Index

Scatterplots in 3D

The CloudChart or XYZ Scatter is a surprisingly versatile method for diagramming data in 3 dimensions. The four examples shown here illustrate a few of the possibilities.

A Simple Scatter plot in XYZ space

sp.Heading = "XYZ Scatter";
sp.HeadingStyle = HeadingStyles.Right;

zdata = new int[] {12,65,77,117,9,112};
xdata = new int[] {17,31,29,21,30,21};
ydata = new int[] {190,270,310,300,190,230};

sp.CloudChartStyle = CloudChartStyles.WallShading|CloudChartStyles.Risers|CloudChartStyles.HaloMarkers;
sp.ZAxisStyle = ZAxisStyles.ForceZero;
sp.XAxisStyle = XAxisStyles.GridLines;
sp.YAxisStyle = YAxisStyles.GridLines|YAxisStyles.Flat;

sp.SetZTickMarks(50);
sp.SetYTickMarks(20);
sp.SetMarkerScales(2);
sp.SetMarkers(MarkerStyle.Ball);

sp.DrawCloudChart(xdata,ydata,zdata);

This style of chart would often be used with a large dataset (several thousand points) to get a feel for the general shape of a distribution. In this example ‘risers’ have been drawn from the xy plane to give a better idea of where the points are placed.

Shaded planes to compare several series

series1 = new int[] {5,6,7,4,3,6,5,4};
series2 = new int[] {4,5,4,7,4,5,5,3};
xdata = new int[] {4,5,7,8,9,11,12,15};

sp.Heading = "Shaded\nPlanes";
sp.HeadingStyle = HeadingStyles.Right;
sp.SetViewpoint(33,18,54);
sp.SetColors(new Color[]{Color.OrangeRed,Color.ForestGreen});
sp.SetFillStyles(FillStyle.Opacity66);

sp.CloudChartStyle = CloudChartStyles.NoMarkers|CloudChartStyles.SurfaceShading|CloudChartStyles.Lines|CloudChartStyles.GridLines;

sp.SetYRange(0.5,2.5);
sp.YAxisStyle = YAxisStyles.PlainAxis;
sp.ZAxisStyle = ZAxisStyles.ForceZero;

sp.DrawCloudChart(xdata,new int[]{2,2,2,2,2,2,2,2},series2);  // First plane
sp.DrawCloudChart(xdata,new int[]{1,1,1,1,1,1,1,1},series1);  // Second plane

This diagram shows the cloud-chart being used in a similar way to the Excel Ribbon chart to compare series. This is generally done for visual effect rather than as a serious attempt to compare the data values. However it does illustrate the versatility of the Cloudchart when used as a general-purpose 3D drawing tool. If you start by setting fixed ranges on all 3 axes, you can draw any number of lines of filled shapes in the rctangular co-ordinate system within the chart walls.

This chart is also drawn with a slightly modified viewpoint. The best viewing angle for any particular dataset is obviously a matter of experiment.

Fitted quadratic surface

Just as the ScatterPlot can fit a regression-line to the data, the Cloudchart can fit a regression surface.

sp.Heading = "Modelled\nSurface";
sp.HeadingStyle = HeadingStyles.Right;
zdata = new int[] {12,65,77,117,9,112};
xdata = new int[] {17,31,29,21,30,24};
ydata = new int[] {190,270,310,300,190,230};

sp.SetZTickMarks(50);
sp.CloudChartStyle = CloudChartStyles.WallShading|CloudChartStyles.ModelFit;
sp.SetWallFillStyles(FillStyle.Halftone);
sp.SetOrderOfFit(2,1);

sp.ZAxisStyle = ZAxisStyles.ForceZero;
sp.YAxisStyle = YAxisStyles.Flat;
sp.SetPenWidths(1.2);
sp.SetMarkers(MarkerStyle.Node);

sp.DrawCloudChart(xdata,ydata,zdata);

The model in this case is quadratic in the X-direction and linear in Y to give the simple folded surface shown. The order of fit may be up to 4 (quartic) in either direction.

Trend surface with contour lines

zdata = new int[] {100,15,27,117,19,112};
xdata = new int[] {17,31,29,21,30,24};
ydata = new int[] {190,270,310,300,190,230};
sp.Heading = "Trend\nSurface";
sp.HeadingStyle = HeadingStyles.Right;

sp.SetZTickMarks(50);  // Contour interval also
sp.CloudChartStyle = CloudChartStyles.WallShading|CloudChartStyles.TrendLine|CloudChartStyles.Contours|CloudChartStyles.GridLines|CloudChartStyles.TiledSurface;
sp.Flexibility = 1;

sp.ZAxisStyle = ZAxisStyles.ForceZero;
sp.YAxisStyle = YAxisStyles.Flat;
sp.SetFillStyles(FillStyle.Opacity30);
sp.SetPenWidths(0.8);
sp.SetMarkers(MarkerStyle.Node);

sp.DrawCloudChart(xdata,ydata,zdata);

This is again the analagous style to the ‘trendline’ available in the ScatterPlot. The surface is a gaussian-weighted smooth which can be controlled with the Flexibility property. With so few points, the sample sets the flex very low indeed as otherwise the surface would resemble a series of plateaux around each point. With a realistically large data array (probably several hundred points) the default flexibility would be more suitable.

Contour lines are drawn at each Z-axis tickmark, and the ‘grid’ is computed at the intersection of each x-y tick. The MeshDensity property can be used to add more points into the mesh to make a smoother surface.

Summary

Cloudcharts can be a really effective way to visualize genuine 3D datasets. However for serious data analysis it is probably better to use a set of simple 2D charts to show appropriate sections through the data.