120" />
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
<asp:TableCell ColumnSpan="2" HorizontalAlign="Center">
<asp:CheckBox ID="chkAutoTopBottom" Text="Auto top-bottom" runat="server" Checked="true" />
<asp:Button ID="btnDraw" runat="server" Text="Draw" />
<asp:Label runat="server" ID="lblMessage" Text="" ForeColor="Red" />
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell ColumnSpan="4">
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Table ID="TableGraphic" runat="server" Width="100%" BackColor="#FAFAFA" HorizontalAlign="Left">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Panel runat="server" ID="Panel1">
</asp:Panel>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:Content>
<asp:Content ID="Content4" ContentPlaceHolderID="afterMC" runat="server" Visible="false">
<asp:HiddenField runat="server" ID="Xm" Value="0" />
<asp:HiddenField runat="server" ID="Xb" Value="0" />
<asp:HiddenField runat="server" ID="Xmargin" Value="0" />
<asp:HiddenField runat="server" ID="Xmin" Value="0" />
<asp:HiddenField runat="server" ID="Ym" Value="0" />
<asp:HiddenField runat="server" ID="Yb" Value="0" />
<asp:HiddenField runat="server" ID="Ymargin" Value="0" />
</asp:Content>
===============================================================
Imports System.Drawing
Imports System.Drawing.Drawing2D
Imports System.Drawing.Image
Imports System.IO
Partial Public Class graphic
Inherits System.Web.UI.Page
Dim nID As Int32
Const nFn As Int32 = 4
Const nDiv As Int32 = 10
Public Const w As Int32 = 600
Public Const h As Int32 = 600
Dim vMtxParser(nFn - 1) As matrixParser
Dim vPoly(nFn - 1) As Polynomial, iP As Int32
Dim oVars(nFn - 1) As VarsAndFns
Dim vFn() As String
Dim vIsEmptyStr(nFn - 1) As Boolean
Dim vIsPoly(nFn - 1) As Boolean
Dim vDbl(3) As Double
Dim sErrMsg As String = "Graphic n/a"
Dim min As Single = Single.MaxValue
Dim max As Single = -min
Dim cImg As HtmlImage
Dim origH, origW As Int32
Dim marginPt0 As New Point(110, 60)
Dim marginPt1 As New Point(100, 50)
Const margDch As Int32 = 65
Sub logfile(ex As Exception)
Try
Dim sFn() As String = {f1.Text, _
f2.Text, _
f3.Text, _
f4.Text}
Dim sTB() As String = {tbLeft.Text, _
tbRight.Text, _
tbBottom.Text, _
tbTop.Text}
C_session.logFile(ex, _
Join(sFn, "|"), _
Join(sTB, "|"), Page, nID, "polycalc.txt")
Catch ex2 As Exception
End Try
End Sub
Protected Sub Page_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
Dim sImagePath As String = MapPath("~/precis/images/grTable.png")
Try
cImg = New UI.HtmlControls.HtmlImage
cImg.Alt = "Graphic"
cImg.Attributes.Add("class", "grPos")
GetGraphic(sImagePath)
Me.Panel1.Controls.Add(cImg)
Catch ex As Exception
logfile(ex)
lblMessage.Text = "n/a"
End Try
End Sub
Private Sub btnDraw_Click(sender As Object, e As EventArgs) Handles btnDraw.Click
End Sub
Sub GetGraphic(sGridImagePath As String)
Try
If Not validateInputs() Then
lblMessage.Text = sErrMsg
Exit Try
End If
vFn = {f1.Text, _
f2.Text, _
f3.Text, _
f4.Text}
Me.getvMtxP_and_vPoly(vFn)
' Load a square grid of ten rows
' and columns (i.e. 11 horizontal lines
' and 11 vertical lines):
Dim bmp As New Bitmap(sGridImagePath)
origH = bmp.Height
origW = bmp.Width
Dim gr As Graphics = Graphics.FromImage(bmp)
gr.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias
gr.InterpolationMode = InterpolationMode.HighQualityBicubic
Dim vPen() As Pen = {New Pen(Brushes.Black, 0), _
New Pen(Brushes.Blue, 0), _
New Pen(Brushes.Green, 0), _
New Pen(Brushes.Red, 0)}
Dim vPts(-1)()() As PointF, iv As Int32
' vPts(i) holds all the points of a function (for ex. f(x)=1/x)
' vPts(i)(j) has all the points of a continous interval of the
' function. If f(x)=1/x, point x=0 is a discontinuity (f(x)=infinity):
' vPts(i)(0) has all the points f(x)=1/x where x<0
' vPts(i)(0) has all the points f(x)=1/x where x>0
' vPts(i)(j)(k) is a concrete point of the function, for example:
' vPts(i)(0)(0) may be point (x=-4, y=1/-4)
' vPts(i)(0)(1) may be point (x=-3.9, y=1/-3.9)
' ....
' vPts(i)(1)(0) may be point (x=0.1, y=1/0.1)
' vPts(i)(1)(1) may be point (x=0.2, y=1/0.2)
' ....
' (here, the increment 0.1 is ficticious, really the step depends on
' the interval Xleft, Xright and the number of points to draw,
' see method evalFnToGraphicsPath())
For i As Int32 = 0 To vIsEmptyStr.Length - 1
If Not vIsEmptyStr(i) Then
' Get function's path points:
ReDim Preserve vPts(iv)
vPts(iv) = _
Me.evalFnToGraphicsPath( _
i, vDbl(0), vDbl(1), w)
iv += 1
End If
Next
iv = 0
For i As Int32 = 0 To vIsEmptyStr.Length - 1
If Not vIsEmptyStr(i) Then
' Get function's path points:
For j As Int32 = 0 To vPts(iv).GetLength(0) - 1
gr.TranslateTransform(0, -min, MatrixOrder.Append)
' Scale X, Y axis:
If max <> min Then
gr.ScaleTransform(bmp.Width / w, _
bmp.Height / (max - min), MatrixOrder.Append)
End If
' Add into image's Graphics gr:
gr.DrawCurve(vPen(i), vPts(iv)(j))
' restore origin and scale:
gr.ResetTransform()
Next
iv += 1
End If
Next
If chkAutoTopBottom.Checked Then
vDbl(2) = max
vDbl(3) = min
tbTop.Text = vDbl(2).ToString(MathGlobal8.us)
tbBottom.Text = vDbl(3).ToString(MathGlobal8.us)
Else
max = vDbl(2)
min = vDbl(3)
End If
mouseeventInit(bmp.Width, bmp.Height)
' Flip image because gr's vertical axis increments
' downwards and graphic's Y axis will increment
' upwards:
bmp.RotateFlip(RotateFlipType.Rotate180FlipX)
' Get a bigger bitmap...
Dim bmp1 As New Bitmap(w + margDch, h) ' bmp.Width + marginPt0.X, bmp.Height + marginPt0.Y)
Dim gr1 As Graphics = Graphics.FromImage(bmp1)
gr1.Clear(Color.White)
' ...and copy former image to (100,50) to allow
' space on the left and top for the strings:
gr1.DrawImage(bmp, New Point(marginPt1.X, marginPt1.Y))
gr1.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias
' Draw X's and Y's coordinates values as strings:
drawStrings(gr1)
' Release resources:
gr.Dispose()
bmp.Dispose()
Using ms As New MemoryStream
' Save bmp1 into memory...
bmp1.Save(ms, Imaging.ImageFormat.Png)
' ...and set, to the image control on the
' aspx page, the memory file in base64 string format:
cImg.Src = "data:image/png;base64," + Convert.ToBase64String(ms.ToArray)
End Using
' Release resources:
gr1.Dispose()
bmp1.Dispose()
Catch ex As Exception
Throw ex
'lblMessage.Text = sErrMsg
End Try
End Sub
Sub mouseeventInit(bmpW As Int32, bmpH As Int32)
Try
'If Not Page.IsPostBack Then
' Exit Sub
'End If
cImg.Attributes.Add("onmousemove", "coord(event,this);")
' Set Xm,Xb,Ym,Yb for mouseover event:
Dim m As Double = (max - min) / bmpH
Ym.Value = m.ToString(MathGlobal8.us)
Yb.Value = ((max + min + m * bmpH) / 2.0).ToString(MathGlobal8.us)
Ymargin.Value = (marginPt0.Y * bmpH / h).ToString(MathGlobal8.us)
m = (vDbl(1) - vDbl(0)) / bmpW
Xm.Value = m.ToString(MathGlobal8.us)
Xb.Value = ((vDbl(1) + vDbl(0) - m * bmpW) / 2.0).ToString(MathGlobal8.us)
Xmargin.Value = (marginPt1.X).ToString(MathGlobal8.us)
Xmin.Value = min '.ToString(MathGlobal8.us)
Catch ex As Exception
Throw ex
End Try
End Sub
Function validateInputs() As Boolean
Dim mP As New matrixParser
Try
' Axis' X values will be in the
' interval [vDbl(0), vDbl(1)]
' Verify tbLeft -- tbRight
' ------------------------
' eval eventual arithmetic (for ex. 2/3) ...
mP.parse(tbLeft.Text)
' ...but must reduce to a double value:
vDbl(0) = mP.retCjo(0).pRe.ToDouble
mP.parse(tbRight.Text)
vDbl(1) = mP.retCjo(0).pRe.ToDouble
If vDbl(1) < vDbl(0) Then
' If left < right, swap values:
Dim dbl As Double = vDbl(0)
vDbl(0) = vDbl(1)
vDbl(1) = dbl
ElseIf vDbl(0) = vDbl(1) Then
Return False
End If
If vDbl(1) - vDbl(0) <= 1000 * Double.MinValue Then
Return False
End If
If chkAutoTopBottom.Checked = False Then
' Axis' Y values will be in the
' interval [vDbl(2), vDbl(3)]:
' values outside these bounds
' will not be graphed.
' If not auto-Top-Bottom checked, consider
' inputs in textboxes tbTop, tbBottom.
' Verify tbTop -- tbBottom
' ------------------------
mP.parse(tbTop.Text)
vDbl(3) = mP.retCjo(0).pRe.ToDouble
mP.parse(tbBottom.Text)
vDbl(2) = mP.retCjo(0).pRe.ToDouble
If vDbl(2) < vDbl(3) Then
' If top < bottom, swap values:
Dim dbl As Double = vDbl(2)
vDbl(2) = vDbl(3)
vDbl(3) = dbl
ElseIf vDbl(2) = vDbl(3) Then
Return False
End If
If vDbl(2) - vDbl(3) <= 1000 * Double.MinValue Then
Return False
End If
Else
' If auto-Top-Bottom checked
' allow any double value:
vDbl(2) = Double.MaxValue
vDbl(3) = -Double.MaxValue
End If
Catch ex As Exception
Throw ex
'Return False
End Try
Return True
End Function
Private Sub getvMtxP_and_vPoly(sFn() As String)
Try
For i As Int32 = 0 To nFn - 1
If sFn(i) IsNot Nothing AndAlso _
sFn(i).Length Then
vMtxParser(i) = New matrixParser()
vMtxParser(i).parse(sFn(i), "", oVars(i))
If oVars(i).length <= 1 Then
' Find out if sFn is a Polynomial expression
' because, if so, evaluation will be less
' time consuming:
If vMtxParser(i).ret.exprMtx.IsPolynomial Then
vIsPoly(i) = True
vPoly(i) = vMtxParser(i).ret.curExpr.getPolynomial
End If
Else
' more than 1 variable, discard:
vIsEmptyStr(i) = True
End If
Else
vIsEmptyStr(i) = True
End If
Next
Catch ex As Exception
Throw ex
End Try
End Sub
Private Sub drawStrings(ByRef gr As Graphics) ' Get graph's strings
Try
Dim iv As Int32 = 0
Dim incrV As Double = (max - min) / nDiv
Dim incrH As Double = (vDbl(1) - vDbl(0)) / nDiv
Dim dist As Double = origH / nDiv
Dim fntStr As New Font("Calibri", 11)
Dim ptImg As New Point(100, 30)
Dim oldsX(10) As String
Dim Xdec(10) As Int32
Dim oldsY(10) As String
Dim Ydec(10) As Int32
Dim nDec As Int32 = 3
Dim maxDec As Int32 = 9
Dim curPos As Single = 0
repite:
Dim Vert As Double = max
Dim Horiz As Double = vDbl(0)
For row = 0 To 10
' Left side strings:
Dim sX As String = ""
If Math.Abs(Vert) > 1000 Then
sX = Vert.ToString("e" + Xdec(row).ToString, MathGlobal8.us)
Else
sX = Math.Round(Vert, Xdec(row)).ToString(MathGlobal8.us)
End If
For i As Int32 = 0 To row - 1
If oldsX(i) = sX Then
If Xdec(row) < maxDec Then
Xdec(i) += 1
Xdec(row) += 1
GoTo repite
End If
End If
Next
oldsX(row) = sX
Vert = max - incrV * (row + 1)
' Strings at the top:
Dim sY As String = ""
If Math.Abs(Horiz) > 1000 Then
sY = Horiz.ToString("e" + Ydec(row).ToString, MathGlobal8.us)
Else
sY = Math.Round(Horiz, Ydec(row)).ToString(MathGlobal8.us)
End If
For i As Int32 = 0 To row - 1
If oldsY(i) = sY Then
If Ydec(row) < maxDec Then
Ydec(i) += 1
Ydec(row) += 1
GoTo repite
End If
End If
Next
oldsY(row) = sY
Horiz = vDbl(0) + incrH * (row + 1)
Next
For row = 0 To 10
Dim s As SizeF = gr.MeasureString(oldsX(row), fntStr)
gr.DrawString(oldsX(row), fntStr, _
Brushes.Black, _
New Point(ptImg.X - s.Width - 3, _
ptImg.Y + s.Height / 2 + dist * row))
s = gr.MeasureString(oldsY(row), fntStr)
gr.DrawString(oldsY(row), fntStr, _
Brushes.Black, _
New Point(ptImg.X - s.Width / 2 - 1 + dist * row, _
ptImg.Y - 2))
Next
gr.ScaleTransform(origW / w, _
origH / (max - min), MatrixOrder.Append)
gr.ResetTransform()
Catch ex As Exception
Throw ex
End Try
End Sub
Function evalFnToGraphicsPath(iFn As Int32, x1 As Double, x2 As Double, nPts As Int32) As PointF()()
Dim pts(0)() As PointF, iP0, iP1 As Int32
Try
Dim xStep As Single = (x2 - x1) / nPts
Dim x As Single = x1
Dim y As Double
Dim i As Int32
ReDim pts(0)(nPts)
Dim bClosed As Boolean = False
Dim bExclude As Boolean = False
Dim PaZeros(-1) As Double
Dim nZeros As Int32 = 0
Dim iCurZero As Int32 = 0
Dim DenP As Polynomial = Nothing
Dim curPt As New PointF
Dim oldPt0, oldPt1 As PointF
Dim diff As Double = Double.MaxValue
Dim cjo As Complex
Dim expr As Expression = vMtxParser(iFn).ret.exprMtx.getExpr(0, 0)
Dim Pa As Polynomial = vPoly(iFn)
Do
x = xStep * CSng(i)
' Try-catch in case of for ex. singular points:
Try
If vIsPoly(iFn) Then
' Evaluate Pa(x+x1):
y = Pa.evalPrecis(New Precis(x + x1)).ToDouble
Else
cjo = expr.eval_1var_DblToCjo(x + x1)
If cjo IsNot Nothing Then
If cjo.pIm.IsZero Then
y = cjo.pRe.ToDouble
Else
bExclude = True
End If
Else
bExclude = True
End If
End If
Catch ex As Exception
bExclude = True
End Try
If iP1 > 2 AndAlso Not bExclude AndAlso _
vDbl(3) <= y AndAlso y <= vDbl(2) Then
' Get the slope of line oldPt0-oldPt1:
Dim m1 As Single = (oldPt1.Y - oldPt0.Y) / 1
' ...and of line oldPt1-(x,y):
Dim m2 As Single = (y - oldPt1.Y) / 1
Dim atg As Double = Math.Abs(Math.PI / 2 - Math.Abs(Math.Atan2(m1, m2)))
'If atg < diff Then
' diff = atg
' lblMessage.Text = diff.ToString(MathGlobal8.us)
'End If
If Math.Sign(m1) <> Math.Sign(m2) AndAlso _
Math.Abs(m1) > 10 AndAlso Math.Abs(m2) > 10 AndAlso _
atg < 1.6 Then
bExclude = True
End If
End If
If iP1 Then
oldPt1.X = pts(iP0)(iP1 - 1).X
oldPt1.Y = pts(iP0)(iP1 - 1).Y
If iP1 > 1 Then
oldPt0.X = pts(iP0)(iP1 - 2).X
oldPt0.Y = pts(iP0)(iP1 - 2).Y
End If
End If
If bExclude Then
' 'y' value out of bounds
If Not bClosed Then
ReDim Preserve pts(iP0)(iP1 - 1)
iP0 += 1
ReDim Preserve pts(iP0), pts(iP0)(nPts - 1)
iP1 = 0
End If
bExclude = False
Else
pts(iP0)(iP1).X = i
pts(iP0)(iP1).Y = y
iP1 += 1
min = Math.Min(min, y)
max = Math.Max(max, y)
bClosed = False
End If
i += 1
Loop While i <= nPts
ReDim Preserve pts(iP0)(iP1 - 1)
Catch ex As Exception
Throw ex
End Try
Return pts
End Function
End Class
xrjf 213 Posting Whiz
Because of some fixes I take the opportunity to attach a zip file including the image, mates8.dll (v8.3.58), the markup file and the code behind file.
<%@ Page Language="VB" AutoEventWireup="false" CodeFile="fnGrapher.aspx.vb" Inherits="fnGrapher" %>
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title>Function grapher</title>
<style type="text/css" media="screen">
body { font-family: Calibri;
font-size: medium;
}
.margin { margin-left: 10px; position:relative; top:0px;}
.grPos { position:relative; left: 20px; top: 0px;}
</style>
<script type="text/javascript">
if (document.getElementById)
getElemById = function (id) {
return document.getElementById(id);
}
else if (document.all)
getElemById = function (id) {
return document.all[id];
// note that we use square brackets here
}
function coord(e, mi) {
try {
var Xm, Xb, Xmargin, Ym, Yb, Ymargin, Xmin;
Xm = getElemById('<% = Xm.ClientID %>').value; Xm = parseFloat(Xm);
Xb = getElemById('<% = Xb.ClientID%>').value; Xb = parseFloat(Xb);
Xmargin = getElemById('<% = Xmargin.ClientID%>').value; Xmargin = parseFloat(Xmargin);
Xmin = getElemById('<% = Xmin.ClientID%>').value; Xmin = parseFloat(Xmin);
Ym = getElemById('<% = Ym.ClientID%>').value; Ym = parseFloat(Ym);
Yb = getElemById('<% = Yb.ClientID%>').value; Yb = parseFloat(Yb);
Ymargin = getElemById('<% = Ymargin.ClientID%>').value; Ymargin = parseFloat(Ymargin);
var rct = mi.getBoundingClientRect();
var x0 = e.clientX - rct.left - Xmargin;
var y0 = e.clientY - rct.top - Ymargin;
var oX = getElemById('<% =tbX.ClientID %>');
var oY = getElemById('<% =tbY.ClientID%>');
oX.value = Xm * x0 + Xb;
oY.value = -Ym * y0 + Yb;
var str = '' + oX.value;
var pos = str.indexOf('.');
if (pos > -1 && str.length - pos > 2 && Math.abs(oX.value) > 1)
{ oX.value = Math.round(oX.value * 1000 + 0.005) / 1000; }
str = '' + oY.value;
pos = str.indexOf('.');
if (pos > -1 && str.length - pos > 2 && Math.abs(oY.value) > 1)
{ oY.value = Math.round(oY.value * 1000 + 0.005) / 1000; }
}
catch (err) {
alert(err);
}
}
</script>
</head>
<body>
<form id="form1" runat="server">
<div style="width:100%">
<asp:Table ID="Table1" runat="server" CssClass="margin" Width="700" BackColor="#EADA90" BorderColor="#C0C0C0" BorderWidth="1" HorizontalAlign="Center">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Table ID="Table2" runat="server" Width="100%">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label1" runat="server" Text="Left: "></asp:Label><br />
<asp:TextBox ID="tbLeft" runat="server" Width="100">-4</asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label2" runat="server" Text="Right: "></asp:Label><br />
<asp:TextBox ID="tbRight" runat="server" Width="100">4</asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label3" runat="server" Text="Bottom: "></asp:Label><br />
<asp:TextBox ID="tbBottom" runat="server" Width="100"></asp:TextBox>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Center">
<asp:Label ID="Label4" runat="server" Text="Top: "></asp:Label><br />
<asp:TextBox ID="tbTop" runat="server" Width="100"></asp:TextBox>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell>
<asp:Label ID="Label5" runat="server" Text="Function 1:" ForeColor="black"></asp:Label><br />
<asp:Textbox id="f1" runat="server" Columns="18" TextMode="MultiLine" Rows="5">x^3-1</asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label6" runat="server" Text="Function 2:" ForeColor="blue"></asp:Label><br />
<asp:Textbox id="f2" runat="server" Columns="18" TextMode="MultiLine" Rows="5"></asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label7" runat="server" Text="Function 3:" ForeColor="green"></asp:Label><br />
<asp:Textbox id="f3" runat="server" Columns="18" TextMode="MultiLine" Rows="5"></asp:Textbox>
</asp:TableCell>
<asp:TableCell>
<asp:Label ID="Label8" runat="server" Text="Function 4:" ForeColor="red"></asp:Label><br />
<asp:Textbox id="f4" runat="server" Columns="18" TextMode="MultiLine" Rows="5">0</asp:Textbox>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Table runat="server">
<asp:TableRow>
<asp:TableCell>
<asp:Label runat="server" ForeColor="Red" Text="X: " ></asp:Label>
<asp:TextBox runat="server" ID="tbX" Text="" Width="120" ></asp:TextBox>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
<asp:TableCell HorizontalAlign="Left">
<asp:Table runat="server">
<asp:TableRow>
<asp:TableCell>
<asp:Label runat="server" ForeColor="Red" Text="Y: " ></asp:Label>
<asp:TextBox runat="server" ID="tbY" Text="" Width="120" ></asp:TextBox>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
<asp:TableCell ColumnSpan="2" HorizontalAlign="Center">
<asp:Table runat="server">
<asp:TableRow>
<asp:TableCell Wrap="false">
<asp:CheckBox ID="chkAutoTopBottom" Text="Auto top-bottom" runat="server" Checked="true" ></asp:CheckBox>
</asp:TableCell>
<asp:TableCell Width="100">
<asp:Button ID="btnDraw" runat="server" Text="Draw" ></asp:Button>
</asp:TableCell>
<asp:TableCell>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
<asp:TableCell>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell ColumnSpan="4">
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Label runat="server" ID="lblMessage" Text="" ForeColor="Red" ></asp:Label>
</asp:TableCell>
</asp:TableRow>
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Table ID="TableGraphic" runat="server" Width="100%" BackColor="#FAFAFA" HorizontalAlign="Left">
<asp:TableRow>
<asp:TableCell HorizontalAlign="Left">
<asp:Panel runat="server" ID="Panel1">
</asp:Panel>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
</asp:TableCell>
</asp:TableRow>
</asp:Table>
<asp:HiddenField runat="server" ID="Xm" Value="0" ></asp:HiddenField>
<asp:HiddenField runat="server" ID="Xb" Value="0" ></asp:HiddenField>
<asp:HiddenField runat="server" ID="Xmargin" Value="0" ></asp:HiddenField>
<asp:HiddenField runat="server" ID="Xmin" Value="0" ></asp:HiddenField>
<asp:HiddenField runat="server" ID="Ym" Value="0" ></asp:HiddenField>
<asp:HiddenField runat="server" ID="Yb" Value="0" ></asp:HiddenField>
<asp:HiddenField runat="server" ID="Ymargin" Value="0" ></asp:HiddenField>
</div>
</form>
</body>
</html>
xrjf 213 Posting Whiz
Imports System.Drawing
Imports System.Drawing.Drawing2D
Imports System.Drawing.Image
Imports System.IO
Imports mates8
Partial Class fnGrapher
Inherits System.Web.UI.Page
Dim nID As Int32
Const nFn As Int32 = 4
Const nDiv As Int32 = 10
Public Const w As Int32 = 600
Public Const h As Int32 = 600
Dim vMtxParser(nFn - 1) As matrixParser
Dim vPoly(nFn - 1) As Polynomial, iP As Int32
Dim oVars(nFn - 1) As VarsAndFns
Dim vFn() As String
Dim vIsEmptyStr(nFn - 1) As Boolean
Dim vIsPoly(nFn - 1) As Boolean
Dim vDbl(3) As Double
Dim sErrMsg As String = "Graphic n/a"
Dim min As Single = Single.MaxValue
Dim max As Single = -min
Dim cImg As HtmlImage
Dim origH, origW As Int32
Dim marginPt0 As New Point(110, 60)
Dim marginPt1 As New Point(100, 50)
Dim iComplexPts, iOutOfRange As Int32
Const margDch As Int32 = 65
Protected Sub Page_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
Dim sImagePath As String = MapPath("~/grTable.png")
Try
lblMessage.Visible = False
lblMessage.Text = ""
iComplexPts = 0 : iOutOfRange = 0
cImg = New UI.HtmlControls.HtmlImage
cImg.Alt = "Graphic"
cImg.Attributes.Add("class", "grPos")
GetGraphic(sImagePath)
Me.Panel1.Controls.Add(cImg)
If iComplexPts OrElse iOutOfRange Then
If iComplexPts Then
lblMessage.Text = iComplexPts.ToString + " complex points couldn't be drawn."
End If
If iOutOfRange Then
lblMessage.Text += iOutOfRange.ToString + " out of range points couldn't be drawn."
End If
End If
Catch ex As Exception
If lblMessage.Text.Length = 0 Then
If iComplexPts OrElse iOutOfRange Then
If iComplexPts Then
lblMessage.Text = iComplexPts.ToString + " complex points couldn't be drawn."
End If
If iOutOfRange Then
lblMessage.Text += iOutOfRange.ToString + " out of range points couldn't be drawn."
End If
Else
lblMessage.Text = "n/a"
End If
End If
Finally
If lblMessage.Text.Length Then
lblMessage.Visible = True
End If
End Try
End Sub
Private Sub btnDraw_Click(sender As Object, e As EventArgs) Handles btnDraw.Click
'Dim sImagePath As String = MapPath("~/precis/images/grTable.png")
'GetGraphic(sImagePath)
End Sub
Sub GetGraphic(sGridImagePath As String)
Try
If Not validateInputs() Then
lblMessage.Text = "n/a: invalid input values."
Exit Try
End If
vFn = {f1.Text, _
f2.Text, _
f3.Text, _
f4.Text}
Me.getvMtxP_and_vPoly(vFn)
' Load a square grid of ten rows
' and columns (i.e. 11 horizontal lines
' and 11 vertical lines):
Dim bmp As New Bitmap(sGridImagePath)
origH = bmp.Height
origW = bmp.Width
Dim gr As Graphics = Graphics.FromImage(bmp)
gr.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias
gr.InterpolationMode = InterpolationMode.HighQualityBicubic
Dim vPen() As Pen = {New Pen(Brushes.Black, 0), _
New Pen(Brushes.Blue, 0), _
New Pen(Brushes.Green, 0), _
New Pen(Brushes.Red, 0)}
Dim vPts(-1)()() As PointF, iv As Int32
' vPts(i) holds all the points of a function (for ex. f(x)=1/x)
' vPts(i)(j) has all the points of a continous interval of the
' function. If f(x)=1/x, point x=0 is a discontinuity (f(x)=infinity):
' vPts(i)(0) has all the points f(x)=1/x where x<0
' vPts(i)(0) has all the points f(x)=1/x where x>0
' vPts(i)(j)(k) is a concrete point of the function, for example:
' vPts(i)(0)(0) may be point (x=-4, y=1/-4)
' vPts(i)(0)(1) may be point (x=-3.9, y=1/-3.9)
' ....
' vPts(i)(1)(0) may be point (x=0.1, y=1/0.1)
' vPts(i)(1)(1) may be point (x=0.2, y=1/0.2)
' ....
' (here, the increment 0.1 is ficticious, really the step depends on
' the interval Xleft, Xright and the number of points to draw,
' see method evalFnToGraphicsPath())
Dim max2 As Double = -Double.MaxValue
Dim min2 As Double = Double.MaxValue
For i As Int32 = 0 To vIsEmptyStr.Length - 1
If Not vIsEmptyStr(i) Then
' Get function's path points:
ReDim Preserve vPts(iv)
vPts(iv) = _
Me.evalFnToGraphicsPath( _
i, vDbl(0), vDbl(1), w)
iv += 1
max2 = Math.Max(max2, max)
min2 = Math.Min(min2, min)
End If
Next
max = max2 : min = min2
iv = 0
For i As Int32 = 0 To vIsEmptyStr.Length - 1
If Not vIsEmptyStr(i) Then
' Get function's path points:
For j As Int32 = 0 To vPts(iv).GetLength(0) - 1
gr.TranslateTransform(0, -min, MatrixOrder.Append)
' Scale X, Y axis:
If max <> min Then
gr.ScaleTransform(bmp.Width / w, _
bmp.Height / (max - min), MatrixOrder.Append)
End If
' Add into image's Graphics gr:
gr.DrawCurve(vPen(i), vPts(iv)(j))
If chkAutoTopBottom.Checked Then
End If
' restore origin and scale:
gr.ResetTransform()
Next
iv += 1
End If
Next
If chkAutoTopBottom.Checked Then
vDbl(2) = max
vDbl(3) = min
tbTop.Text = vDbl(2).ToString(MathGlobal8.us)
tbBottom.Text = vDbl(3).ToString(MathGlobal8.us)
Else
max = vDbl(2)
min = vDbl(3)
End If
If max = min Then
lblMessage.Text = "n/a: top and bottom values can't be equal or void."
Throw New Exception(lblMessage.Text)
End If
mouseeventInit(bmp.Width, bmp.Height)
' Flip image because gr's vertical axis increments
' downwards and graphic's Y axis will increment
' upwards:
bmp.RotateFlip(RotateFlipType.Rotate180FlipX)
' Get a bigger bitmap...
Dim bmp1 As New Bitmap(w + margDch, h) ' bmp.Width + marginPt0.X, bmp.Height + marginPt0.Y)
Dim gr1 As Graphics = Graphics.FromImage(bmp1)
gr1.Clear(Color.White)
' ...and copy former image to (100,50) to allow
' space on the left and top for the strings:
gr1.DrawImage(bmp, New Point(marginPt1.X, marginPt1.Y))
gr1.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias
' Draw X's and Y's coordinates values as strings:
drawStrings(gr1)
' Release resources:
gr.Dispose()
bmp.Dispose()
Using ms As New MemoryStream
' Save bmp1 into memory...
bmp1.Save(ms, Imaging.ImageFormat.Png)
' ...and set, to the image control on the
' aspx page, the memory file in base64 string format:
cImg.Src = "data:image/png;base64," + Convert.ToBase64String(ms.ToArray)
End Using
' Release resources:
gr1.Dispose()
bmp1.Dispose()
Catch ex As Exception
Throw ex
'lblMessage.Text = sErrMsg
End Try
End Sub
Sub mouseeventInit(bmpW As Int32, bmpH As Int32)
Try
'If Not Page.IsPostBack Then
' Exit Sub
'End If
cImg.Attributes.Add("onmousemove", "coord(event,this);")
' Set Xm,Xb,Ym,Yb for mouseover event:
Dim m As Double = (max - min) / bmpH
Ym.Value = m.ToString(MathGlobal8.us)
Yb.Value = ((max + min + m * bmpH) / 2.0).ToString(MathGlobal8.us)
Ymargin.Value = (marginPt0.Y * bmpH / h).ToString(MathGlobal8.us)
m = (vDbl(1) - vDbl(0)) / bmpW
Xm.Value = m.ToString(MathGlobal8.us)
Xb.Value = ((vDbl(1) + vDbl(0) - m * bmpW) / 2.0).ToString(MathGlobal8.us)
Xmargin.Value = (marginPt1.X).ToString(MathGlobal8.us)
Xmin.Value = min '.ToString(MathGlobal8.us)
Catch ex As Exception
Throw ex
End Try
End Sub
Function validateInputs() As Boolean
Dim mP As New matrixParser
Try
' Axis' X values will be in the
' interval [vDbl(0), vDbl(1)]
' Verify tbLeft -- tbRight
' ------------------------
' eval eventual arithmetic (for ex. 2/3) ...
If tbLeft.Text = "" Then tbLeft.Text = "-4"
If tbRight.Text = "" Then tbRight.Text = "4"
If tbTop.Text = "" Then tbLeft.Text = "4"
If tbBottom.Text = "" Then tbLeft.Text = "-4"
mP.parse(tbLeft.Text)
' ...but must reduce to a double value:
vDbl(0) = mP.retCjo(0).pRe.ToDouble
mP.parse(tbRight.Text)
vDbl(1) = mP.retCjo(0).pRe.ToDouble
If vDbl(1) < vDbl(0) Then
' If left < right, swap values:
Dim dbl As Double = vDbl(0)
vDbl(0) = vDbl(1)
vDbl(1) = dbl
ElseIf vDbl(0) = vDbl(1) Then
Return False
End If
If vDbl(1) - vDbl(0) <= 1000 * Double.MinValue Then
Return False
End If
If chkAutoTopBottom.Checked = False Then
' Axis' Y values will be in the
' interval [vDbl(2), vDbl(3)]:
' values outside these bounds
' will not be graphed.
' If not auto-Top-Bottom checked, consider
' inputs in textboxes tbTop, tbBottom.
' Verify tbTop -- tbBottom
' ------------------------
mP.parse(tbTop.Text)
vDbl(3) = mP.retCjo(0).pRe.ToDouble
mP.parse(tbBottom.Text)
vDbl(2) = mP.retCjo(0).pRe.ToDouble
If vDbl(2) < vDbl(3) Then
' If top < bottom, swap values:
Dim dbl As Double = vDbl(2)
vDbl(2) = vDbl(3)
vDbl(3) = dbl
ElseIf vDbl(2) = vDbl(3) Then
Return False
End If
If vDbl(2) - vDbl(3) <= 1000 * Double.MinValue Then
Return False
End If
Else
' If auto-Top-Bottom checked
' allow any double value:
vDbl(2) = Double.MaxValue
vDbl(3) = -Double.MaxValue
End If
Catch ex As Exception
Throw ex
'Return False
End Try
Return True
End Function
Private Sub getvMtxP_and_vPoly(sFn() As String)
Try
For i As Int32 = 0 To nFn - 1
If sFn(i) IsNot Nothing AndAlso _
sFn(i).Length Then
vMtxParser(i) = New matrixParser()
vMtxParser(i).parse(sFn(i), "", oVars(i))
If oVars(i).length <= 1 Then
' Find out if sFn is a Polynomial expression
' because, if so, evaluation will be less
' time consuming:
If vMtxParser(i).ret.exprMtx.IsPolynomial Then
vIsPoly(i) = True
vPoly(i) = vMtxParser(i).ret.curExpr.getPolynomial
End If
Else
' more than 1 variable, discard:
'vIsEmptyStr(i) = True
lblMessage.Text = "<span style=""color:black"">n/a: more than one variable {"
For nV As Int32 = 0 To oVars(i).length - 1
lblMessage.Text += oVars(i).getVarNameByID(nV)
If nV < oVars(i).length - 1 Then
lblMessage.Text += ","
Else
lblMessage.Text += "}"
End If
Next
lblMessage.Text += " in function " + sFn(i)
lblMessage.Text += " <br />Tip: for ex. enter x^2-1, do NOT enter the definition" + _
" <span style=""color:red"">f(x)=</span>x^2-1</span>"
Throw New Exception(lblMessage.Text)
End If
Else
vIsEmptyStr(i) = True
End If
Next
Catch ex As Exception
Throw ex
End Try
End Sub
Private Sub drawStrings(ByRef gr As Graphics) ' Get graph's strings
Try
Dim iv As Int32 = 0
Dim incrV As Double = (max - min) / nDiv
Dim incrH As Double = (vDbl(1) - vDbl(0)) / nDiv
Dim dist As Double = origH / nDiv
Dim fntStr As New Font("Calibri", 10)
Dim ptImg As New Point(100, 30)
Dim oldsX(10) As String
Dim Xdec(10) As Int32
Dim oldsY(10) As String
Dim Ydec(10) As Int32
Dim nDec As Int32 = 3
Dim maxDec As Int32 = 9
Dim curPos As Single = 0
repite:
Dim Vert As Double = max
Dim Horiz As Double = vDbl(0)
For row = 0 To 10
' Left side strings:
Dim sX As String = ""
If Vert < 100 AndAlso Xdec(row) < 2 Then
Xdec(row) = 2
ElseIf Vert < 10 AndAlso Xdec(row) < 3 Then
Xdec(row) = 3
End If
If Math.Abs(Vert) > 10 ^ 5 Then
If Xdec(row) < 2 Then Xdec(row) = 2
sX = Vert.ToString("g" + Xdec(row).ToString, MathGlobal8.us)
Else
sX = Math.Round(Vert, Xdec(row)).ToString(MathGlobal8.us)
End If
For i As Int32 = 0 To row - 1
If oldsX(i) = sX Then
If Xdec(row) < maxDec Then
Xdec(i) += 1
Xdec(row) += 1
GoTo repite
End If
End If
Next
oldsX(row) = sX
Vert = max - incrV * (row + 1)
' Strings at the top:
Dim sY As String = ""
If Horiz < 100 AndAlso Ydec(row) < 2 Then
Ydec(row) = 2
ElseIf Horiz < 10 AndAlso Ydec(row) < 3 Then
Ydec(row) = 3
End If
If Math.Abs(Horiz) > 10 ^ 5 Then
If Ydec(row) < 2 Then Ydec(row) = 2
sY = Horiz.ToString("g" + Ydec(row).ToString, MathGlobal8.us)
Else
sY = Math.Round(Horiz, Ydec(row)).ToString(MathGlobal8.us)
End If
For i As Int32 = 0 To row - 1
If oldsY(i) = sY Then
If Ydec(row) < maxDec Then
Ydec(i) += 1
Ydec(row) += 1
GoTo repite
End If
End If
Next
oldsY(row) = sY
Horiz = vDbl(0) + incrH * (row + 1)
Next
For row = 0 To 10
Dim s As SizeF = gr.MeasureString(oldsX(row), fntStr)
gr.DrawString(oldsX(row), fntStr, _
Brushes.Black, _
New Point(ptImg.X - s.Width - 3, _
ptImg.Y + s.Height / 2 + dist * row))
s = gr.MeasureString(oldsY(row), fntStr)
gr.DrawString(oldsY(row), fntStr, _
Brushes.Black, _
New Point(ptImg.X - s.Width / 2 - 1 + dist * row, _
ptImg.Y - 2))
Next
gr.ScaleTransform(origW / w, _
origH / (max - min), MatrixOrder.Append)
gr.ResetTransform()
Catch ex As Exception
Throw ex
End Try
End Sub
Function evalFnToGraphicsPath(iFn As Int32, x1 As Double, x2 As Double, nPts As Int32) As PointF()()
Dim pts(0)() As PointF, iP0, iP1 As Int32
Try
Dim xStep As Single = (x2 - x1) / nPts
Dim x As Single = x1
Dim y As Double
Dim i As Int32
ReDim pts(0)(nPts)
Dim bClosed As Boolean = False
Dim bExclude As Boolean = False
Dim PaZeros(-1) As Double
Dim nZeros As Int32 = 0
Dim iCurZero As Int32 = 0
Dim DenP As Polynomial = Nothing
Dim curPt As New PointF
Dim oldPt0, oldPt1 As PointF
Dim diff As Double = Double.MaxValue
Dim cjo As Complex
Dim expr As Expression = vMtxParser(iFn).ret.exprMtx.getExpr(0, 0)
Dim Pa As Polynomial = vPoly(iFn)
Do
x = xStep * CSng(i)
' Try-catch in case of for ex. singular points:
Try
If vIsPoly(iFn) Then
' Evaluate Pa(x+x1):
y = Pa.evalPrecis(New Precis(x + x1)).ToDouble
Else
cjo = expr.eval_1var_DblToCjo(x + x1)
If cjo IsNot Nothing Then
If cjo.pIm.IsZero Then
y = cjo.pRe.ToDouble
Else
bExclude = True
iComplexPts += 1
End If
Else
bExclude = True
End If
End If
Catch ex As Exception
bExclude = True
End Try
If Not bExclude AndAlso _
(vDbl(3) > y OrElse vDbl(2) < y) Then
bExclude = True
End If
If iP1 > 2 AndAlso Not bExclude AndAlso _
vDbl(3) <= y AndAlso y <= vDbl(2) Then
' Get the slope of line oldPt0-oldPt1:
Dim m1 As Single = (oldPt1.Y - oldPt0.Y) / 1
' ...and of line oldPt1-(x,y):
Dim m2 As Single = (y - oldPt1.Y) / 1
Dim atg As Double = Math.Abs(Math.PI / 2 - Math.Abs(Math.Atan2(m1, m2)))
'If atg < diff Then
' diff = atg
' lblMessage.Text = diff.ToString(MathGlobal8.us)
'End If
If Math.Sign(m1) <> Math.Sign(m2) AndAlso _
Math.Abs(m1) > 10 AndAlso Math.Abs(m2) > 10 AndAlso _
atg < 1.6 Then
bExclude = True
End If
End If
If iP1 Then
oldPt1.X = pts(iP0)(iP1 - 1).X
oldPt1.Y = pts(iP0)(iP1 - 1).Y
If iP1 > 1 Then
oldPt0.X = pts(iP0)(iP1 - 2).X
oldPt0.Y = pts(iP0)(iP1 - 2).Y
End If
End If
If bExclude OrElse Double.IsInfinity(y) _
OrElse Double.IsNaN(y) Then
If Double.IsInfinity(y) OrElse _
Double.IsNaN(y) Then
iOutOfRange += 1
End If
' 'y' value out of bounds
If Not bClosed Then
If iP1 Then
ReDim Preserve pts(iP0)(iP1 - 1)
iP0 += 1
ReDim Preserve pts(iP0), pts(iP0)(nPts - 1)
iP1 = 0
End If
End If
bExclude = False
Else
pts(iP0)(iP1).X = i
pts(iP0)(iP1).Y = y
iP1 += 1
min = Math.Min(min, y)
max = Math.Max(max, y)
bClosed = False
End If
i += 1
Loop While i <= nPts
If iP1 Then
ReDim Preserve pts(iP0)(iP1 - 1)
ElseIf iP0 Then
ReDim Preserve pts(iP0 - 1)
Else
ReDim Preserve pts(-1)
End If
Catch ex As Exception
Throw ex
End Try
Return pts
End Function
End Class
xrjf 213 Posting Whiz
In a recent fix Line #137 has been replaced by:
If Me.chkAutoTopBottom.Checked Then
max = max2 : min = min2
Else
max = vDbl(2) : min = vDbl(3)
End If
and, in mouseEventInit() method - line #226 -, Ymargin.value by:
Ymargin.Value = ((marginPt0.Y + marginPt1.Y) / 2.0 * bmpH / h).ToString(MathGlobal8.us)
xrjf 213 Posting Whiz
In order to improve the messages, lines 171 through 174:
If max = min Then
lblMessage.Text = "n/a: top and bottom values can't be equal or void."
Throw New Exception(lblMessage.Text)
End If
may be replaced by:
If max = min Then
If vDbl(2) = vDbl(3) Then
lblMessage.Text = "n/a: top and bottom values can't be equal or void."
Else
lblMessage.Text = iComplexPts.ToString + " complex points couldn't be drawn."
End If
Throw New Exception(lblMessage.Text)
End If
Also, depending on the criteria one follows for functions having complex values, lines 455-476:
cjo = expr.eval_1var_DblToCjo(x + x1)
If cjo IsNot Nothing Then
If cjo.pIm.IsZero Then
y = cjo.pRe.ToDouble
Else
bExclude = True
iComplexPts += 1
End If
Else
bExclude = True
End If
may be replaced by:
cjo = expr.eval_1var_DblToCjo(x + x1)
If cjo IsNot Nothing Then
y = cjo.pRe.ToDouble
Dim dbIm As Double = cjo.pIm.ToDouble
If (Not cjo.pRe.IsZero AndAlso _
Math.Abs(cjo.pIm.ToDouble / cjo.pRe.ToDouble) > 10 ^ -8) OrElse _
(cjo.pRe.IsZero AndAlso Not cjo.pIm.IsZero) Then
bExclude = True
iComplexPts += 1
End If
Else
bExclude = True
End If
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