3D surface plots

BinderNotebook

Summary: This example shows how to create 3D surface plots in F#.

Let's first create some data for the purpose of creating example charts:

open System
open Plotly.NET

//---------------------- Generate linearly spaced vector ----------------------
let linspace (min, max, n) =
    if n <= 2 then
        failwithf "n needs to be larger then 2"

    let bw = float (max - min) / (float n - 1.)
    Array.init n (fun i -> min + (bw * float i))

//---------------------- Create example data ----------------------
let size = 100
let x = linspace (-2. * Math.PI, 2. * Math.PI, size)
let y = linspace (-2. * Math.PI, 2. * Math.PI, size)

let f x y = -(5. * x / (x ** 2. + y ** 2. + 1.))

let z = Array.init size (fun i -> Array.init size (fun j -> f x.[j] y.[i]))

let surface = Chart.Surface(zData = z)
// Create simple example data were x y and z is given (z is a xy-Matrix)
let x' = [ 0.; 2.5 ]
let y' = [ 0.; 2.5 ]

let z' =
    [ [ 1.; 1. ] // row wise (length x)
      [ 1.; 2. ] ] // column (length y)

open Plotly.NET.TraceObjects

let surface2 =
    Chart.Surface(zData = z', X = x', Y = y', Opacity = 0.5, Contours = Contours.initXyz (Show = true))
namespace Plotly
namespace Plotly.NET
module Defaults from Plotly.NET
<summary> Contains mutable global default values. Changing these values will apply the default values to all consecutive Chart generations. </summary>
val mutable DefaultDisplayOptions: DisplayOptions
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type DisplayOptions = inherit DynamicObj new: unit -> DisplayOptions static member addAdditionalHeadTags: additionalHeadTags: XmlNode list -> (DisplayOptions -> DisplayOptions) static member addDescription: description: XmlNode list -> (DisplayOptions -> DisplayOptions) static member combine: first: DisplayOptions -> second: DisplayOptions -> DisplayOptions static member getAdditionalHeadTags: displayOpts: DisplayOptions -> XmlNode list static member getDescription: displayOpts: DisplayOptions -> XmlNode list static member getPlotlyReference: displayOpts: DisplayOptions -> PlotlyJSReference static member init: ?AdditionalHeadTags: XmlNode list * ?Description: XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions static member initCDNOnly: unit -> DisplayOptions ...

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new: unit -> DisplayOptions
static member DisplayOptions.init: ?AdditionalHeadTags: Giraffe.ViewEngine.HtmlElements.XmlNode list * ?Description: Giraffe.ViewEngine.HtmlElements.XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions
type PlotlyJSReference = | CDN of string | Full | Require of string | NoReference
<summary> Sets how plotly is referenced in the head of html docs. </summary>
union case PlotlyJSReference.NoReference: PlotlyJSReference
namespace System
val linspace: min: float * max: float * n: int -> float[]
val min: float
val max: float
val n: int
val failwithf: format: Printf.StringFormat<'T,'Result> -> 'T
<summary>Print to a string buffer and raise an exception with the given result. Helper printers must return strings.</summary>
<param name="format">The formatter.</param>
<returns>The formatted result.</returns>
<example>See <c>Printf.failwithf</c> (link: <see cref="M:Microsoft.FSharp.Core.PrintfModule.PrintFormatToStringThenFail``2" />) for examples.</example>
val bw: float
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val float: value: 'T -> float (requires member op_Explicit)
<summary>Converts the argument to 64-bit float. This is a direct conversion for all primitive numeric types. For strings, the input is converted using <c>Double.Parse()</c> with InvariantCulture settings. Otherwise the operation requires an appropriate static conversion method on the input type.</summary>
<param name="value">The input value.</param>
<returns>The converted float</returns>
<example id="float-example"><code lang="fsharp"></code></example>


--------------------
[<Struct>] type float = Double
<summary>An abbreviation for the CLI type <see cref="T:System.Double" />.</summary>
<category>Basic Types</category>


--------------------
type float<'Measure> = float
<summary>The type of double-precision floating point numbers, annotated with a unit of measure. The unit of measure is erased in compiled code and when values of this type are analyzed using reflection. The type is representationally equivalent to <see cref="T:System.Double" />.</summary>
<category index="6">Basic Types with Units of Measure</category>
type Array = interface ICollection interface IEnumerable interface IList interface IStructuralComparable interface IStructuralEquatable interface ICloneable member Clone: unit -> obj member CopyTo: array: Array * index: int -> unit + 1 overload member GetEnumerator: unit -> IEnumerator member GetLength: dimension: int -> int ...
<summary>Provides methods for creating, manipulating, searching, and sorting arrays, thereby serving as the base class for all arrays in the common language runtime.</summary>
val init: count: int -> initializer: (int -> 'T) -> 'T[]
<summary>Creates an array given the dimension and a generator function to compute the elements.</summary>
<param name="count">The number of elements to initialize.</param>
<param name="initializer">The function to generate the initial values for each index.</param>
<returns>The created array.</returns>
<exception cref="T:System.ArgumentException">Thrown when count is negative.</exception>
<example id="init-1"><code lang="fsharp"> Array.init 4 (fun v -&gt; v + 5) </code> Evaluates to <c>[| 5; 6; 7; 8 |]</c></example>
<example id="init-2"><code lang="fsharp"> Array.init -5 (fun v -&gt; v + 5) </code> Throws <c>ArgumentException</c></example>
val i: int
val size: int
val x: float[]
type Math = static member Abs: value: decimal -> decimal + 7 overloads static member Acos: d: float -> float static member Acosh: d: float -> float static member Asin: d: float -> float static member Asinh: d: float -> float static member Atan: d: float -> float static member Atan2: y: float * x: float -> float static member Atanh: d: float -> float static member BigMul: a: int * b: int -> int64 + 2 overloads static member BitDecrement: x: float -> float ...
<summary>Provides constants and static methods for trigonometric, logarithmic, and other common mathematical functions.</summary>
field Math.PI: float = 3.14159265359
val y: float[]
val f: x: float -> y: float -> float
val x: float
val y: float
val z: float[][]
val j: int
val surface: GenericChart.GenericChart
type Chart = static member AnnotatedHeatmap: zData: seq<#seq<'a1>> * annotationText: seq<#seq<string>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?X: seq<'a3> * ?MultiX: seq<seq<'a3>> * ?XGap: int * ?Y: seq<'a4> * ?MultiY: seq<seq<'a4>> * ?YGap: int * ?Text: 'a5 * ?MultiText: seq<'a5> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?ZSmooth: SmoothAlg * ?Transpose: bool * ?UseWebGL: bool * ?ReverseYAxis: bool * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible and 'a5 :> IConvertible) + 1 overload static member Area: x: seq<#IConvertible> * y: seq<#IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: MarkerSymbol * ?MultiMarkerSymbol: seq<MarkerSymbol> * ?Marker: Marker * ?LineColor: Color * ?LineColorScale: Colorscale * ?LineWidth: float * ?LineDash: DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: Orientation * ?GroupNorm: GroupNorm * ?FillColor: Color * ?FillPatternShape: PatternShape * ?FillPattern: Pattern * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Bar: values: seq<#IConvertible> * ?Keys: seq<'a1> * ?MultiKeys: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerPatternShape: PatternShape * ?MultiMarkerPatternShape: seq<PatternShape> * ?MarkerPattern: Pattern * ?Marker: Marker * ?Base: #IConvertible * ?Width: 'a4 * ?MultiWidth: seq<'a4> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member BoxPlot: ?X: seq<'a0> * ?MultiX: seq<seq<'a0>> * ?Y: seq<'a1> * ?MultiY: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Text: 'a2 * ?MultiText: seq<'a2> * ?FillColor: Color * ?MarkerColor: Color * ?Marker: Marker * ?Opacity: float * ?WhiskerWidth: float * ?BoxPoints: BoxPoints * ?BoxMean: BoxMean * ?Jitter: float * ?PointPos: float * ?Orientation: Orientation * ?OutlineColor: Color * ?OutlineWidth: float * ?Outline: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?Notched: bool * ?NotchWidth: float * ?QuartileMethod: QuartileMethod * ?UseDefaults: bool -> GenericChart (requires 'a0 :> IConvertible and 'a1 :> IConvertible and 'a2 :> IConvertible) + 2 overloads static member Bubble: x: seq<#IConvertible> * y: seq<#IConvertible> * sizes: seq<int> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: MarkerSymbol * ?MultiMarkerSymbol: seq<MarkerSymbol> * ?Marker: Marker * ?LineColor: Color * ?LineColorScale: Colorscale * ?LineWidth: float * ?LineDash: DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: Orientation * ?GroupNorm: GroupNorm * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Candlestick: ``open`` : seq<#IConvertible> * high: seq<#IConvertible> * low: seq<#IConvertible> * close: seq<#IConvertible> * ?X: seq<'a4> * ?MultiX: seq<seq<'a4>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Text: 'a5 * ?MultiText: seq<'a5> * ?Line: Line * ?IncreasingColor: Color * ?Increasing: FinanceMarker * ?DecreasingColor: Color * ?Decreasing: FinanceMarker * ?WhiskerWidth: float * ?ShowXAxisRangeSlider: bool * ?UseDefaults: bool -> GenericChart (requires 'a4 :> IConvertible and 'a5 :> IConvertible) + 2 overloads static member Column: values: seq<#IConvertible> * ?Keys: seq<'a1> * ?MultiKeys: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerPatternShape: PatternShape * ?MultiMarkerPatternShape: seq<PatternShape> * ?MarkerPattern: Pattern * ?Marker: Marker * ?Base: #IConvertible * ?Width: 'a4 * ?MultiWidth: seq<'a4> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member Contour: zData: seq<#seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?X: seq<'a2> * ?MultiX: seq<seq<'a2>> * ?Y: seq<'a3> * ?MultiY: seq<seq<'a3>> * ?Text: 'a4 * ?MultiText: seq<'a4> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?Transpose: bool * ?ContourLineColor: Color * ?ContourLineDash: DrawingStyle * ?ContourLineSmoothing: float * ?ContourLine: Line * ?ContoursColoring: ContourColoring * ?ContoursOperation: ConstraintOperation * ?ContoursType: ContourType * ?ShowContourLabels: bool * ?ContourLabelFont: Font * ?Contours: Contours * ?FillColor: Color * ?NContours: int * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) static member Funnel: x: seq<#IConvertible> * y: seq<#IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Width: float * ?Offset: float * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?Orientation: Orientation * ?AlignmentGroup: string * ?OffsetGroup: string * ?MarkerColor: Color * ?MarkerOutline: Line * ?Marker: Marker * ?TextInfo: TextInfo * ?ConnectorLineColor: Color * ?ConnectorLineStyle: DrawingStyle * ?ConnectorFillColor: Color * ?ConnectorLine: Line * ?Connector: FunnelConnector * ?InsideTextFont: Font * ?OutsideTextFont: Font * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) static member Heatmap: zData: seq<#seq<'a1>> * ?X: seq<'a2> * ?MultiX: seq<seq<'a2>> * ?Y: seq<'a3> * ?MultiY: seq<seq<'a3>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?XGap: int * ?YGap: int * ?Text: 'a4 * ?MultiText: seq<'a4> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?ZSmooth: SmoothAlg * ?Transpose: bool * ?UseWebGL: bool * ?ReverseYAxis: bool * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) + 1 overload ...
static member Chart.Surface: zData: seq<#seq<'b>> * ?X: seq<#IConvertible> * ?Y: seq<#IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Text: 'e * ?MultiText: seq<'e> * ?Contours: TraceObjects.Contours * ?ColorScale: StyleParam.Colorscale * ?ShowScale: bool * ?CameraProjectionType: StyleParam.CameraProjectionType * ?Camera: LayoutObjects.Camera * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'b :> IConvertible and 'e :> IConvertible)
module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>
val toChartHTML: gChart: GenericChart.GenericChart -> string
val x': float list
val y': float list
val z': float list list
namespace Plotly.NET.TraceObjects
val surface2: GenericChart.GenericChart
static member Chart.Surface: zData: seq<#seq<'b>> * ?X: seq<#IConvertible> * ?Y: seq<#IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Text: 'e * ?MultiText: seq<'e> * ?Contours: Contours * ?ColorScale: StyleParam.Colorscale * ?ShowScale: bool * ?CameraProjectionType: StyleParam.CameraProjectionType * ?Camera: LayoutObjects.Camera * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'b :> IConvertible and 'e :> IConvertible)
argument X: seq<float> option
<summary> Creates a surface plot. Surface plots plot a z value as a function of x and y, creating a three-dimensional surface. The data the describes the coordinates of the surface is set in `z`. Data in `z` should be a 2D array. Coordinates in `x` and `y` can either be 1D arrays or 2D arrays (e.g. to graph parametric surfaces). If not provided in `x` and `y`, the x and y coordinates are assumed to be linear starting at 0 with a unit step. The color scale corresponds to the `z` values by default. For custom color scales, use `surfacecolor` which should be a 2D array, where its bounds can be controlled using `cmin` and `cmax`. </summary>
<param name="zData">Two-dimensional data array representing the surface's z values</param>
<param name="X">Sets the x coordinates.</param>
<param name="Y">Sets the y coordinates.</param>
<param name="Name">Sets the trace name. The trace name appear as the legend item and on hover</param>
<param name="ShowLegend">Determines whether or not an item corresponding to this trace is shown in the legend.</param>
<param name="Opacity">Sets the opactity of the trace</param>
<param name="Text">Sets a text associated with each datum</param>
<param name="MultiText">Sets individual text for each datum</param>
<param name="Contours">Sets the contours on the surface</param>
<param name="ColorScale">Sets the colorscale of the surface</param>
<param name="ShowScale">Whether or not to show the colorbar/colorscale</param>
<param name="CameraProjectionType">Sets the camera projection type of this trace.</param>
<param name="Camera">Sets the camera of this trace.</param>
<param name="UseDefaults">If set to false, ignore the global default settings set in `Defaults`</param>
argument Y: seq<float> option
<summary> Creates a surface plot. Surface plots plot a z value as a function of x and y, creating a three-dimensional surface. The data the describes the coordinates of the surface is set in `z`. Data in `z` should be a 2D array. Coordinates in `x` and `y` can either be 1D arrays or 2D arrays (e.g. to graph parametric surfaces). If not provided in `x` and `y`, the x and y coordinates are assumed to be linear starting at 0 with a unit step. The color scale corresponds to the `z` values by default. For custom color scales, use `surfacecolor` which should be a 2D array, where its bounds can be controlled using `cmin` and `cmax`. </summary>
<param name="zData">Two-dimensional data array representing the surface's z values</param>
<param name="X">Sets the x coordinates.</param>
<param name="Y">Sets the y coordinates.</param>
<param name="Name">Sets the trace name. The trace name appear as the legend item and on hover</param>
<param name="ShowLegend">Determines whether or not an item corresponding to this trace is shown in the legend.</param>
<param name="Opacity">Sets the opactity of the trace</param>
<param name="Text">Sets a text associated with each datum</param>
<param name="MultiText">Sets individual text for each datum</param>
<param name="Contours">Sets the contours on the surface</param>
<param name="ColorScale">Sets the colorscale of the surface</param>
<param name="ShowScale">Whether or not to show the colorbar/colorscale</param>
<param name="CameraProjectionType">Sets the camera projection type of this trace.</param>
<param name="Camera">Sets the camera of this trace.</param>
<param name="UseDefaults">If set to false, ignore the global default settings set in `Defaults`</param>
Multiple items
type Contours = inherit DynamicObj new: unit -> Contours static member init: ?Coloring: ContourColoring * ?End: float * ?LabelFont: Font * ?LabelFormat: string * ?Operation: ConstraintOperation * ?ShowLabels: bool * ?ShowLines: bool * ?Size: float * ?Start: float * ?Type: ContourType * ?Value: #IConvertible -> Contours static member initSurface: ?X: Contour * ?Y: Contour * ?Z: Contour -> Contours static member initXyz: ?Color: Color * ?End: float * ?Highlight: bool * ?HighlightColor: Color * ?HighlightWidth: float * ?Project: ContourProject * ?Show: bool * ?Size: float * ?Start: float * ?UseColorMap: bool * ?Width: float -> Contours static member style: ?X: Contour * ?Y: Contour * ?Z: Contour * ?Coloring: ContourColoring * ?End: float * ?LabelFont: Font * ?LabelFormat: string * ?Operation: ConstraintOperation * ?ShowLabels: bool * ?ShowLines: bool * ?Size: float * ?Start: float * ?Type: ContourType * ?Value: #IConvertible -> (Contours -> Contours) static member styleXyz: ?Color: Color * ?End: float * ?Highlight: bool * ?HighlightColor: Color * ?HighlightWidth: float * ?Project: ContourProject * ?Show: bool * ?Size: float * ?Start: float * ?UseColorMap: bool * ?Width: float -> (Contours -> Contours)
<summary> Contours type inherits from dynamic object </summary>

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new: unit -> Contours
static member Contours.initXyz: ?Color: Color * ?End: float * ?Highlight: bool * ?HighlightColor: Color * ?HighlightWidth: float * ?Project: ContourProject * ?Show: bool * ?Size: float * ?Start: float * ?UseColorMap: bool * ?Width: float -> Contours