So I have a "main" function (SolveSixODES) that calls a secondary function (AllODEs). And when it does this, the x value in the main function gets modified. I don't understand how this can be possible, seeing as it is not a global variable.
Here is the code, my inputs I used are as follows:
x=0, xmax=3, y=0-6, h=0.1, error=0.1
Public Function SolveSixODE(x As Double, xmax As Double, Y As Range, h As Double, error As Double) 'Weird bug: You must leave the first y4 value blank
Dim i As Integer, k(7, 7) As Double, j As Integer, m As Integer 'k(Order #, equation #)
Dim Y5(7) As Double, Y4(7) As Double, Y4Old(7) As Double
Dim delta0(7) As Double, delta1(7) As Double, delRatio(7) As Double, Rmin As Double
For i = 1 To 6 'Moving the input data so it can acutally be used
Y4(i) = Y(i)
Next i
While x < xmax
If x + h < xmax Then
x = x + h
Else
h = xmax - x
x = xmax
End If
For j = 1 To 6 'j is the order i is equation number
For i = 1 To 6 'Calculating all of the k(1) values for eq 1 to 6
k(j, i) = AllODES(x, Y4, i, j, k, h) '!!!!!SOME HOW THIS LOOP MAKES X negative...!!!!!!!
Next i
Next j
For i = 1 To 6
Y4Old(i) = Y4(i) 'Saving old y4 value to calc delta0
Y4(i) = Y4(i) + h * (k(1, i) * (37 / 378) + k(3, i) * (250 / 621) + k(4, i) * (125 / 594) + k(6, i) * (512 / 1771))
Y5(i) = Y4(i) + h * (k(1, i) * (2825 / 27648) + k(3, i) * (18575 / 48384) + k(4, i) * (13525 / 55296) + k(5, i) * (277 / 14336) + k(6, i) * (0.25))
delta0(i) = error * (Abs(Y4Old(i)) + Abs(h * AllODES(x, Y4Old, i, 1, k, h))) 'First order because we don't want to use the k vals
delta1(i) = Abs(Y5(i) - Y4(i))
delRatio(i) = Abs(delta0(i) / delta1(i)) 'Ratio of errors
Next i
Rmin = delRatio(1)
For i = 2 To 6
If delRatio(i) < Rmin Then
Rmin = delRatio(i) 'Determine the smallest error ratio
End If
Next i
If Rmin < 1 Then 'If this is true then the step size was too big must repeat step
x = x - h 'Set x and y's back to previous values
For i = 1 To 6
Y4(i) = Y4Old(i)
Next i
h = 0.9 * h * Rmin ^ 0.25 'adjust h value; 0.9 is a safety factor
Else
h = 0.9 * h * Rmin ^ 0.2 'Otherwise, we march on
End If
m = m + 1
Wend
SolveSixODE = Y4
End Function
Public Function AllODES(x As Double, Y() As Double, EqNumber As Integer, order As Integer, k() As Double, h As Double) As Double
Dim conc(7) As Double, i As Integer, j As Integer
If order = 1 Then
x = x - h
For i = 1 To 6 'Movin the data so I can use it
conc(i) = Y(i) 'also adjusting the x and y values for RK4 (Cash Karp values)
Next i
ElseIf order = 2 Then
x = x - h + h * 0.2
For i = 1 To 6
conc(i) = Y(i) + h * k(1, i) * 0.2
Next i
ElseIf order = 3 Then
x = x - h + 0.3 * h
For i = 1 To 6
conc(i) = Y(i) + h * (0.075 * k(1, i) + 0.225 * k(2, i))
Next i
ElseIf order = 4 Then
x = x - h + 0.6 * h
For i = 1 To 6
conc(i) = Y(i) + h * (0.3 * k(1, i) - 0.9 * k(2, i) + 1.2 * k(3, i))
Next i
ElseIf order = 5 Then
x = x - h + h
For i = 1 To 6
conc(i) = Y(i) + h * ((-11 / 54) * k(1, i) + 2.5 * k(2, i) - (70 / 27) * k(3, i) + (35 / 27) * k(4, i))
Next i
ElseIf order = 6 Then
x = x - h + 0.875 * h
For i = 1 To 6
conc(i) = Y(i) + h * ((1631 / 55296) * k(1, i) + (175 / 512) * k(2, i) + (575 / 13824) * k(3, i) + (44275 / (110592) * k(4, i) + (253 / 4096) * k(5, i)))
Next i
Else
MsgBox ("error")
End If
If EqNumber = 1 Then 'These are the actual equations
AllODES = x + Y(1)
ElseIf EqNumber = 2 Then
AllODES = x
ElseIf EqNumber = 3 Then
AllODES = Y(3)
ElseIf EqNumber = 4 Then
AllODES = 2 * x
ElseIf EqNumber = 5 Then
AllODES = 2 * Y(2)
ElseIf EqNumber = 6 Then
AllODES = 3 * x
Else
MsgBox ("You entered an Eq Number that was dumb")
End If
End Function
It's possible that it is something really trivial that I missed but this seems to contradict my knowledge of how variables work. So if you understand how the function is able to manipulate a variable from another function in this case, I would appreciate any advice and/or explanation!
Thanks in advance!
the x value in the main function gets modified. I don't understand how this can be possible, seeing as it is not a global variable
This is normal because you are passing x by reference to the function AllODES and you do change it there. When the keyword ByVal is not explicitly specified in the function/sub prototype, the default passing mechanism is ByRef, that is, by reference.
Public Function AllODES(x As Double, ...
means
Public Function AllODES(ByRef x As Double, ....
We observe that x is manipulated in this function, so the change will appear in the caller. If you want that the change of x does not report back in the caller's scope, pass x by value:
Public Function AllODES(ByVal x As Double, ....
' ^^^^^
Only in this case the x of the caller and the x of the callee will be two different variables.
I have written a macro which computes x and y values. I am having trouble trying to write those values to cells on Excel.
I get #VALUE error when I try to display the values on the cell.
I have added my code below. Any suggestion about what is wrong with the code will be really helpful and appreciated?
Thanks in advance!
'Compute Points
Function ComputePoints(x1, y1, x2, y2, distance) As Double
'Calculate slope m
Dim m As Double
m = (y2 - y1) / (x2 - x1)
'Calculate intercept
Dim Intercept As Double
Intercept = y1 - m * x1
'Calculate x for distFinal
Dim message As String
Dim a As Double
Dim b As Double
Dim c As Double
Dim root1 As Double
Dim root2 As Double
Dim det As Double
Dim det1 As Double
Dim wb As Workbook
Dim ws As Worksheet
Dim x1Rng As Range
Dim x2Rng As Range
Dim yRng As Range
a = (m ^ 2 + 1)
b = 2 * (Intercept * m - m * y2 - x2)
c = x2 ^ 2 + (Intercept - y2) ^ 2 - distance ^ 2
det = ((b ^ 2) - (4 * a * c))
det1 = Sqr(det)
message = "There is no solution to your equation"
If det < 0 Then
MsgBox message, vbOKOnly, "Error"
Else
root1 = Round((-b + det1) / (2 * a), 2)
root2 = Round((-b - det1) / (2 * a), 2)
End If
'Compute y
Dim y As Double
y = m * root2 + Intercept
' Trying to set cell values to root1, root2, y
Set wb = ActiveWorkbook
Set ws = wb.Sheets("Sheet9")
Set x1Rng = ws.Range("N2")
Set x2Rng = ws.Range("O2")
Set yRng = ws.Range("P2")
x1Rng.Value2 = root1
x2Rng.Value2 = root2
yRng.Value2 = y
ComputePoints = y
End Function
I modified your code slightly to get values directly in excel cells. You need to select 3 horizontal cells, press F2 / =, enter your formula and then press Ctrl Shift Enter to make it an array formula.
This will give you the three output values in the cells.
Function ComputePoints(x1, y1, x2, y2, distance)
Dim results(3) As Variant ' #nightcrawler23
'Calculate slope m
Dim m As Double
m = (y2 - y1) / (x2 - x1)
'Calculate intercept
Dim Intercept As Double
Intercept = y1 - m * x1
'Calculate x for distFinal
Dim message As String
Dim a As Double
Dim b As Double
Dim c As Double
Dim root1 As Double
Dim root2 As Double
Dim det As Double
Dim det1 As Double
a = (m ^ 2 + 1)
b = 2 * (Intercept * m - m * y2 - x2)
c = x2 ^ 2 + (Intercept - y2) ^ 2 - distance ^ 2
det = ((b ^ 2) - (4 * a * c))
det1 = Sqr(det)
message = "There is no solution to your equation"
If det < 0 Then
MsgBox message, vbOKOnly, "Error"
Else
root1 = Round((-b + det1) / (2 * a), 2)
root2 = Round((-b - det1) / (2 * a), 2)
End If
'Compute y
Dim y As Double
y = m * root2 + Intercept
results(1) = root1 ' #nightcrawler23
results(2) = root2 ' #nightcrawler23
results(3) = y ' #nightcrawler23
ComputePoints = results ' #nightcrawler23
End Function
You need to add some code to output error message, when no roots are found
I'm trying to create a a program that will draw hypotrochoids (spirograph). The program below compiles fine. But when I run it I only get a portion of the drawing.. I'm not sure what I'm doing wrong. I'm fairly new to VB.. Any help is appreciated. Thanks.
Here is the screenshot http://imgur.com/a/KxFWk
Public Class Form1
Private Sub Form1_Load(sender As System.Object, e As System.EventArgs) Handles MyBase.Load
End Sub
Private Sub PictureBox1_Paint(sender As Object, e As PaintEventArgs) Handles PictureBox1.Paint
Dim x As Integer
Dim y As Integer
Dim p As Integer
Dim x1 As Integer
Dim y1 As Integer
Dim x2 As Integer
Dim y2 As Integer
x = 75
y = 15
p = 15
x1 = (x + y) * Math.Cos(0) + p * Math.Cos(0)
y1 = (x + y) * Math.Sin(0) + p * Math.Sin(0)
For t = 0 To 500 Step 0.1
x2 = (x + y) * Math.Cos(t) + p * Math.Cos((x + y) * t / y)
y2 = (x + y) * Math.Sin(t) + p * Math.Sin((x + y) * t / y)
e.Graphics.DrawLine(Pens.Blue, x1, y1, x2, y2)
x1 = x2
y1 = y2
Next
End Sub
End Class
The results of the Sin and Cos calculations result in negative numbers where the parameter is greater than 90 for cos and greater than 180 for sin.
To see the whole image, you need to change the offset for x2 and y2 - see the code below. Alter the number 200 in each of the four lines to a value appropriate for your picturebox
x1 = 200 + CInt((x + y) * Math.Cos(0) + p * Math.Cos(0))
y1 = 200 + CInt((x + y) * Math.Sin(0) + p * Math.Sin(0))
For t As Double = 0 To 500 Step 0.1
x2 = 200 + CInt((x + y) * Math.Cos(t) + p * Math.Cos((x + y) * t / y))
y2 = 200 + CInt((x + y) * Math.Sin(t) + p * Math.Sin((x + y) * t / y))
e.Graphics.DrawLine(Pens.Blue, x1, y1, x2, y2)
x1 = x2
y1 = y2
Next
I am using VBA for the first time. I started with a very basic code using Runga Kutta Method. I am not able to run it. Can I know where I am going wrong? Can you also post some solutions for this type of differential equation solvers?
Option Explicit
Dim K1 As Double
Dim K2 As Double
Dim K3 As Double
Dim K4 As Double
Dim y As Double
Dim x As Double
Dim dx As Double
Dim x0 As Integer
Dim y0 As Integer
Function f(x, y) As Double
f = 0.5 * x - 0.5 * y
End Function
Sub RK(x, y, dx)
Dim i As Integer
Dim ynew As Double
dx = 0.5
x0 = 0
y0 = 1
K1 = dx * f(x, y)
K2 = dx * f(x + dx / 2, y + K1 / 2)
K3 = dx * f(x + dx / 2, y + K2 / 2)
K4 = dx * f(x + dx, y + K3)
RK = y + ((K1 + 2 * (K2 + K3 + K4)) / 6)
For i = 0 To 6
ynew = RK(x, y, dx)
x = x + dx
y = ynew
Next i
For j = 1 To 6
Call RK(x, y, dx, ynew)
ActiveCell.Offset(i - 1, 1).Value = x
ActiveCell.Offset(i - 1, 2).Value = y
x = x + dx
y = ynew
Next
End Sub
You need to execute the RK procedure and give it the starting values of x, y and dx.
To do this from within the VBE (Visual Basic Editor) open the Immediate window. If it's not visible press Ctrl+G and it should appear at the bottom of the VBE.
In the Immediate window type something like RK 1, 3, 2 and the results will appear in the two columns to the right of the active cell and take up 6 rows.
If you want the procedure to execute on the press of a button, or when a value is updated you'll need to add an extra bit of code for that.
Edit:
Just noticed these lines - RK = y + ((K1 + 2 * (K2 + K3 + K4)) / 6) and ynew = RK(x, y, dx).
The RK procedure won't return a value and you can't set it as a value either.
This link may help explain it: http://what-when-how.com/excel-vba/vba-sub-and-function-procedures/
I'm trying to make a function in Lua or VB based code to
draw / plot an ellipse and also a filled ellipse.
I don't have much knowledge about this math and I can use some help.
I googled everything there is to google about drawing ellipses with code but I can't find a good simple working example that i can code into my Lua / VB code.
here are a few websites i visited but couldn't make the code work or couldn't convert the code to Lua or VB properly...
https://sites.google.com/site/ruslancray/lab/projects/bresenhamscircleellipsedrawingalgorithm/bresenham-s-circle-ellipse-drawing-algorithm
http://groups.csail.mit.edu/graphics/classes/6.837/F98/Lecture6/circle.html
http://www.blitzbasic.com/codearcs/codearcs.php?code=2817
http://hackipedia.org/Algorithms/Graphics/pdf/A%20Fast%20Bresenham%20Type%20Algorithm%20For%20Drawing%20Ellipses%20by%20John%20Kennedy.pdf
https://scratch.mit.edu/projects/49873666/
http://www.sourcecodesworld.com/source/show.asp?ScriptID=112
How do I draw an ellipse with arbitrary orientation pixel by pixel?
Can anyone help me make code that can draw an ellipse and a filled ellipse?
here is some code I tried to convert to Lua from here:
https://gist.github.com/Wollw/3291916
this code has some problems (missing pixels) and I think it's not converted properly but I don't know how to do it otherwise.
function plotEllipseRect(x0, y0, x1, y1)
-- values of diameter
a = math.abs(x1-x0)
b = math.abs(y1-y0)
b1 = 2.5
-- error increment
dx = 4*(1-a)*b*b
dy = 4*(b1+1)*a*a
-- error of 1.step
err = dx+dy+b1*a*a
-- e2 = 0
if (x0 > x1) then -- if called with swapped points
x0 = x1
x1 = x1 + a
end
if (y0 > y1) then -- .. exchange them
y0 = y1
end
-- starting pixel
y0 = y0 + (b+1)/2
y1 = y0-b1
a = a * 8*a
b1 = 8*b*b
repeat
dot(x1, y0) -- I. Quadrant
dot(x0, y0) -- II. Quadrant
dot(x0, y1) -- III. Quadrant
dot(x1, y1) -- IV. Quadrant
e2 = 2*err
if (e2 <= dy) then -- y step
y0 = y0 + 1
y1 = y1 - 1
dy = dy + a
err = err + dy
end
if (e2 >= dx or 2*err > dy) then -- x step
x0 = x0 + 1
x1 = x1 - 1
dx = dx + b1
err = err + dx
end
until (x0 >= x1)
while (y0-y1 < b) do -- too early stop of flat ellipses a=1
dot(x0-1, y0) -- -> finish tip of ellipse
y0 = y0 + 1
dot(x1+1, y0)
dot(x0-1, y1)
y1 = y1 - 1
dot(x1+1, y1)
end
end
[EDIT:]
I almost got it for the filled one!
see the comments in this code below to know what the problem is...
I use EGSL to test this Lua code:
http://www.egsl.retrogamecoding.org//pages/downloads.php
function DrawEllipse(xc,yc,w,h)
local w2 = w * w
local h2 = h * h
local fw2 = 4 * w2
local fh2 = 4 * h2
xc = xc + w
yc = yc + h
local x = 0
local y = h
local s = 2 * h2 + w2 * (1 - h)
while h2 * x <= w2 * y do
dot(xc + x, yc + y)
dot(xc - x, yc + y)
dot(xc + x, yc - y)
dot(xc - x, yc - y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255)) --random color to see changes
if s >= 0 then
s = s + fw2 * (1 - y)
y = y - 1
color(255,0,255)
line(xc + x, yc + y, xc - x, yc + y)
line(xc + x, yc - y, xc - x, yc - y)
end
s = s + h2 * ((4 * x) + 6)
x = x + 1
end
x = w
y = 0
s = 2 * w2 + h2 * (1 - w)
line(xc + x, yc + y, xc - x, yc + y) --to prevent the first line to be drawn twice
redraw()
inkey()
s = s + w2 * ((4 * y) + 6)
y = y + 1
while w2 * y < h2 * (x-2) do
line(xc + x, yc + y, xc - x, yc + y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255))
line(xc + x, yc - y, xc - x, yc - y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255))
if s >= 0 then
s = s + fh2 * (1 - x)
x = x - 1
end
s = s + w2 * ((4 * y) + 6)
y = y + 1
end
dot(xc + x, yc + y)
dot(xc - x, yc + y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255))
dot(xc + x, yc - y)
dot(xc - x, yc - y)
redraw()
inkey()
end
openwindow (70,70,32,"Resize Window")
color(255,255,0)
DrawEllipse(10,10,20,20) --works perfect!
inkey()
cls()
DrawEllipse(10,10,10,20) --problems with last 2 horizontal lines between the pixels!
inkey()
cls()
DrawEllipse(10,10,20,10) --works perfect to!
closewindow()
The following VB works for me, based on the first link provided; the only difference between mine here and the code at your link is I move xc and yc over, since you cannot can't have negative x or y values for the pixels in a bitmap.
Public Shared Function DrawEllipse(ByVal xc As Integer, ByVal yc As Integer, ByVal w As Integer, ByVal h As Integer, ByVal doFill As Boolean) As Drawing.Bitmap
Dim w2 As Integer = w * w
Dim h2 As Integer = h * h
Dim fw2 As Integer = 4 * w2
Dim fh2 As Integer = 4 * h2
// cheat by moving xc and yc so that we can handle quadrants
xc = w
yc = h
Dim bm As New Drawing.Bitmap(w2, h2)
// first half
Dim x As Integer = 0
Dim y As Integer = h
Dim s As Integer = 2 * h2 + w2 * (1 - h)
While h2 * x <= w2 * y
If doFill Then
For i As Integer = -y To y
bm.SetPixel(xc + x, yc + i, Drawing.Color.Red)
bm.SetPixel(xc - x, yc + i, Drawing.Color.Red)
Next
Else
bm.SetPixel(xc + x, yc + y, Drawing.Color.Red)
bm.SetPixel(xc - x, yc + y, Drawing.Color.Red)
bm.SetPixel(xc + x, yc - y, Drawing.Color.Red)
bm.SetPixel(xc - x, yc - y, Drawing.Color.Red)
End If
If s >= 0 Then
s += fw2 * (1 - y)
y -= 1
End If
s += h2 * ((4 * x) + 6)
x += 1
End While
// second half
x = w
y = 0
s = 2 * w2 + h2 * (1 - w)
While w2 * y <= h2 * x
If doFill Then
For i As Integer = -x To x
bm.SetPixel(xc + i, yc + y, Drawing.Color.Red)
bm.SetPixel(xc + i, yc - y, Drawing.Color.Red)
Next
Else
bm.SetPixel(xc + x, yc + y, Drawing.Color.Red)
bm.SetPixel(xc - x, yc + y, Drawing.Color.Red)
bm.SetPixel(xc + x, yc - y, Drawing.Color.Red)
bm.SetPixel(xc - x, yc - y, Drawing.Color.Red)
End If
If s >= 0 Then
s += fh2 * (1 - x)
x -= 1
End If
s += w2 * ((4 * y) + 6)
y += 1
End While
Return bm
End Function
(Aside: I used // instead of ' for the comments... just for readability here. If you copy to Visual Studio you'll have to fix that)
Ok, I managed to find a solution for the filled ellipse by checking
if the pixel from the second half is gonna be drawn in the x-range of the first half of the ellipse.
function drawellipse(xc, yc, w, h, dofill)
--trouble with the size, 1 pixel to large on x and y to...
w=w/2 --good solution for making it the right size?
h=h/2 --good solution for making it the right size?
local w2 = w * w
local h2 = h * h
local fw2 = 4 * w2
local fh2 = 4 * h2
-- cheat by moving xc and yc so that we can handle quadrants
xc = xc + w
yc = yc + h
-- first half
local x = 0
local y = h
local s = 2 * h2 + w2 * (1 - h)
while h2 * x <= w2 * y do
if dofill then
for i = -y , y do
color(0,255,0)
dot(xc + x, yc + i)
dot(xc - x, yc + i)
--redraw()inkey()
end
else
color(255,0,255)
dot(xc + x, yc + y)
dot(xc - x, yc + y)
dot(xc + x, yc - y)
dot(xc - x, yc - y)
--redraw()inkey()
end
if s >= 0 then
s =s+ fw2 * (1 - y)
y =y- 1
end
s =s+ h2 * ((4 * x) + 6)
x =x+ 1
end
color(255,0,255)
line(xc + x,0,xc - x,0)
test1 = xc + x
test2 = xc - x
print(test1 .. '/' .. test2)
redraw()inkey()
-- second half
x = w
y = 0
s = 2 * w2 + h2 * (1 - w)
while w2 * y <= h2 * x do
if dofill then
for i = -x , x do
if not(xc + i > test2 and xc + i < test1) then
color(255,255,0)
dot(xc + i, yc + y)
dot(xc + i, yc - y)
redraw()inkey()
end
end
else
color(0,255,255)
dot(xc + x, yc + y)
dot(xc - x, yc + y)
dot(xc + x, yc - y)
dot(xc - x, yc - y)
redraw()inkey()
end
if s >= 0 then
s =s+ fh2 * (1 - x)
x =x- 1
end
s =s+ w2 * ((4 * y) + 6)
y =y+ 1
end
end
In vb.net you have both Graphics.DrawEllipse and Graphics.DrawArc. In Lua you may be able to use Cairo which I know has a arc function.
If you where to make a ellipse in a GraphicsPath in .Net and where to reverse engineer how it is stored in memory, you would find out that it is stored as four bezier curves. I implemented my own graphics library in vb.net once, and that was how I did it. The best resource I found at the time where a implementation in Actionscript, that I unfortunately was unable to locate aswell as that graphics library I was talking about.
TLDR; You should have a look at bezier curves.
A completely different, and very simple take on this, although the ellipse doesn't seem as "pretty" as the other algorithms; this just uses the mathematical definition of an ellipse and, looping over x calculates the y coordinate given x, w, and h.
Public Shared Function DrawEllipse2(ByVal xc As Integer, ByVal yc As Integer, ByVal w As Integer, ByVal h As Integer, ByVal doFill As Boolean) As Drawing.Bitmap
Dim bm As New Drawing.Bitmap(w * w, h * h)
For x As Integer = xc - w To xc + w
Dim y As Integer = CInt((Math.Sqrt(1 - ((x * x) / (w * w)))) * h)
If doFill Then
For j As Integer = -y To y
bm.SetPixel(w + x, h + j, Drawing.Color.Red)
Next
Else
bm.SetPixel(w + x, h + y, Drawing.Color.Red)
bm.SetPixel(w + x, h - y, Drawing.Color.Red)
End If
Next
Return bm
End Function