iOS Charting Documentation - SciChart iOS Charts SDK v3.x

The Custom Free Surface 3D Chart Type

In SciChart, Custom Free Surface 3D Charts are provided by the combination of the Free Surface 3D Series and SCICustomSurfaceDataSeries3D underlying DataSeries.

The location of the SCICustomSurfaceDataSeries3D is defined by following properties:

The shape of its surface is defined by a set of user-defined functions, injected in the Constructor during the instantiation. This approach allows the surface to obtain any possible shape.

Some of the SCICustomSurfaceDataSeries3D Constructor are described below:

  • Radial Distance Function – function that determines how distance from the origin to the particular point on the surface differs.
  • Azimuthal Angle Function – function that determines the azimuthal angle between the particular point and the unit vector of the X-Axis, projected on the XZ plane.
  • Polar Angle Function – is a user-defined function that determines inclination (or polar angle) between the particular point and the unit vector of the Y-Axis - Zenith.

NOTE: The U and V coordinates in intervals [uMin...uMax] and [vMin...vMax] respectively are passed as the arguments to each of the three functions above.

  • X Function - function that determines the position of the particular point on the surface by the X-Axis.
  • Y Function - function that determines the position of the particular point on the surface by the Y-Axis.
  • Z Function - function that determines the position of the particular point on the surface by the Z-Axis.

NOTE: The Radial Distance, Radial Distance and Azimuthal Angle are passed as the arguments to each of the three functions above. More information about the radial distance, azimuthal and polar angle can be found here: Spherical coordinate system.

Custom Free Surface Chart 3D

NOTE: Examples for the Custom Free Surface 3D can be found in the SciChart iOS Examples Suite as well as on GitHub:

Let’s see some examples of declaring some 3D Free Surfaces:

Create a Custom Free Surface 3D Chart

To create a Custom Free Surface 3D Chart like the above - use the following code:

SCIUVFunc radialDistanceFunc = ^(double u, double v) { return 5.0 + sin(5.0 * (u + v)); }; SCIUVFunc azimuthalAngleFunc = ^(double u, double v) { return u; }; SCIUVFunc polarAngleFunc = ^(double u, double v) { return v; }; SCIValueFunc xFunc = ^(double r, double theta, double phi) { return r * sin(theta) * cos(phi); }; SCIValueFunc yFunc = ^(double r, double theta, double phi) { return r * cos(theta); }; SCIValueFunc zFunc = ^(double r, double theta, double phi) { return r * sin(theta) * sin(phi); }; SCICustomSurfaceDataSeries3D *ds = [[SCICustomSurfaceDataSeries3D alloc] initWithXType:SCIDataType_Double yType:SCIDataType_Double zType:SCIDataType_Double uSize:30 vSize:30 radialDistanceFunc:radialDistanceFunc azimuthalAngleFunc:azimuthalAngleFunc polarAngleFunc:polarAngleFunc xFunc:xFunc yFunc:yFunc zFunc:zFunc]; unsigned int colors[7] = { 0xFF00008B, 0xFF0000FF, 0xFF00FFFF, 0xFFADFF2F, 0xFFFFFF00, 0xFFFF0000, 0xFF8B0000 }; float stops[7] = { 0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0}; SCIGradientColorPalette *palette = [[SCIGradientColorPalette alloc] initWithColors:colors stops:stops count:7]; SCIFreeSurfaceRenderableSeries3D *rs0 = [SCIFreeSurfaceRenderableSeries3D new]; rs0.dataSeries = ds; rs0.drawMeshAs = SCIDrawMeshAs_SolidWireframe; rs0.stroke = 0x77228B22; rs0.contourInterval = 0.1; rs0.contourStroke = 0x77228B22; rs0.strokeThickness = 2.0; rs0.lightingFactor = 0.8; rs0.meshColorPalette = palette; rs0.paletteMinMaxMode = SCIFreeSurfacePaletteMinMaxMode_Relative; rs0.paletteMinimum = [[SCIVector3 alloc] initWithX:0.0 y:5.0 z:0.0]; rs0.paletteMaximum = [[SCIVector3 alloc] initWithX:0.0 y:7.0 z:0.0];
let radialDistanceFunc: SCIUVFunc = { u, v in 5.0 + sin(5.0 * (u + v)) } let azimuthalAngleFunc: SCIUVFunc = { u, _ in u } let polarAngleFunc: SCIUVFunc = { _, v in v } let xFunc: SCIValueFunc = { r, theta, phi in r * sin(theta) * cos(phi) } let yFunc: SCIValueFunc = { r, theta, phi in r * cos(theta) } let zFunc: SCIValueFunc = { r, theta, phi in r * sin(theta) * sin(phi) } let ds = SCICustomSurfaceDataSeries3D(xType: .double, yType: .double, zType: .double, uSize: 30, vSize: 30, radialDistanceFunc: radialDistanceFunc, azimuthalAngleFunc: azimuthalAngleFunc, polarAngleFunc: polarAngleFunc, xFunc: xFunc, yFunc: yFunc, zFunc: zFunc, uMin: 0.0, uMax: Double.pi * 2, vMin: 0, vMax: Double.pi) let colors: [UInt32] = [0xFF00008B, 0xFF0000FF, 0xFF00FFFF, 0xFFADFF2F, 0xFFFFFF00, 0xFFFF0000, 0xFF8B0000] let stops: [Float] = [0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0] let palette = SCIGradientColorPalette(colors: colors, stops: stops, count: 7) let rs0 = SCIFreeSurfaceRenderableSeries3D() rs0.dataSeries = ds rs0.drawMeshAs = .solidWireframe rs0.stroke = 0x77228B22 rs0.contourInterval = 0.1 rs0.contourStroke = 0x77228B22 rs0.strokeThickness = 2.0 rs0.lightingFactor = 0.8 rs0.meshColorPalette = palette rs0.paletteMinMaxMode = .relative rs0.paletteMinimum = SCIVector3(x: 0.0, y: 5.0, z: 0.0) rs0.paletteMaximum = SCIVector3(x: 0.0, y: 7.0, z: 0.0)
const int uSize = 40, vSize = 20; var dataSeries3D = new CustomSurfaceDataSeries3D<double, double, double>(uSize, vSize, (u, v) => 5.0 + Math.Sin(5 * (u + v)), (u, v) => u, (u, v) => v, (r, theta, phi) => r * Math.Sin(theta) * Math.Cos(phi), (r, theta, phi) => r * Math.Cos(theta), (r, theta, phi) => r * Math.Sin(theta) * Math.Sin(phi)); var rSeries3D = new SCIFreeSurfaceRenderableSeries3D { DataSeries = dataSeries3D, DrawMeshAs = SCIDrawMeshAs.SolidWireframe, Stroke = 0x77228B22, ContourInterval = 0.1f, ContourStroke = 0x77228B22, StrokeThickness = 1f, MeshColorPalette = new SCIGradientColorPalette( new[] { ColorUtil.Sapphire, ColorUtil.Blue, ColorUtil.Cyan, ColorUtil.GreenYellow, ColorUtil.Yellow, ColorUtil.Red, ColorUtil.DarkRed }, new[] { 0, .1f, .3f, .5f, .7f, .9f, 1 }), PaletteMinimum = new SCIVector3(0, 5, 0), PaletteMaximum = new SCIVector3(0, 7, 0), };

NOTE: See other constrained and unconstrained Free Surface Series types in the corresponding articles.

Create a Simple Sphere

Let’s create a simple Sphere with a Radius = 10. See the user-defined functions which is used in the SCICustomSurfaceDataSeries3D in the code below:

SCIUVFunc radialDistanceFunc = ^(double u, double v) { return 10.0; }; SCIUVFunc azimuthalAngleFunc = ^(double u, double v) { return u; }; SCIUVFunc polarAngleFunc = ^(double u, double v) { return v; }; SCIValueFunc xFunc = ^(double r, double theta, double phi) { return r * sin(theta) * cos(phi); }; SCIValueFunc yFunc = ^(double r, double theta, double phi) { return r * cos(theta); }; SCIValueFunc zFunc = ^(double r, double theta, double phi) { return r * sin(theta) * sin(phi); }; SCICustomSurfaceDataSeries3D *ds = [[SCICustomSurfaceDataSeries3D alloc] initWithXType:SCIDataType_Double yType:SCIDataType_Double zType:SCIDataType_Double uSize:30 vSize:30 radialDistanceFunc:radialDistanceFunc azimuthalAngleFunc:azimuthalAngleFunc polarAngleFunc:polarAngleFunc xFunc:xFunc yFunc:yFunc zFunc:zFunc];
let radialDistanceFunc: SCIUVFunc = { u, v in 10.0 } let azimuthalAngleFunc: SCIUVFunc = { u, _ in u } let polarAngleFunc: SCIUVFunc = { _, v in v } let xFunc: SCIValueFunc = { r, theta, phi in r * sin(theta) * cos(phi) } let yFunc: SCIValueFunc = { r, theta, phi in r * cos(theta) } let zFunc: SCIValueFunc = { r, theta, phi in r * sin(theta) * sin(phi) } let ds = SCICustomSurfaceDataSeries3D(xType: .double, yType: .double, zType: .double, uSize: 30, vSize: 30, radialDistanceFunc: radialDistanceFunc, azimuthalAngleFunc: azimuthalAngleFunc, polarAngleFunc: polarAngleFunc, xFunc: xFunc, yFunc: yFunc, zFunc: zFunc, uMin: 0.0, uMax: Double.pi * 2, vMin: 0, vMax: Double.pi)
const int uSize = 40, vSize = 20; var dataSeries3D = new CustomSurfaceDataSeries3D<double, double, double>(uSize, vSize, (u, v) => 5.0 + Math.Sin(5 * (u + v)), (u, v) => u, (u, v) => v, (r, theta, phi) => r * Math.Sin(theta) * Math.Cos(phi), (r, theta, phi) => r * Math.Cos(theta), (r, theta, phi) => r * Math.Sin(theta) * Math.Sin(phi));

Simple Sphere 3D

Create a Simple Cylinder

Let’s create a simple Cylinder with a Radius = 10 and Height = 40. See the code below:

SCIUVFunc radialDistanceFunc = ^(double u, double v) { return 0.0; }; SCIUVFunc azimuthalAngleFunc = ^(double u, double v) { return u; }; SCIUVFunc polarAngleFunc = ^(double u, double v) { return v; }; SCIValueFunc xFunc = ^(double r, double theta, double phi) { return 10 * sin(M_PI / 2) * cos(phi); }; SCIValueFunc yFunc = ^(double r, double theta, double phi) { return 40 * cos(theta); }; SCIValueFunc zFunc = ^(double r, double theta, double phi) { return 10 * sin(M_PI / 2) * sin(phi); }; SCICustomSurfaceDataSeries3D *ds = [[SCICustomSurfaceDataSeries3D alloc] initWithXType:SCIDataType_Double yType:SCIDataType_Double zType:SCIDataType_Double uSize:30 vSize:30 radialDistanceFunc:radialDistanceFunc azimuthalAngleFunc:azimuthalAngleFunc polarAngleFunc:polarAngleFunc xFunc:xFunc yFunc:yFunc zFunc:zFunc];
let radialDistanceFunc: SCIUVFunc = { u, v in 0.0 } let azimuthalAngleFunc: SCIUVFunc = { u, _ in u } let polarAngleFunc: SCIUVFunc = { _, v in v } let xFunc: SCIValueFunc = { r, theta, phi in 10 * sin(.pi / 2) * cos(phi) } let yFunc: SCIValueFunc = { r, theta, phi in 40 * cos(theta) } let zFunc: SCIValueFunc = { r, theta, phi in 10 * sin(.pi / 2) * sin(phi) } let ds = SCICustomSurfaceDataSeries3D(xType: .double, yType: .double, zType: .double, uSize: 30, vSize: 30, radialDistanceFunc: radialDistanceFunc, azimuthalAngleFunc: azimuthalAngleFunc, polarAngleFunc: polarAngleFunc, xFunc: xFunc, yFunc: yFunc, zFunc: zFunc, uMin: 0.0, uMax: Double.pi * 2, vMin: 0, vMax: Double.pi)
const int uSize = 30, vSize = 30; var dataSeries3D = new CustomSurfaceDataSeries3D<double, double, double>(uSize, vSize, (u, v) => 0.0, (u, v) => u, (u, v) => v, (r, theta, phi) => 10 * Math.Sin(Math.PI / 2) * Math.Cos(phi), (r, theta, phi) => 40 * Math.Cos(theta), (r, theta, phi) => 10 * Math.Sin(Math.PI / 2) * Math.Sin(phi));

Simple Cylinder 3D