## Static Methods Relevant to Point2Bvr Objects

###

add

Statics Class

Creates a two-dimensional point behavior. The location of the point is calculated by adding the corresponding coordinates of the given point and vector behaviors.

public static Point2Bvr add(
Point2Bvr pt,
Vector2Bvr vec
);

##### Parameters

pt
  A Point2Bvr object.
vec
  A Vector2Bvr object.

##### Return Values

Returns the Point2Bvr object.

##### See Also

sub

###

bSpline

Statics Class

Creates a Point2Bvr behavior based on a B-spline function. The function depends on the control elements, the knot vector, the mathematical degree, and the weights of the control elements (these are optional).

A B-spline function without weights is piecewise polynomial and with weights is piecewise rational (the quotient of two polynomials). It requires that:

numberOfControlElements = numberOfKnots - degree + 1

The control elements define the approximate direction and shape of the function. The knots represent junction values, in parameter space, between the connected polynomial parts.

Given a degree d and a number of knots k, the function is valid in the range knotd to knotk-d+1, and is otherwise undefined. For example, for a degree 2 curve, the valid range is from the second knot to the next to the last knot, inclusive.

The returned Point2Bvr is the traversal of the spline function according to the evaluation parameter. The evaluation parameter is a NumberBvr that must be in the valid range of the spline, which is [knotd, knotk-d+1]. Any values outside this range are automatically clamped to the end values.

public static Point2Bvr bSpline(
int degree,
NumberBvr[] knots,
Point2Bvr[] control_elements,
NumberBvr[] weights,
NumberBvr evaluation
);

##### Parameters

degree
  A number representing the mathematical degree of the B-spline to evaluate. Must be 1, 2, or 3.
knots
  An array of NumberBvr objects representing the knots used to calculate the B-spline.
control_elements
  An array of Point2Bvr objects representing the control elements used to calculate the B-spline.
weights
  An array of NumberBvr objects representing the weights used to calculate the rational B-spline. There must be the same number of weights as control elements. For non-rational B-splines, the value of weights is null.
evaluation
  A NumberBvr object that controls the spline evaluation.

##### Return Values

Returns the Point2Bvr object.

###

derivative

Statics Class

Creates a two-dimensional vector behavior of the instantaneous derivative (rate of change) of the given point behavior. For example, a constant yields a constant derivative of [0 0], and point2(time, 0) (without additional time substitutions) yields a constant derivative of [1 0].

public static Vector2Bvr derivative(
Point2Bvr pt
);

##### Parameters

pt
  A Point2Bvr object.

##### Return Values

Returns the Vector2Bvr object.

###

distance

Statics Class

Creates a number behavior representing the distance between two point behaviors.

public static NumberBvr distance(
Point2Bvr p1,
Point2Bvr p2
);

##### Parameters

p1 and p2
  The Point2Bvr objects.

##### Return Values

Returns the NumberBvr object.

##### See Also

distanceSquared

###

distanceSquared

Statics Class

Creates a number behavior representing the square of the distance between two point behaviors. This is the same as the distance method except that the distance is squared.

public static NumberBvr distanceSquared(
Point2Bvr p1,
Point2Bvr p2
);

##### Parameters

p1 and p2
  The Point2Bvr objects.

##### Return Values

Returns the NumberBvr object.

##### See Also

distance

###

point2

Statics Class

Creates a two-dimensional point behavior. The location of the point is given in Cartesian coordinates.

public static Point2Bvr point2(
NumberBvr x,
NumberBvr y
);

##### Parameters

x and y
  The NumberBvr objects, specifying the coordinate values. The x specifies the distance along the x-axis from the origin to the point, and y specifies the distance along the y-axis. These parameters can also be of type double.

##### Return Values

Returns the Point2Bvr object.

##### See Also

point2Polar

###

point2Polar

Statics Class

Creates a two-dimensional point behavior. The location of the point is given in polar coordinates.

public static Point2Bvr point2Polar(
NumberBvr XYangle,
NumberBvr length
);

##### Parameters

XYangle
  The NumberBvr object specifying the angle, in radians, between the positive x-axis and the ray that goes from the origin to the point. This parameter can also be of type double.
length
  The NumberBvr object specifying the distance from the origin to the point. This parameter can also be of type double.

##### Return Values

Returns the Point2Bvr object.

##### See Also

point2

###

sub

Statics Class

Creates a two-dimensional vector behavior. The coordinate values of the vector are calculated by subtracting the coordinates of p2 from the corresponding coordinates of p1.

public static Vector2Bvr sub(
Point2Bvr p1,
Point2Bvr p2
);

##### Parameters

p1 and p2
  The Point2Bvr objects.

##### Return Values

Returns the Vector2Bvr object.

###

sub

Statics Class

Creates a two-dimensional point behavior. The location of the point is calculated by subtracting the coordinates of the given vector behavior from the corresponding coordinates of the given point behavior.

public static Point2Bvr sub(
Point2Bvr pt,
Vector2Bvr vec
);

##### Parameters

pt
  A Point2Bvr object.
vec
  A Vector2Bvr object.

##### Return Values

Returns the Point2Bvr object.

##### See Also

add

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