# JSXGraph 1.7.0 Reference

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Class Index | File Index

Elements

Classes

- _global_
- Angle
- Arc
- Arrow
- Arrowparallel
- Axis
- Bisector
- Bisectorlines
- Boxplot
- Button
- Cardinalspline
- Chart
- Checkbox
- Circle
- Circumcenter
- Circumcircle
- CircumcircleArc
- CircumcircleSector
- Comb
- Conic
- Curve
- Curve3D
- CurveDifference
- CurveIntersection
- CurveUnion
- Derivative
- Ellipse
- ForeignObject
- Functiongraph
- Functiongraph3D
- Glider
- Grid
- Group
- Hatch
- Hyperbola
- Image
- ImplicitCurve
- Incenter
- Incircle
- Inequality
- Input
- Integral
- Intersection
- JXG
- JXG.AbstractRenderer
- JXG.Board
- JXG.Board.infobox
- JXG.C
- JXG.CA
- JXG.CanvasRenderer
- JXG.Chart
- JXG.Circle
- JXG.Complex
- JXG.Composition
- JXG.Coords
- JXG.CoordsElement
- JXG.Curve
- JXG.Curve3D
- JXG.Dump
- JXG.EventEmitter
- JXG.Expect
- JXG.ForeignObject
- JXG.GeometryElement
- JXG.GeometryElement3D
- JXG.GeonextParser
- JXG.Group
- JXG.Image
- JXG.JessieCode
- JXG.JSXGraph
- JXG.Legend
- JXG.Line
- JXG.Line3D
- JXG.Math
- JXG.Math.BoxQuadtree
- JXG.Math.Clip
- JXG.Math.Extrapolate
- JXG.Math.Geometry
- JXG.Math.ImplicitPlot
- JXG.Math.IntervalArithmetic
- JXG.Math.Metapost
- JXG.Math.Nlp
- JXG.Math.Numerics
- JXG.Math.Plot
- JXG.Math.Poly
- JXG.Math.Poly.Monomial
- JXG.Math.Poly.Polynomial
- JXG.Math.Poly.Ring
- JXG.Math.ProbFuncs
- JXG.Math.Quadtree
- JXG.Math.Statistics
- JXG.Math.Symbolic
- JXG.NoRenderer
- JXG.Options
- JXG.Plane3D
- JXG.Point
- JXG.Point3D
- JXG.Polygon
- JXG.PrefixParser
- JXG.Server
- JXG.Server.modules
- JXG.Surface3D
- JXG.SVGRenderer
- JXG.Text
- JXG.Ticks
- JXG.Transformation
- JXG.Turtle
- JXG.Util
- JXG.Util.Base64
- JXG.Util.Unzip
- JXG.Util.UTF8
- JXG.View3D
- JXG.VMLRenderer
- JXG.XML
- Label
- Legend
- Line
- Line3D
- Locus
- MajorArc
- MajorSector
- Measurement
- Metapostspline
- Midpoint
- MinorArc
- MinorSector
- mirrorelement
- Mirrorpoint
- NonReflexAngle
- Normal
- Orthogonalprojection
- OtherIntersection
- Parabola
- Parallel
- Parallelogram
- Parallelpoint
- ParametricSurface3D
- Perpendicular
- PerpendicularPoint
- PerpendicularSegment
- Point
- Point3D
- PolarLine
- PolePoint
- Polygon
- PolygonalChain
- RadicalAxis
- Reflection
- ReflexAngle
- RegularPolygon
- Riemannsum
- Sector
- Segment
- Semicircle
- Slider
- Slopefield
- Slopetriangle
- Smartlabel
- Spline
- Stepfunction
- Tangent
- Tapemeasure
- Text
- Ticks
- Tracecurve
- Transformation
- Turtle
- Vectorfield
- Vectorfield3D
- View3D

# Class Riemannsum

JXG.GeometryElement
↳ JXG.Curve
↳ Riemannsum

This element is used to provide a constructor for Riemann sums, which is realized as a special curve. The returned element has the method Value() which returns the sum of the areas of the bars.

In case of type "simpson" and "trapezoidal", the horizontal line approximating the function value is replaced by a parabola or a secant. IN case of "simpson", the parabola is approximated visually by a polygonal chain of fixed step width.
Defined in: curve.js.
Extends JXG.Curve.

Class Summary
Constructor Attributes | Constructor Name and Description
--- | ---
| Riemannsum(f,n,type_,a_,b_)

Fields borrowed from class JXG.Curve:
  dataX, dataY, lineCap, numberPoints, qdt, ticks
Fields borrowed from class JXG.GeometryElement:
  _org_type, _pos, ancestors, baseElement, board, childElements, dash, dashScale, descendants, draft, dragToTopOfLayer, dump, elementClass, elType, fillColor, fillOpacity, fixed, frozen, gradient, gradientAngle, gradientCX, gradientCY, gradientEndOffset, gradientFR, gradientFX, gradientFY, gradientR, gradientSecondColor, gradientSecondOpacity, gradientStartOffset, hasLabel, highlight, highlighted, highlightFillColor, highlightFillOpacity, highlightStrokeColor, highlightStrokeOpacity, highlightStrokeWidth, id, inherits, isDraggable, isLabel, isReal, lastDragTime, layer, methodMap, mouseover, name, needsRegularUpdate, needsUpdate, notExistingParents, numTraces, parents, precision, priv, quadraticform, rendNode, rotatable, scalable, shadow, snapToGrid, stdform, strokeColor, strokeOpacity, strokeWidth, subs, symbolic, tabindex, trace, traceAttributes, traces, transformations, transitionDuration, transitionProperties, type, viewport, visible, visProp, visPropCalc, withLabel

Fields borrowed from class JXG.Curve:
  dataX, dataY, lineCap, numberPoints, qdt, ticks
Fields borrowed from class JXG.GeometryElement:
  _org_type, _pos, ancestors, baseElement, board, childElements, dash, dashScale, descendants, draft, dragToTopOfLayer, dump, elementClass, elType, fillColor, fillOpacity, fixed, frozen, gradient, gradientAngle, gradientCX, gradientCY, gradientEndOffset, gradientFR, gradientFX, gradientFY, gradientR, gradientSecondColor, gradientSecondOpacity, gradientStartOffset, hasLabel, highlight, highlighted, highlightFillColor, highlightFillOpacity, highlightStrokeColor, highlightStrokeOpacity, highlightStrokeWidth, id, inherits, isDraggable, isLabel, isReal, lastDragTime, layer, methodMap, mouseover, name, needsRegularUpdate, needsUpdate, notExistingParents, numTraces, parents, precision, priv, quadraticform, rendNode, rotatable, scalable, shadow, snapToGrid, stdform, strokeColor, strokeOpacity, strokeWidth, subs, symbolic, tabindex, trace, traceAttributes, traces, transformations, transitionDuration, transitionProperties, type, viewport, visible, visProp, visPropCalc, withLabel

Method Summary
Method Attributes | Method Name and Description
--- | ---
| Value() Returns the value of the Riemann sum, i.e.

Methods borrowed from class JXG.Curve:
  addTransform, allocatePoints, generateTerm, getTransformationSource, hasPoint, interpolationFunctionFromArray, maxX, minX, moveTo, notifyParents, update, updateCurve, updateDataArray, updateRenderer, updateTransform, X, Y, Z
Methods borrowed from class JXG.GeometryElement:
  _set, addChild, addDescendants, addParents, addParentsFromJCFunctions, addRotation, addTicks, animate, bounds, clearTrace, cloneToBackground, countChildren, createGradient, createLabel, draggable, formatNumberLocale, fullUpdate, generatePolynomial, getAttribute, getAttributes, getLabelAnchor, getName, getParents, getProperty, getSnapSizes, getTextAnchor, getType, handleSnapToGrid, hide, hideElement, noHighlight, normalize, prepareUpdate, remove, removeAllTicks, removeChild, removeDescendants, removeTicks, resolveShortcuts, setArrow, setAttribute, setDash, setDisplayRendNode, setLabel, setLabelText, setName, setParents, setPosition, setPositionDirectly, setProperty, show, showElement, snapToPoints, updateVisibility, useLocale

Events borrowed from class JXG.GeometryElement:
  attribute, attribute:key, down, drag, keydrag, mousedown, mousedrag, mousemove, mouseout, mouseover, mouseup, move, out, over, pendown, pendrag, penup, touchdown, touchdrag, touchup, up

Class Detail
Riemannsum(f,n,type_,a_,b_)

Parameters:
{function|array_number|function_string|function_function|number_function|number} f,n,type_,a_,b_
  Parent elements of Riemannsum are a Either a function term f(x) describing the function graph which is filled by the Riemann bars, or an array consisting of two functions and the area between is filled by the Riemann bars.

  n determines the number of bars, it is either a fixed number or a function.

  type is a string or function returning one of the values: 'left', 'right', 'middle', 'lower', 'upper', 'random', 'simpson', or 'trapezoidal'. Default value is 'left'. "simpson" is Simpson's 1/3 rule.

  Further parameters are an optional number or function for the left interval border a, and an optional number or function for the right interval border b.

  Default values are a=-10 and b=10.

See:
  JXG.Curve

Examples:

    // Create Riemann sums for f(x) = 0.5*x*x-2*x.
      var s = board.create('slider',[[0,4],[3,4],[0,4,10]],{snapWidth:1});
      var f = function(x) { return 0.5*x*x-2*x; };
      var r = board.create('riemannsum',
                  [f, function(){return s.Value();}, 'upper', -2, 5],
                  {fillOpacity:0.4}
                  );
      var g = board.create('functiongraph',[f, -2, 5]);
      var t = board.create('text',[-2,-2, function(){ return 'Sum=' + JXG.toFixed(r.Value(), 4); }]);

      // Riemann sum between two functions
      var s = board.create('slider',[[0,4],[3,4],[0,4,10]],{snapWidth:1});
      var g = function(x) { return 0.5*x*x-2*x; };
      var f = function(x) { return -x*(x-4); };
      var r = board.create('riemannsum',
                  [[g,f], function(){return s.Value();}, 'lower', 0, 4],
                  {fillOpacity:0.4}
                  );
      var f = board.create('functiongraph',[f, -2, 5]);
      var g = board.create('functiongraph',[g, -2, 5]);
      var t = board.create('text',[-2,-2, function(){ return 'Sum=' + JXG.toFixed(r.Value(), 4); }]);

Method Detail
{Number} Value()
Returns the value of the Riemann sum, i.e. the sum of the (signed) areas of the rectangles.

Returns:
  {Number} value of Riemann sum.

Documentation generated by JsDoc Toolkit 2.4.0 on Wed Feb 14 2024 15:53:29 GMT+0100 (heure normale d’Europe centrale)