# Lisp Parabola

This is pretty simple. Its a start. Func1 defines the equation ax^2 + bx + c with the specific values of a b and c and returns the value when passed the current value of X.  C:para calls the parabola function and sets the x minimum, maximum and x increment.

screenshot from the visual lisp editor.

if instead of unconnected lines, we want to graph with a 2D Polyline, the command is PLine, it takes the same point list. We start the Pline command with the first point, then enter the loop and calculate the next point each time through the loop, leaving the command processor running and just feeding it one point each time.

For graphing polar equations – Polar Coordinates – P(R,Ɵ) – A point is defined by how far it is from the origin (R – Radius) and what angle (Ɵ – Theta) a line from the origin to the point makes with the horizontal axis. (I am using A for angle instead of Ɵ in the code)

To change the command from separate lines to connected polyline, we start the pline command outside the loop and only calculate one point in the loop, just as for the rectangular cartesian program.

# Creating the Graph Point Data

Autocad AddLightWeightPolyline method requires an array of doubles. It does not require the lowerbound of the array to be zero. An array simply has to have an even number of elements, one element for each X and each Y alternating. (x1, y1, x2, y2, x3, y3…) For indexes and loops I typically use the counting numbers, which do not include zero. I am evaluating an autocad work-alike program that is similar but requires arrays to be zero-based. It does not throw an error with a one-based array but results are a failure. it creates zero values for non-existent indexes that it expects. However there is no reason the arrays cannot be zero-based so they run in both packages. To that end for that reason i am re-doing the graph loops.

Only the array needs to be zero based. The loop still executes one time for each point. The index of the array starts with zero.

Calculation of points for Coordinate XY graphing –

Autocad does not care what indexes the array pt (below) was created with. The work-alike absolutely requires a starting index of zero.

```Dim plineobj As AcadLWPolyline
```

in line drawing mode, subtracting lbound from ubound adding one and dividing by two will give the number of points in the array. There is one less line. Since we know lbound is zero we could remove that. The loop iterates once for each line drawn. We could do the loop to handle any lbound value, but it would be a little messy with no immediate benefit. For now we expect a zero base array.

```Sub draw_lines(ByRef pt() As Double)
Dim i As Integer, numpts As Integer, numlines As Integer
Dim x1 As Double, x2 As Double, y1 As Double, y2 As Double
Dim pt1(0 To 2) As Double
Dim pt2(0 To 2) As Double

numpts = (UBound(pt) - LBound(pt) + 1) / 2
numlines = numpts - 1

'this requires a zero base array
For i = 1 To numlines
x1 = pt(i * 2 - 2)
y1 = pt(i * 2 - 1)
x2 = pt(i * 2)
y2 = pt(i * 2 + 1)

pt1(0) = x1: pt1(1) = y1: pt1(2) = 0
pt2(0) = x2: pt2(1) = y2: pt2(2) = 0

Next i

Update
End Sub
```

Lines w/limits mode we use when the Y value approaches infinity, such as y=1/x near x=0. It is otherwise the same.

```Sub draw_lines_wlimits(xlim As Double, ylim As Double, ByRef pt() As Double)
Dim i As Integer, numpts As Integer, numlines As Integer
Dim x1 As Double, x2 As Double, y1 As Double, y2 As Double
Dim pt1(0 To 2) As Double
Dim pt2(0 To 2) As Double

numpts = (UBound(pt) - LBound(pt) + 1) / 2
numlines = numpts - 1

'this requires a zero base array
For i = 1 To numlines
x1 = pt(i * 2 - 2)
y1 = pt(i * 2 - 1)
x2 = pt(i * 2)
y2 = pt(i * 2 + 1)

If Abs(x1) < xlim And Abs(y1) < ylim And Abs(x2) < xlim And Abs(y2) < ylim Then
pt1(0) = x1: pt1(1) = y1: pt1(2) = 0
pt2(0) = x2: pt2(1) = y2: pt2(2) = 0
End If
Next i

Update
End Sub
```

point mode

```
Sub draw_points(ByRef pt() As Double)
Call pointmode
Dim i As Integer, numpts As Integer
Dim x1 As Double, y1 As Double

Dim pt1(0 To 2) As Double
numpts = (UBound(pt) - LBound(pt) + 1) / 2

'this requires a zero base array
For i = 1 To numpts
x1 = pt(i * 2 - 2)
y1 = pt(i * 2 - 1)
pt1(0) = x1: pt1(1) = y1: pt1(2) = 0
Next i

Update
End Sub

```

Autocad has Euclidean roots. Its a classic geometry tool. And it has VBA. It is not necessary to download and install the VBA module to have full access to VBA through Excel.

this blog online 1 year with 100 pages, approx, More to come.

i apologize for the old posts with messed up links and code mangling. wordpress changed their editor last year and between them and me changing the theme, we messed up a few pages that were ok when first published. i just noticed some new broken links.

Lissajous curves gone wrong. I unchecked the convert to Radians button in the Parametric form before graphing, so that Sin(360) is interpreted by VBA not as Sin(2 pi) but Sin(360) or in radians Sin(57 * 2 pi) approx, but more importantly the step increment between points instead of being 1 degree is 1 radian or 57 degrees.

# the Cochleoid

the Cochleoid is a polar spiral that spirals in on itself, because Sin A varies between -1 and 1, but A gets ever larger.

at point 8 A is 210, not 30, but because the Sin is negative, R is negative. The graph passes thru 0,0 every time the sin is zero.

running the graph from negative 1080 (-6 pi) to -1 (to avoid divide by zero error) draws the mirror image graph from the inside out.

wolfram reference
http://mathworld.wolfram.com/Cochleoid.html

Tablestyles can be added and programmed without duplicating code by using a global variable for the AcadTableStyle object. This is a flexible method for getting a handle on them.

but first – make font tables in autocad – run a loop from 0 to 255 to advance the Chr(#), change the textstyle of the table style to instantly change the table.

```Sub test_array_to_acadtable3()

'0 to 255 ascii table
'font style is set in the table style
'send the array to the maketable routine

Dim rows As Integer, i As Integer
Dim columns As Integer, j As Integer

rows = 16
columns = 16

Dim ar_mult() As String
ReDim ar_mult(1 To rows, 1 To columns)

For i = 1 To rows
For j = 1 To columns
ar_mult(i, j) = Chr((i - 1) * 16 + (j - 1))
Next j
Next i

Call makethetable3(ar_mult)
End Sub

```

# VBA Arrays and Autocad Tables

Here is the basic routine for making an autocad table from an array in its simplest form from a one-based array, and a generalized form that creates a table from any two-dimensional array.

```
'test to make a one-based two dimensional array of numbers
'and send the array to the maketable routines

Dim rows As Integer, i As Integer
Dim columns As Integer, j As Integer
'change these to anything you like
rows = 14
columns = 16

Dim ar_mult() As Integer
ReDim ar_mult(1 To rows, 1 To columns)

For i = 1 To rows
For j = 1 To columns
ar_mult(i, j) = i * j
Next j
Next i

'makes two identical tables
Call makethetable2(ar_mult)
Call makethetable3(ar_mult)
End Sub

'test to make a random-based two dimensional array of numbers
'and send the array to the maketable routine
'that has been generalized to accept an array of any base

Dim rows As Integer, i As Integer
Dim columns As Integer, j As Integer
'change these to anything you like
rows = 14
columns = 16

Dim ar_mult() As Integer
ReDim ar_mult(3 To rows + 2, 3 To columns + 2)

For i = 3 To rows + 2
For j = 3 To columns + 2
ar_mult(i, j) = (i - 2) * (j - 2)
Next j
Next i

Call makethetable3(ar_mult)
End Sub

Sub makethetable3(ar As Variant)
'table is two-dimensional and any-base
Dim i As Integer, j As Integer
Dim rowcount As Integer, colcount As Integer
Dim rowLbound As Integer, colLbound As Integer
Dim rowUbound As Integer, colUbound As Integer

Dim drowh As Double, dcolw As Double
Dim pt0(0 To 2) As Double

rowLbound = LBound(ar, 1)
colLbound = LBound(ar, 2)
rowUbound = UBound(ar, 1)
colUbound = UBound(ar, 2)
rowcount = rowUbound - rowLbound + 1
colcount = colUbound - colLbound + 1

drowh = 0.125
dcolw = 0.625
tbl.UnmergeCells 0, 0, 0, 0
tbl.TitleSuppressed = True

For i = rowLbound To rowUbound
For j = colLbound To colUbound
tbl.SetText i - colLbound, j - rowLbound, ar(i, j)
Next j
Next i
End Sub

Sub makethetable2(ar As Variant)
'the simpler routine
'assume table is two-dimensional and one-base
'no attempt to set up a tablestyle
'which makes the unmerge method necessary

Dim i As Integer, j As Integer
Dim rowcount As Integer, colcount As Integer
Dim drowh As Double, dcolw As Double
Dim pt0(0 To 2) As Double

rowcount = UBound(ar, 1)
colcount = UBound(ar, 2)
drowh = 0.125
dcolw = 0.625
'create the table sized for the array
tbl.UnmergeCells 0, 0, 0, 0
tbl.TitleSuppressed = True

For i = 1 To rowcount
For j = 1 To colcount
tbl.SetText i - 1, j - 1, ar(i, j)
Next j
Next i

End Sub

```

any selection of data on a spreadsheet can be saved to an array with a single line of code, and the array fed to the makethetable routine. of course the formatting is terrible but we have tools for that.

```
Sub make_table_from_selection()
Dim ar_tbl As Variant
ar_tbl = Selection.Value
'a selection assigned to a variant
'creates a one-based two-dimension array
'the first dim is the row, the second is the column

'MsgBox LBound(ar_tbl, 1)  returns 1
'MsgBox LBound(ar_tbl, 2)  returns 1