Showing posts with label shapes. Show all posts
Showing posts with label shapes. Show all posts

05 August, 2023

Shapes Based On Johan Gielis's Superformula

The Gielis's Superformula is used to model variety of abstract and natural shapes. It finds application in biology, technology, mathematics, and physics.

I'm providing here a small representation of shapes created with my relatively simple VBA macro listed at the end of this post. You can experiment with different values of the parameters a,b,m,n1,n2, and n3 to get all kinds of shapes and find some useful models. To control the resolution of your shapes you can adjust the number of points, nP. Optionally, I've applied some Excel formatting of the plots.

Sub SuperformulaPlot()
'Generates Gielis's Superformula plot
'Calculates X and Y values and assigns them to the chart series
'Creates a 2D scatter plot; no markers

Dim nP As Integer, i As Integer
Dim xVal() As Double, yVal() As Double, theta As Double, r As Double
Dim a As Double, b As Double, m As Double, n1 As Double, n2 As Double, n3 As Double
Dim chartObj As ChartObject
nP = 500    'You can adjust the number of points to increase/decrease the resolution of the curve
a = WorksheetFunction.RandBetween(1, 5) 'Random parameters a,b,m,n1,n2,n3; experiment!
b = WorksheetFunction.RandBetween(1, 5)
m = WorksheetFunction.RandBetween(1, 10)
n1 = WorksheetFunction.RandBetween(1, 10)
n2 = WorksheetFunction.RandBetween(1, 20)
n3 = WorksheetFunction.RandBetween(1, 10)
'a = 1: b = 1: m = 2: n1 = 5: n2 = 5: n3 = 5    'just some default values
ReDim xVal(1 To nP)
ReDim yVal(1 To nP)
For i = 1 To nP
    theta = 2 * WorksheetFunction.Pi * (i - 1) / nP
    r = (Abs(Cos(m * theta / 4) / a) ^ n2 + Abs(Sin(m * theta / 4) / b) ^ n3) ^ (-1 / n1)
    xVal(i) = r * Cos(theta)
    yVal(i) = r * Sin(theta)
Next i
'Create a 2D scatter plot
Set chartObj = ActiveSheet.ChartObjects.Add(Left:=120, Width:=500, Top:=10, Height:=400)
With chartObj.Chart
    .ChartType = xlXYScatterSmoothNoMarkers
    .SeriesCollection(1).Values = yVal      'Add data to the chart
    .SeriesCollection(1).xValues = xVal
    .HasLegend = False
    .HasTitle = True
    .ChartTitle.Text = "SuperPlot "& a & "-"& b & "-"& m & "-"& n1 & "-"& n2 & "-" & n3 & "; "& nP
    .Axes(xlCategory, xlPrimary).HasTitle = True
    .Axes(xlCategory, xlPrimary).AxisTitle.Text = "X"
    .Axes(xlValue, xlPrimary).HasTitle = True
    .Axes(xlValue, xlPrimary).AxisTitle.Text = "Y"
End With
End Sub

30 July, 2023

Charts Based On Parametric Equations: Sinusoidal (Oscilloscope-type) Curves

Curves that can be used in physics for analysing pairs of simple harmonic motions are generally known as Lissajous Curves. They describe the superposition of two oscillations taking place at the right angle to each other,  at different frequencies. Their main application can be found in oscilloscopes. These instruments allow observation of two superimposed sine waves coming from varying signal voltages of sinusoidal nature. Depending on the frequency and amplitude of each wave, and the phase between them, we can see interesting patterns emerging.

Because the superimposed two perpendicular oscillations can be described with parametric equations for x and y in the Cartesian coordinate system, we can quite easily demonstrate the resulting shapes graphically using Excel charts. Let's look first at some of "oscilloscopic" patterns generated with Excel.

16 July, 2023

Excel Shapes: Positioning, Formatting and Layout In Worksheets

Excel Shapes are frequently used to enhance visual appeal of worksheets as well as to convey information. It's relatively easy to work with the Shapes. You can insert, resize, rotate, format, and position them within the worksheet, according to your needs.

This post is about special case of positioning and manipulating of Shapes. Namely, I'll show the way of inserting and moving them so that they are located/centred precisely at the crosspoint of 4 surrounding it cells. Furthermore, in this case I'll use a worksheet with squared cells. If you need to know how to make cells square please refer to one of my previous posts (Make cells SQUARE) .

Here are just two examples showing what I'm talking about:

These are the formatted Shapes called "Donut" and "Gear with nine teeth". They are placed exactly at the point where the four cells meet together. It's not that easy to do that by hand, so I've created the following Excel macro, to handle this task swiftly:

06 June, 2023

Drawing and Connecting Any Graphical Elements

In Excel, you can create diagrams, flowcharts and other visual aids of quite high complexity, without using any dedicated graphic design software. All you need for this purpose is utilizing the Insert tab and the Illustrations group within it. The Illustrations group includes pictures, shapes, icons, 3D Models, SmartArt, etc.

And within Shapes there is a group of Lines. Most of them are Connectors that can be attached to any of the illustrations and connect them with any others. The last three lines in the group, namely Curve, Freeform Shape, and Scribble, are not Connectors, but allow you to enrich the Excel collection of graphical creations with your own customized shapes/drawings.

Here's an example of possibilities offered by precise connections of the shapes. Just a simple idea:

Instead of adding your graphic elements one by one, you can choose from available selection of SmartArt graphics. Once you insert all your graphic elements in a desired order/arrangement, you can connect them by following these steps:
  • select appropriate connector from the Lines collection
  • click anywhere on the first graphic element; connection points will appear for you to choose one of them and attach the connector line
  • drag the cursor to a connection point on the second connection object
  • to adjust appearance of the line, you can right-click on it and choose "Format Shape" to modify the line colour, thickness, style etc.
You can also add text/labels to your graphic elements by right-clicking on them and selecting "Edit Text". The elements can be repositioned if needed, and the connectors will remain attached to and moved with the graphics. Pretty convenient.

26 May, 2023

Creating Shapes, Graphics, Illustrations - Part 2

Here is yet another way of creating graphics in Excel - using VBA macro, like this one:

Sub DrawDefShape()
'Draws any defined shape representing Bézier curves
Dim x As Integer, y As Integer
Dim pt(1 To 7, 1 To 2) As Single
Dim rng As Range
Set rng = Sheets("Data").Range("A2:B8")
'Fill array of control point coordinates with values
For x = 1 To 7
    For y = 1 To 2
        pt(x, y) = rng.Cells(x, y).Value
    Next y
Next x
Set myDoc = Worksheets("Data")
myDoc.Shapes.AddCurve SafeArrayOfPoints:=pt
'Display the whole 2D array in MsgBox
For i = 1 To UBound(pt)
dPts = dPts & pt(i, 1) & "   " & pt(i, 2) & vbNewLine
Next i
MsgBox dPts
End Sub

Before going into the details of the macro structure and its use, let's look at some examples of curves and shapes you can easily create with it. Here they are:

24 May, 2023

Creating Shapes, Graphics, Illustrations - Part 1

Although Excel is not designed as a comprehensive graphic design tool, we can create in Excel all kinds of shapes/illustrations, actually without limits. There are many ways to do that, and the main methods are:

  • Obviously - charts: while primarily used for data visualization, the charting capabilities of Excel can be utilized to create simple illustrations. By manipulating the data  (applying various conditional formatting rules) and using other formatting options, you can create visually appealing illustrations within the charting framework.
  • Inserting predefined shapes: Excel provides a variety of predefined shapes that you can insert from the "Insert" tab on the ribbon. These shapes include rectangles, circles, arrows, lines, and more. They can be customized in terms of size, color, rotation, and other formatting options.
  • Using drawing tools (to draw shapes): Excel allows you to draw custom shapes using the "Shapes" tool. You can choose from different shapes, such as polygons, curves, and freeform shapes. By selecting the "Draw" option, you can manually create the desired shape by clicking and dragging on the worksheet.
  • Using SmartArt: this feature feature allows you to create diagrams, flowcharts, and other visual representations. SmartArt provides a variety of predefined layouts and styles, making it easy to create professionally-looking illustrations. You can access SmartArt through the "Insert" tab as well.
  • Combining shapes: Excel also enables you to combine multiple shapes to create new ones. This can be done by selecting the desired shapes, right-clicking, and choosing the "Group" or "Combine Shapes" option.
  • Editing shapes: Once a shape is created, you can further customize it by resizing, rotating, or changing its fill color, outline color, and other formatting options. This can be done by selecting the shape and using the available formatting tools.
  • In addition, the Lasso Select tool is now available in Excel. This technique allows you to select non-contiguous cells or objects in Excel.

The following examples give some idea of how you can use these methods to design various graphic solutions and what you can create using Excel tools.


20 January, 2022

Animation - Flying Objects

The following VBA (Visual Basic Application) code makes Excel shapes and some other graphics flying. In this instance I'm shooting a rocket on my worksheet across the computer screen. This shape is based on Excel graphic named "Graphic 4".

Option Explicit
Public Declare Sub Sleep Lib "kernel32" (ByVal iMilliseconds As Long)

Sub Flyer()
    Sheet1.Shapes("Graphic 4").Left = 1000   'Starting X
    Sheet1.Shapes("Graphic 4").Top = 450   'Starting Y
    MoveShp Sheet1.Shapes("Graphic 4"), 0!, 0!, #12:00:01 AM#   'Shape inserted
End Sub
Sub MoveShp(shp As Shape, ByVal coLeft As Single, ByVal coTop As Single, t As Date)
' Moves the shape from start to finish over the interval t
    Const xch = 0.018
    Const n1 As Long = 30       'Accelerate/decelerate steps
    Const n2 As Long = 60   'Coast steps
    Const n As Long = 2 * n1 + n2    'Total steps
    Dim i As Long   'Step index
    Dim stpv As Single   'Coasting, pixels/step
    Dim v As Single     'Velocity at current step
    Dim cLiLeft As Single, cLiTop As Single   'Left and Top num
    Dim cMi As Single      'Frctn denom
    Dim coLeftPr As Single, coTopPr As Single  'Previous Left and Top position
    stpv = 1 / (n - n1)
    With shp
        coLeft = coLeft - .Left: coTop = coTop - .Top
        coLeftPr = .Left: coTopPr = .Top
        For i = 1 To n
            Select Case i
            Case 1 To n1    'Accelerate
                v = stpv * (1 + Cos(xch * 180 * (1 + i / n1))) / 2
            Case n1 + 1 To n - n1   'Constant velocity
                v = stpv
            Case Else       'Decelerate
                v = stpv * (1 + Cos(xch * 180 * (1 + (n - i) / n1))) / 2
            End Select
            .Left = .Left + v * (coLeft - cLiLeft) / (1 - cMi)
            .Top = .Top + v * (coTop - cLiTop) / (1 - cMi)
            cMi = cMi + v
            cLiLeft = .Left - coLeftPr: cLiTop = .Top - coTopPr
            Sleep t * 86400000# / n
        Next i
    End With
End Sub

To use the code in Excel on your computer follow these steps:

  • find and insert Graphic 4 shape into your worksheet (if you want to use any other Excel graphic, remember to change the shape name in the above code)
  • copy the code and paste it into any module of your project (workbook)
  • select the "Flyer" macro from Macros in the ribbon to run it.

If you assign the macro to the shape (by right-clicking it and selecting "Assign Macro..." option), then just click on the shape and it will fly...

Try to run it using some other shapes/objects.



28 September, 2021

TIPS for CLICKS: Cell Borders with Shapes

Borders around Excel cells make worksheet contents visually enhanced and easier for evaluation. They clarify the format and layout of the data, make it appear more orderly and also highlight important information. Drop-down menu of Borders provides multiple pre-built options for that, as you can see some of them here:

However, some Excel users sometimes would like to apply different type of borders (e.g. rounded-corner borders) instead of the square-cornered ones. There is no such an option in Excel. Fortunately, there is a workaround available for such unconventional type of 'borders'.

23 September, 2021

Tips for Clicks: CELL tricks

Elementary: what is the Excel cell?

It is much more than "rectangular-shaped box on a worksheet", where you can enter any combination of numbers or words...

First of all, it can be rectangularly- as well as squarely-shaped. Secondly, you can enter into a cell (within specified limits) not only any kind of text and any kind of graphics, but also pictures and drawings, and enter them in many layers, displayed or hidden.

Here is an example of content fitted in just ONE cell, in multiple displays.