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.
| Constructor Attributes | Constructor Name and Description |
|---|---|
| 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
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, nonnegativeOnly, 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