## Static Methods Relevant to Vector3Bvr Objects

###

add

Statics Class

Creates a three-dimensional vector behavior. The direction and length of the vector are calculated by adding the corresponding coordinates of the given vectors.

public static Vector3Bvr add(
Vector3Bvr v1,
Vector3Bvr v2
);

##### Parameters

v1 and v2
  The Vector3Bvr objects.

##### Return Values

Returns the Vector3Bvr object.

##### See Also

sub

###

bSpline

Statics Class

Creates a Vector3Bvr 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 Vector3Bvr 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 Vector3Bvr bSpline(
int degree,
NumberBvr[] knots,
Vector3Bvr[] 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 Vector3Bvr 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.

##### Return Values

Returns the Vector3Bvr object.

###

cross

Statics Class

Creates a vector behavior that represents the "cross product" of the given vectors. The new vector has a length that is equal to the product of the lengths of the original vectors and the sine of the angle between them. The new vector has a direction that is perpendicular to the plane formed by the original vectors and that obeys the right-hand rule.

public static Vector3Bvr cross(
Vector3Bvr v1,
Vector3Bvr v2
);

##### Parameters

v1 and v2
  The Vector3Bvr objects.

##### Return Values

Returns the Vector3Bvr object.

###

derivative

Statics Class

Creates a new, three-dimensional vector behavior that is the instantaneous derivative (rate of change) of the given vector behavior. For example, a constant vector behavior yields a constant derivative of [0 0 0], and vector3(time, 0, 0) (without any additional time substitutions) yields a constant derivative vector of [1 0 0].

public static Vector3Bvr derivative(
Vector3Bvr vec
);

##### Parameters

vec
  A Vector3Bvr object.

##### Return Values

Returns the Vector3Bvr object.

###

dot

Statics Class

Creates a number behavior that represent the "dot product" of the given vectors. The dot product is the product of the lengths of the vectors and the cosine of the angle between them.

public static NumberBvr dot(
Vector3Bvr v1,
Vector3Bvr v2
);

##### Parameters

v1 and v2
  Vector3Bvr objects.

##### Return Values

Returns the NumberBvr object.

###

integral

Statics Class

Creates an three-dimensional vector that represents the sum of the all values of vec from the given start time to the present.

public static Vector3Bvr integral(
Vector3Bvr vec
);

##### Parameters

a
  The Vector3Bvr object.

##### Return Values

Returns the Vector3Bvr object.

###

neg

Statics Class

Creates a new three-dimensional vector behavior that has the same length as the original vector, but points in the opposite direction.

public static Vector3Bvr neg(
Vector3Bvr v1
);

##### Parameters

v1
  A Vector3Bvr object that is the original vector.

##### Return Values

Returns the Vector3Bvr object.

###

sub

Statics Class

Creates a three-dimensional vector behavior. The direction and length of the vector are calculated by subtracting the coordinates of v2 from the corresponding coordinates of v1.

public static Vector3Bvr sub(
Vector3Bvr v1,
Vector3Bvr v2
);

##### Parameters

v1 and v2
  Vector3Bvr objects.

##### Return Values

Returns the Vector3Bvr object.

##### See Also

add

###

vector3Spherical

Statics Class

Creates a three-dimensional vector behavior, having a direction and length as specified by the given spherical coordinates.

public static Vector3Bvr vector3Spherical(
NumberBvr XYangle,
NumberBvr YZangle,
NumberBvr length
);

##### Parameters

XYangle
  A NumberBvr object of the counter-clockwise XY angle, in radians, of the point about the positive y-axis. The angle begins at the positive z-ray, so that [0 0 1] has a XYangle of 0, and [1 0 0] has a XYangle of pi/2. This parameter can also be of type double.
YZangle
  A NumberBvr object of the counter-clockwise elevation angle, in radians, of the point above the XZ-plane. A YZangle of pi/2 means the point is straight up (on the positive y-ray), and a YZangle of -pi/2 is straight down (on the negative y-ray). This parameter can also be of type double.
length
  A NumberBvr object specifying the length of the vector. This parameter can also be of type double.

##### Return Values

Returns the Vector3Bvr object.

##### Remarks

The following table correlates Cartesian coordinates with polar coordinates:

Cartesian | XYangle | YZangle | Length
Coordinates
[0 0 0] | X | X | 0
[d 0 0] | pi/2 | 0 | d
[-d 0 0] | -pi/2 | 0 | d | X = Don't Care
[0 d 0] | X | pi/2 | d
[0 -d 0] | X | -pi/2 | d
[0 0 d] | 0 | 0 | d
[0 0 -d] | pi | 0 | d

##### See Also

vector3

###

vector3

Statics Class

Creates a three-dimensional vector behavior, having a direction and length as specified by the given Cartesian coordinates.

public static Vector3Bvr vector3(
NumberBvr x,
NumberBvr y,
NumberBvr z
);

##### Parameters

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

##### Return Values

Returns the Vector3Bvr object.

##### See Also

vector3Spherical

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