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| (1) Advantage of 3D graph |
| (2) Calculation Procedure , 3D |
| (2)-1 Number of Dimensions |
| (2)-2 Data Selection |
| (2)-3 Rotational Matrix |
| (2)-4 Calculation |
| (2)-5 Conversion of Values on Axis |
| (3) A Circle and a Square in the Air |
| (4) 3D Rotation |
| (5) Rotational Matrix |
| (6) Calculation of 3D Rotation in Excel |
| (7) Draw 3D Scatter Plots in Excel |
| (8) Add Original Axis to the 3D Scatter Plots |
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| (1) Advantage of 3D graph |
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| If the outcome is somehow complicated, you can use either color for different ranges or 3D plots. 3D plots can show more detail than display data in colors. |
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| It is possible to rotate the 3D graph on an Excel spreadsheet. You can see the graph from the top, from side, or from opposite side of the graph, which may be hidden in the usual way of viewing. |
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| (2) Calculation Procedure , 3D |
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| (2)-1 Number of Dimensions |
| The calculation of temperature distribution of a material is 4th dimension. Because the positions of material are three, and another is the calculated temperature. |
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| (2)-2 Data Selection |
| Select data range for the 3D rotations. |
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| (2)-3 Rotational Matrix |
| Convert the coordination system by the rotation matrix. |
| The original data (x, y, and z) turns into (Rx, Ry, Rz). |
| The clockwise direction of rotation is plus. |
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| (4) 3D Rotation |
| Any display is 2D, and therefore, it is necessary to select two of the three (Rx, Ry, Rz). |
| The scattered plots are suggested for the display. |
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| (2)-5 Conversion of Values on Axis |
| It is suggested to include the original axis (x-axis, y-axis, z-axis) as data. The rotated original axis are seen on the 3D graph. |
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| (3) A Circle and a Square in the Air |
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| Let's assume that a circle and a square are floating in the air. The following graphs show the usual graphs. As they are 3D, there are two (2) graphs, one from top, another from side. |
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| The lines of both the circle and the square discontinue in order to see the rotation on the screen. |
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| (4) 3D Rotation |
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| The following picture show the (Rx, Rz) graph, which come from the converted ones (Rx, Ry, Rz). |
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| The slide bars are also shown. It is possible to rotate the 3D graph by sliding the bars. |
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| (5) Rotational Matrix |
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| The rotation matrix is shown as follows. |
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| The matrix product can be obtained by the original coordination (x, y, z) and the matrix. |
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| (6) Calculation of 3D Rotation in Excel |
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| Please let me skip the calculation method of the matric product in Excel spreadsheet. The sheet function MMULT is used for the calculation. |
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| The function MMULT in the cell S16 is seen in the fx. There are four (4) matrix in the function. The original coordination are from P16 to R16. The rotation matrix around z-axis is $D$48 to $F$50. The range from $D$44 to $F$46 indicate rotation around y-axis, the range from $D$40 to $F$42 is rotation around x-axis. The MMULT rotates the original coordination according to the sequence in the function. |
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| The rotation angles of the case are twenty seven (27) degrees around x-axis, and minus thirty four (-34) degrees around z-axis. |
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| The following table show some of the calculated ones. |
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| (7) Draw 3D Scatter Plots in Excel |
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| Two (2) out of three (3) axis data are necessary for the 3D graph. Let's take the Rx and Rz. It is difficult to understand the rotation, especially for the circle, because it looks same at any angle of rotation. Therefore, one line was omitted as a marker of the rotation. |
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| (8) Add Original Axis to the 3D Scatter Plots |
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| Excel draws the Rx and Rx axis by default. However, it is visually easy to see the original x, y, and z axis. |
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| It is suggested to prepare a different table for the axis. It is ok to add the data to the original ones; however, please pay attention not to include the axis data if you need teh average values of each colums, for example. The author prepares another table for the axis, and "Add data" to the graph. |
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| The example show the minimum and the maximum data, which are zero (0) and twenty five (25). In order to see the positions of the original ones on the rotated axis, it is suggested to use zero (0), ten (10), twenty (20), and twenty five (25), and the markers for the axis may be short line or at least any different marker from the circle and the square. The original values on the axis should be added. |
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| Author: T. Oda |
| The page was prepared in Excel, and html and css files were automatically generated by the excel2web. |