module:extras/evaluators.Roulette

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### new module:extras/evaluators.Roulette(rollingCurve, fixedCurve, polePoint, [revolutions])

Augments: Curve

A curve evaluator object for a curve drawn by a curve that rolls along another curve whose position is fixed.

This object generates two-dimensional curves, which are returned by the evaluate method as three-dimensional points with the third element (Z coordinate) set to 0.

Parameters

Methods

### module:extras/evaluators.Roulette#accel(u)

Finds an approximate acceleration vector at the given U coordinate of this curve. The implementation in Curve calls the evaluator’s accel method if it implements it; otherwise, does a numerical differentiation using the velocity vector.

The acceleration of a curve is a vector which is the second-order derivative of the curve’s position at the given coordinate. The vector returned by this method should not be “normalized” to a glmath.

Parameters

Return Value

An array describing an acceleration vector. It should have at least as many elements as the number of dimensions of the underlying curve. (Type: Array.<number>)

### module:extras/evaluators.Roulette#arcLength(u)

Finds an approximate arc length (distance) between the start of this curve and the point at the given U coordinate of this curve. The implementation in Curve calls the evaluator’s arcLength method if it implements it; otherwise, calculates a numerical integral using the velocity vector.

The arc length function returns a number; if the curve is “smooth”, this is the integral, from the starting point to u, of the length of the velocity vector.

Parameters

Return Value

The approximate arc length of this curve at the given U coordinate. (Type: number)

### module:extras/evaluators.Roulette#changeEnds(ep1, ep2)

Creates a curve evaluator object for a curve that is generated using the same formula as this one (and uses the same U coordinates), but has a different set of end points. For example, this method can be used to shrink the path of a curve from [0, π] to [0, π/8].

Note, however, that in general, shrinking the range of a curve will not shrink the length of a curve in the same proportion, unless the curve’s path runs at constant speed with respect to time. For example, shrinking the range of a curve from [0, 1] to [0, 0.5] will not generally result in a curve that’s exactly half as long as the original curve.

For some curves, this method can also be used to grow the path of the curve.

Parameters

Return Value

Return value. (Type: Curve)

### module:extras/evaluators.Roulette#endPoints()

Returns the starting and ending U coordinates of this curve.

Return Value

A two-element array. The first element is the starting coordinate of the curve, and the second is its ending coordinate. Returns [0, 1] if the evaluator doesn’t implement an endPoints method.

### (static) module:extras/evaluators~Roulette.epitrochoid(outerRadius, rollerRadius, distFromRollerCenter, [rotationDegrees], [revolutions])

Creates a curve evaluator object for an epitrochoid, a curve drawn by a circle that rolls along the outside of another circle, whose position is fixed, with a center of (0,0). The rolling circle will start at the positive X axis of the fixed circle unless otherwise given in the parameter rotationDegrees.

This is a special case of a roulette in which the fixed and rolling curves are circles, and the pole point is the starting point of a circle with the same center as the rolling circle.

The following curves can be generated with this class (in the following descriptions, O = outerRadius, R means rollerRadius, and D = distFromRollerCenter).<ul>

  • Epicycloid: D = R (epitrochoid touching the fixed circle).
  • Curtate epicycloid: D < R (epitrochoid not touching the fixed circle).
  • Prolate epicycloid: D > R (epitrochoid crossing the fixed circle).
  • Cardioid: R = O; D = O.
  • Nephroid: R = O/2; D = O/2.
  • Ranunculoid: R = O/5; D = O/5.
  • N-cusped epicycloid: R = O/N; D = O/N.
  • Circle: O = 0; the radius will be R - D.

    • </ul>

    Parameters

    ### module:extras/evaluators.Roulette#evaluate(u)

    Finds the position of this curve at the given U coordinate.

    Parameters

    Return Value

    An array describing a position. It should have at least as many elements as the number of dimensions of the underlying curve. (Type: Array.<number>)

    ### module:extras/evaluators.Roulette#fitRange(ep1, ep2)

    Creates a curve evaluator object for a curve that follows the same path as this one but has its U coordinates remapped to fit the given range. For example, this method can be used to shrink the range of U coordinates from [-π, π] to [0, 1] without shortening the path of the curve. Here, -π now maps to 0, and π now maps to 1.

    Parameters

    Return Value

    Return value. (Type: Curve)

    ### module:extras/evaluators.Roulette#getLength()

    Convenience method for getting the total length of this curve.

    Return Value

    The distance from the start of the curve to its end. (Type: number)

    ### module:extras/evaluators.Roulette#getPoints(count)

    Gets an array of positions on the curve at fixed intervals of U coordinates. Note that these positions will not generally be evenly spaced along the curve unless the curve uses an arc-length parameterization.

    Parameters

    Return Value

    An array of curve positions. The first element will be the start of the curve. If “count” is 2 or greater, the last element will be the end of the curve. (Type: Array.<Array.<number» | Array.<Object>)

    ### module:extras/evaluators.Roulette#getPointsAsObjects(count)

    Gets an array of positions on the curve at fixed intervals of U coordinates. Note that these positions will not generally be evenly spaced along the curve unless the curve uses an arc-length parameterization. The positions will be in the form of objects with up to four properties: x, y, z, and w retrieve the first, second, third, and fourth coordinate of each position, respectively.

    Parameters

    Return Value

    An array of curve positions. The first element will be the start of the curve. If “count” is 2 or greater, the last element will be the end of the curve. (Type: Array.<Array.<number» | Array.<Object>)

    Examples

    The following example initializes a three.js BufferGeometry with the points retrieved by this method. This example requires the three.js library.

    var points=curve.getPointsAsObjects(50)
var buffer=new THREE.BufferGeometry()
.setFromPoints(points);

    ### (static) module:extras/evaluators~Roulette.hypotrochoid(outerRadius, innerRadius, distFromInnerCenter, [rotationDegrees], [revolutions])

    Creates a curve evaluator object for a hypotrochoid, a curve drawn by a circle that rolls along the inside of another circle, whose position is fixed, with a center of (0,0).

    This is a special case of a roulette in which the fixed and rolling curves are circles, and the pole point is the starting point of a circle with the same center as the rolling circle.

    The following curves can be generated with this class (in the following descriptions, O = outerRadius, R means innerRadius, and D = distFromInnerCenter).<ul>

  • Hypocycloid: D = R (hypotrochoid touching the fixed circle).
  • Curtate hypocycloid: D < R (hypotrochoid not touching the fixed circle).
  • Prolate hypocycloid: D > R (hypotrochoid crossing the fixed circle).
  • Circle: O = R\*2; the circle will have radius R - D.
  • Ellipse: O = R\*2; the ellipse (unrotated) will have width abs(R+D)\*2 and height abs(R-D)\*2.
  • Line segment with length O\*2: O = R\*2; D = R.
  • Deltoid: O = R\*3; D = R.
  • Astroid: O = R\*4; D = R.
  • N-pointed hypocycloid: O = R \* N; D = R.

    • </ul>

    Parameters

    ### module:extras/evaluators.Roulette#jerk(u)

    Finds an approximate jerk vector at the given U coordinate of this curve. The implementation in Curve calls the evaluator’s jerk method if it implements it; otherwise, does a numerical differentiation using the acceleration vector.

    The jerk of a curve is a vector which is the third-order derivative of the curve’s position at the given coordinate. The vector returned by this method should not be “normalized” to a glmath.

    Parameters

    Return Value

    An array describing a jerk vector. It should have at least as many elements as the number of dimensions of the underlying curve. (Type: Array.<number>)

    ### module:extras/evaluators.Roulette#normal(u)

    Finds an approximate principal normal vector at the given U coordinate of this curve. The implementation in Curve calls the evaluator’s normal method if it implements it; otherwise, does a numerical differentiation using the velocity vector.

    The principal normal of a curve is the derivative of the “normalized” velocity vector divided by that derivative’s length. The normal returned by this method should be “normalized” to a glmath. (Compare with Surface#gradient.)

    Parameters

    Return Value

    An array describing a normal vector. It should have at least as many elements as the number of dimensions of the underlying curve. (Type: Array.<number>)

    ### (static) module:extras/evaluators~Roulette.rose(num, denom, distFromInnerCenter, [rotationDegrees])

    Creates a curve evaluator object for a rose, a special form of hypotrochoid (roulette curve generated when one circle rolls inside another fixed circle).

    Parameters

    Return Value

    The resulting curve evaluator object. (Type: Roulette)

    ### module:extras/evaluators.Roulette#tangent(u)

    Convenience method for finding an approximate tangent vector of this curve at the given U coordinate. The tangent vector is the same as the velocity vector, but “normalized” to a unit vector.

    Parameters

    Return Value

    An array describing a normal vector. It should have at least as many elements as the number of dimensions of the underlying curve. (Type: Array.<number>)

    ### module:extras/evaluators.Roulette#toArcLengthParam()

    Gets a curve evaluator object for a curve that follows the same path as this one but has its U coordinates remapped to an arc length parameterization. Arc length parameterization allows for moving along a curve’s path at a uniform speed and for generating points which are spaced evenly along that path – both features are more difficult with most other kinds of curve parameterization.

    The end points of the curve (obtained by calling the endPoints method) will be (0, N), where N is the distance to the end of the curve from its start.

    When converting to an arc length parameterization, the curve should be continuous and have a speed greater than 0 at every point on the curve. The arc length parameterization used in this method is approximate.

    Return Value

    Return value. Returns this object if this curve already uses an arc length parameterization. (Type: Curve)

    Examples

    The following example uses the arc-length parameterization to generate, uniformly at random, a point that lies anywhere on a curve.

    var arclen = curve.toArcLengthParam();
var point = arclen.evaluate(Math.random()*arclen.getLength())

    ### (static) module:extras/evaluators~Roulette.trochoid(radius, distFromCenter, [distance])

    Creates a curve evaluator object for a trochoid, a curve drawn by a circle that rolls along the X axis.

    The following curves can be generated with this class (in the following descriptions, R = radius and D = distFromCenter).<ul>

  • Cycloid: D = R (trochoid touching the X axis).
  • Curtate cycloid: D < R (trochoid not touching the X axis).
  • Prolate cycloid: D > R (trochoid crossing the X axis).

    • </ul>

    Parameters

    ### module:extras/evaluators.Roulette#velocity(u)

    Finds an approximate velocity vector at the given U coordinate of this curve. The implementation in Curve calls the evaluator’s velocity method if it implements it; otherwise, does a numerical differentiation using the position (from the evaluate method).

    The velocity of a curve is a vector which is the derivative of the curve’s position at the given coordinate. The vector returned by this method should not be “normalized” to a glmath.

    Parameters

    Return Value

    An array describing a velocity vector. It should have at least as many elements as the number of dimensions of the underlying curve. (Type: Array.<number>)

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