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Elements
Classes

Element 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.

Element Summary
Constructor Attributes Constructor Name and Description
 
Method Summary
Method Attributes Method Name and Description
 
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
Element Detail
Riemannsum
This element has no direct constructor. To create an instance of this element you have to call JXG.Board#create with type "riemannsum".

Possible parent array combinations are:
{function|array} f
{number|function} n
{string|function} type   Optional
{function|number} a   Optional
{function|number} b   Optional

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.

Attributes borrowed from other Elements
Attributes borrowed from class JXG.Curve:
lineCap
Attributes borrowed from class JXG.GeometryElement:
dash, dashScale, draft, dragToTopOfLayer, fillColor, fillOpacity, fixed, frozen, gradient, gradientAngle, gradientCX, gradientCY, gradientEndOffset, gradientFR, gradientFX, gradientFY, gradientR, gradientSecondColor, gradientSecondOpacity, gradientStartOffset, highlight, highlightFillColor, highlightFillOpacity, highlightStrokeColor, highlightStrokeOpacity, highlightStrokeWidth, isLabel, layer, needsRegularUpdate, precision, priv, rotatable, scalable, shadow, snapToGrid, strokeColor, strokeOpacity, strokeWidth, tabindex, trace, traceAttributes, transitionDuration, transitionProperties, viewport, visible, withLabel

Fields borrowed from other Elements
Fields borrowed from class JXG.Curve:
dataX, dataY, numberPoints, qdt, ticks
Fields borrowed from class JXG.GeometryElement:
_org_type, _pos, ancestors, baseElement, board, childElements, descendants, dump, elementClass, elType, hasLabel, highlighted, id, inherits, isDraggable, isReal, lastDragTime, methodMap, mouseover, name, needsUpdate, notExistingParents, numTraces, parents, quadraticform, rendNode, stdform, subs, symbolic, traces, transformations, type, visProp, visPropCalc

Methods borrowed from other Elements
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 other Elements
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
Documentation generated by JsDoc Toolkit 2.4.0 on Fri Jun 14 2024 14:43:47 GMT+0200 (Mitteleuropäische Sommerzeit)